This technical document was prepared

under the direction of Donna Kostanich,

Assistant Division Chief for Sampling and

Estimation, Decennial Statistical Studies

Division. The overall management and

coordination of the review was conducted

by Dawn Haines and Douglas Olson.

The combined efforts of numerous U.S.

Census Bureau staff have culminated in

the publication of this document. Some

staff members wrote chapters, while

others reviewed chapters. In some cases,

staff members filled both capacities.

Contributing to the March 2001 portion of

Accuracy and Coverage Evaluation of

Census 2000: Design and Methodology

were Patrick Cantwell, Inez Chen,

Danny Childers, Peter Davis,

James Farber, Deborah Fenstermaker,

Richard Griffin, Dawn Haines,

Howard Hogan, Michael Ikeda,

Donna Kostanich, Vincent

Thomas Mule, Mary Mulry, Alfredo

Navarro, Douglas Olson, J. Gregory

Robinson, Robert Sands, and Michael

Starsinic. Joseph Waksberg, of Westat,

Inc., reviewed these chapters for readability and consistency.

Contributing to the A.C.E. Revision II section of Accuracy and Coverage Evaluation

of Census 2000: Design and Methodology

were Tamara Adams, Michael Beaghen,

William Bell, Patrick Cantwell,

Deborah Fenstermaker, Richard

Griffin, Dawn Haines, Michael Ikeda,

Donna Kostanich, Elizabeth Krejsa,

Vincent Thomas Mule, Mary Mulry,

Rita Petroni, Robert Sands, Eric

Schindler, Bruce Spencer, of Northwestern University, and David Whitford.

Rhonda Geddings provided administrative support.

Bernadette Beasley, Meshel Butler,

Helen Curtis, Susan Kelly, and Kim

Ottenstein of the Administrative and

Customer Services Division, Walter

Odom, Chief, provided publications and

printing management, graphics design,

and composition and editorial review

for print and electronic media. General

direction and production management

were provided by James Clark, Assistant

Division Chief.

Margaret Smith of ACSD provided assistance in placing the electronic version of

this document on the Internet (see

www.census.gov/dmd/www/refroom.html).

We are grateful for the assistance of the

individuals listed and all others who

contributed but are not specifically

mentioned. The preparation and publication of this document was possible

because of their invaluable contributions.

ACKNOWLEDGMENTS

Vacant,

Principal Associate Director

and Chief Financial Officer

Vacant,

Principal Associate

Director for Programs

Preston Jay Waite,

Associate Director

for Decennial Census

Nancy M. Gordon,

Associate Director

for Demographic Programs

SUGGESTED CITATION

FILES: Census 2000,

Accuracy and Coverage

Evaluation of Census 2000:

Design and Methodology

U.S. Census Bureau, 2004

Cynthia Z.F. Clark,

Associate Director

for Methodology and

Standards

Marvin D. Raines,

Associate Director

for Field Operations

Arnold A. Jackson,

Assistant Director

for Decennial Census

ECONOMICS

AND STATISTICS

ADMINISTRATION

Economics

and Statistics

Administration

Kathleen B. Cooper,

Under Secretary

for Economic Affairs

U.S. CENSUS BUREAU

Charles Louis Kincannon,

Director

Hermann Habermann,

Deputy Director and

Chief Operating Officer
Foreword

The U.S. Census Bureau conducted the Accuracy and

Coverage Evaluation (A.C.E.) survey to measure the

coverage of the population in Census 2000. The A.C.E.

was designed to serve two purposes: (1) to measure the

net coverage of the population, both in total and for major

subgroups, and (2) to provide data that could serve as the

basis for correcting the census counts for such uses as

Congressional redistricting, state and local redistricting,

funds allocation and governmental program administration. The A.C.E. survey provides critical information that

can be used to improve the census-taking process.

However, the design, methodology, operations and data

collection efforts are extremely complex and not widely

understood. The work described in this publication was a

major undertaking, and the technical documentation is

intended to increase awareness and knowledge, and subsequently improve the 2010 Census and coverage measurement techniques.

Despite the fact that coverage measurement techniques

have been utilized by the Census Bureau for several

decades, this is the first comprehensive documentation of

its kind. This technical document describes the methodologies that were used to produce estimates of Census

2000 coverage error from the A.C.E. The first part of this

document discusses the entire survey design used to

produce the original estimates of net undercount released

in March 2001. Analysis and evaluations indicated that

there were serious errors in the March 2001 A.C.E.

Research efforts to fix the detected errors resulted in

improved coverage estimates referred to as A.C.E. Revision II. The second part of this document describes the

methodology used to correct for errors in the March 2001

A.C.E.

After extensive analysis and consideration, the Census

Bureau ultimately decided not to use the A.C.E. - neither

the March 2001 nor the Revision II results - to correct the

Census 2000 counts or any other data products. A.C.E.

Revision II, the superior of the two results, provides useful

coverage measurement information that can be used for

research purposes. All of these results, decisions, supporting analyses, technical assessments, and limitations can

be found on the Census Bureau’s Web site at

www.census.gov/dmd/www/EscapRep.html.

This document is intended to promote knowledge and

encourage collaboration on coverage measurement issues.

As such, we welcome comments and suggestions from

colleagues on technical issues and also on the value of

this document.

Charles Louis Kincannon

Director, U.S. Census Bureau

U.S. Census Bureau
Section I: A.C.E. March 2001

Chapters

1. Introduction to the A.C.E. ........................ 1–1

2. Accuracy and Coverage Evaluation Overview ............. 2–1

3. Design of the A.C.E. Sample....................... 3–1

4. A.C.E. Field and Processing Activities.................. 4–1

5. Targeted Extended Search........................ 5–1

6. Missing Data Procedures ........................ 6–1

7. Dual System Estimation ......................... 7–1

8. Model-Based Estimation for Small Areas ................ 8–1

Appendixes

A. Census 2000 Missing Data ....................... A–1

B. Demographic Analysis.......................... B–1

C. Weight Trimming ............................ C–1

D. Error Profile for A.C.E. Estimates .................... D–1

Section I References............................... 1

Section II: A.C.E. Revision II March 2003

Chapters

1. Introduction to A.C.E. Revision II .................... 1–1

2. Summary of A.C.E. Revision II Methodology .............. 2–1

3. Correcting Data for Measurement Error................. 3–1

4. A.C.E. Revision II Missing Data Methods ................ 4–1

5. Further Study of Person Duplication in Census 2000 ......... 5–1

6. A.C.E. Revision II Estimation ...................... 6–1

7. Assessing the Estimates......................... 7–1

Section II References .............................. 1

CONTENTS

iv
Accuracy and Coverage Evaluation

of Census 2000:

Design and Methodology

Section I

A.C.E. March 2001

U.S. Census Bureau, Census 2000
Chapter 1.

Introduction to the A.C.E.

INTRODUCTION

The U.S. Census Bureau conducted the Accuracy and Coverage Evaluation (A.C.E.) to measure the coverage of the

population in Census 2000 and to allow for the possibility

of correcting the census results for the measured undercount. It also provides a wealth of information on the

census process and may, thus, enable improvement in

future censuses. This document is written to provide a

clear and permanent record of the methods and operations used in this project.

The current chapter presents the objectives and scope of

the A.C.E., and discusses limitations of what it was

attempting to accomplish. It includes a brief history of the

evolution of the statistical and operational methods upon

which the A.C.E. is based. Chapter 2 presents an overview

of the various statistical steps necessary to produce estimates of census coverage and how they are tied into the

operation of the survey. The sequence of major activities

and their timing is given. Subsequent chapters discuss

in detail A.C.E. sampling, interviewing, processing, and

estimation steps.

Goals

The evaluation of the completeness of census enumeration has been an integral part of the decennial census

since the 1950 census. This evaluation has taken on many

forms including demographic analysis, administrative

record checks, matches to independent surveys, and

dependent record rechecks and reinterviews.

The evaluation of the five censuses from 1950 to 1990

clearly showed that each of the traditional decennial

censuses undercounted the total population, and further,

missed certain identifiable population groups at greater

rates than others. Specifically, these evaluations clearly

showed that undercounts were not merely random occurrences, but predictable biases in the census taking process. The undercount has been consistently higher for the

African-American population than for the rest of the population, and while the data set is not so extensive, the evidence also pointed to consistently higher undercounts for

Hispanics, Asians, Pacific Islanders, and American Indians

than for the White non-Hispanic population. The undercount was also related to socioeconomic status, chiefly

measured by home ownership, with renters having consistently higher undercounts. The U.S. Census Bureau

designed the Accuracy and Coverage Evaluation to measure this differential undercount and, if possible, correct

the counts, thereby making the census more accurate.

As mentioned earlier, the A.C.E. was designed to serve two

purposes. One goal was to measure coverage of the population, both total and in various major subdivisions such

as race/ethnicity, sex, major geographical areas, and

socioeconomical groupings. These measurements indicate

whether changes made in enumeration methods in the

2000 census were successful in improving the census and

show where improvements may be necessary in future

censuses. Another goal was to provide data that could

serve as the basis for correcting the census counts. In

planning the A.C.E., the Census Bureau focused on the

accuracy of population totals for both geographic areas

and demographic groups. Consideration was given to the

possibility of both improving the population totals

(numeric accuracy) and population shares (distributive

accuracy). Although early planning considered using dual

system estimation to produce a ‘‘one number census,’’

after the Supreme Court ruled on the use of sampling for

congressional apportionment in 1999, the survey was

redesigned and refocused on non-apportionment uses.

One important use was congressional redistricting. Thus

an important consideration in the design was to improve

the accuracy of congressional districts, which average

around 650,000 people. The U.S. Census Bureau also recognized other uses, including state and local redistricting,

funds allocation, and program administration. The traditional goals of coverage evaluation to inform users and

aid in the planning of the next census continue to be

important. These goals greatly influenced the sample and

estimation design.

The A.C.E. Defined

The A.C.E. is a post-enumeration survey, based on the

theory of dual system estimation. The results of the dual

system estimation can be used with model-based estimation to produce census files adjusted for the measured

net undercount (or net overcount). The design involved

comparing (matching) the information from an independent sample survey to initial census records.

In this process, the Census Bureau conducted field

interviewing and computerized and clerical matching of

records. Using the results of this matching, the Census

Bureau applied dual system estimation to develop

estimates of coverage for various population groups. The

initial plans were to apply correction factors to the census

files that could be used to produce all required Census

Introduction to the A.C.E. Section I—Chapter 1 1–1

U.S. Census Bureau, Census 2000
2000 tabulations, other than apportionment. The correction aspect of Census 2000 tabulations was later abandoned. The A.C.E. can be summarized as follows:

• Select a stratified random sample of blocks for the

A.C.E.

• Create an independent list of housing units in the

sample of A.C.E. blocks.

• Begin conducting telephone interviews of housing units

that mailed in a completed questionnaire and that could

be clearly linked to a telephone number.

• After the initial census nonresponse follow-up, conduct

a personal visit interview at every housing unit on the

independent list not already interviewed by telephone.

• Match the results of the A.C.E. interview to the census

and vice versa.

• Search the census records for duplicates.

• Resolve cases that require additional information for

matching by conducting a personal visit follow-up interview.

• Use the information from other, similar people to impute

missing information.

• Categorize the A.C.E. data by age, sex, tenure,

race/ethnicity and other appropriate predefined variables into estimation groupings called post-strata.

• Calculate the coverage correction factors for each poststratum using the dual system estimator.

• If appropriate, apply the coverage correction factors to

correct the initial census data using a model-based estimator and tabulate the statistically corrected census

results.

There are a number of assumptions inherent in the A.C.E.

Proper application of the dual system estimation (DSE)

model requires the A.C.E. be conducted independently of

the census and that the rules used to determine correct

enumerations are the same as the rules used to determine

cases eligible for matches. The DSE model can be sensitive

to measurement errors. It is important to obtain consistent

reporting of Census Day residence. Inclusion of fictitious

persons and errors in matching can directly influence the

DSE. There are other assumptions necessary in developing

models for handling nonresponse and other missing information. The A.C.E. design was based very much on the

theoretical concepts discussed and publicly presented by

the Census Bureau in advance of the census. These concepts included careful attention to statistical independence, a strict application of the concepts of sufficient

information, and careful attention to balancing the concepts used to measure census misses, as well as census

erroneous inclusions. For a more detailed discussion of

this approach see Hogan (2000).

Design Limitations of the A.C.E.

The A.C.E. was designed to measure the household population for large social, economic, ethnic, racial and geographic groups and compare them with the census counts.

The results provide a measure of net undercount and a

mechanism to correct that net undercount, if that appears

advisable. Although the goal of the A.C.E. was to measure

the net undercount, it also provides information on the

separate components of the net undercount such as omissions and various types of erroneous enumerations in the

census. Measures of gross error cannot be obtained

directly and exclusively from these components because

of the strict definition of ‘‘correct’’ that is needed to implement the dual system estimator. For example, A.C.E. treats

census enumerations as not correctly enumerated if they

lacked sufficient information for accurate matching. This

requirement allows for more precise matching, but

increases both the number of nonmatching cases and the

number of cases coded as erroneous. A similar strict rule

on correct block location of an address also increases both

the non-matches and erroneous enumerations. These rules

may be inapplicable in the census outside the DSE context.

The design of the A.C.E. does not provide information on

very local or unique errors in the census process. Specifically, the A.C.E. was not designed to correct for particular

errors made by, say, a census taker or a local census manager, or to correct for local errors in the census address

list. The Census Bureau had other programs in place to

deal with these issues, such as the quality assurance process, the coverage improvement follow-up, and the local

update of census addresses. The A.C.E. was designed,

rather, to correct for large systematic errors in census taking, most especially the historic differential undercount.

Finally, the A.C.E. was not designed to measure the undercount for some special population groups such as the

group quarters population (including college dormitories,

institutions, and military barracks), the population that

uses homeless shelters and/or soup kitchens, or the

remote areas of Alaska. The Census Bureau instituted specialized procedures for these groups in order to achieve

the best count possible. Extending the A.C.E. methods to

all of these populations would have been very costly and

difficult to implement properly.

HISTORY

Starting with 1950, every census has included a formal

study of the coverage of the population. The 2000 Accuracy and Coverage Evaluation (A.C.E.) is very much a continuation of that tradition.

1950 through 1970

The U.S. Census Bureau conducted its first postenumeration survey, or PES, as part of the 1950 census.

The essential elements in a post-enumeration survey are a

1–2 Section I—Chapter 1 Introduction to the A.C.E.

U.S. Census Bureau, Census 2000
second attempt to enumerate a sample of households and,

using case-by-case matching, to determine the number

and characteristics of people not included in the first census enumeration. This first PES was not based on dual system estimation.

During the next two decades the Census Bureau experimented with alternative coverage measurement methods

based on case-by-case matching including a ‘‘Reverse

Record Check,’’ administrative record checks, and a match

to the Current Population Survey. In addition, there were

various alternative versions of PES designs.

Soon after the completion of the 1950 census, methods of

aggregate demographic analysis for coverage analysis

were developed at Princeton University by Ansley Coale

and colleagues. See Coale (1955), Coale and Rives (1973),

and Coale and Zelnick (1963) for details. Demographic

analysis (DA) is the construction of an estimate of the

‘‘true’’ population using birth, death, migration and other

data sources. This methodology can provide independent

measures of the census net undercount by age, sex, and

Black/non-Black; however, it is subject to its own limitations and uncertainties. An important limitation is the lack

of data to independently estimate the Hispanic, Asian, and

American Indian populations or other detailed demographic groups, such as homeowners or renters. Nor can

demographic analysis provide estimates for geographic

areas below the national level. In addition, the level of

emigration and undocumented immigration must be

estimated using indirect methods. Since the U.S. only had

reasonably complete birth registration since 1935, sophisticated analysis was needed in 1950 for the population

over age 15. Early studies were restricted to the nativeborn White population, but with time were expanded to

include the native-born African-American population as

well.

Later work at the U.S. Census Bureau by Jacob Siegel and

colleagues expanded the estimates to the total population,

with the first official estimates being issued in conjunction

with the 1970 census (Siegel, 1974). The 1970 estimates

recognized the need to address the problem of ‘‘race misclassification in the complete count.’’ By the time of the

1970 census, the population covered by birth registration

included those under age 35, with tests of birth registration completeness having been conducted in 1940, 1950,

and the mid-1960’s. Medicare data now provided a basis

for estimates for those over age 65.

However, the difficulty of measuring migration, an important component of DA, gained attention. These studies

noted ‘‘The figures on net immigration for the 1960 to

1970 decade should be considered as estimates subject to

considerable error.’’ Importantly, the estimates did ‘‘not

include any allowance for...unrecorded alien immigration,

particularly illegal immigration.’’ See Siegel (1974) for

more details.

During these same decades, the methods of dual system

estimation were being refined for use in the human population. Although introduced over a century ago for use in

animal populations, dual system estimation was first used

with human populations in an important article by Sekar

and Deming (1949) that applied the technique to measuring births. Dual system estimation was widely used to

measure births and deaths in developing countries during

the 1970’s in conjunction with important operational and

theoretical work. The ideas from dual system estimation

soon applied to post-enumeration surveys. See most

importantly Marks (1979).

1980

The design of the A.C.E. traces most directly to the 1980

Post-Enumeration Program (PEP). This was the first large

scale post-enumeration survey to use dual system estimation. In addition, it included several important innovations, as well as important lessons on the design of a PES.

The 1980 PEP was based on a match of people included in

the April and the August Current Population Survey to the

1980 census. This match was used to determine the proportion of people counted in the census. It was a sample

of people known to exist and be residents of the U.S., and

was labeled the Population or P sample.

All matching was done by clerks and technicians. In order

to make it possible to do the matching, each person’s

address needed to be assigned the correct census geographic code (geocoded). This process was slow and error

prone.

In addition, a separate sample of census records was

drawn. This was known as the Enumeration or E sample.

The census records included in the E sample were checked

in the office to see if they were duplicated, followed by a

field operation to determine whether the people were real,

lived at the address on Census Day, and whether the unit

was assigned the correct census geographic code (correctly geocoded).

One important concept introduced in 1980 was that of

sufficient information for matching. ‘‘Sufficient information

for matching’’ means that a record, from either the P or E

sample, contains sufficient information, including most

importantly a name, to allow accurate matching and

follow-up. Records that lack this information are removed

from matching, processing and estimation. For the E

sample, this exclusion is done in two parts: census

imputed records (‘‘non-data-defined’’) are excluded from

the sampling frame, and then sampled ‘‘data-defined’’

records are reviewed for name and other necessary information.

Another concept used earlier but made explicit in 1980

was that of ‘‘search area.’’ A person was only considered

correctly enumerated if he/she was counted in a specific,

Introduction to the A.C.E. Section I—Chapter 1 1–3

U.S. Census Bureau, Census 2000
defined area that included the address where he/she

should have been enumerated. This ‘‘search area’’ was to

be applied to both the P and the E samples.

The 1980 PEP was also, very importantly, the first PES to

be, itself, carefully evaluated (Fay et al., 1988). This evaluation proved invaluable to the design of the 1990 PES.

Among the important findings were:

• Sampling variances were very high.

• Geocoding a sample of housing units was costly and

error prone.

• Drawing independent P and E samples made it very hard

to apply the same concepts, especially that of search

area.

• Levels of missing data needed to be reduced and methods to account for the missing data needed to be

refined.

• Matching needed to be made more accurate and faster.

• An independent sample of people living in institutions

proved nearly impossible to match and process, both

because the interviews relied on the same set of administrative records and because administrators often

refused to give names, even to the Census Bureau.

By 1980, the precision of demographic analysis benefited

from the fact that the part of the population not covered

by either adequate birth registration data or Medicare data

was now reduced to only those 45 to 65 (in 1980).

However, immigration, especially illegal/undocumented/

unauthorized immigration, remained a problem. Early

demographic estimates for 1980, which again did not

contain an allowance for illegal immigration, showed a net

overcount of the population. However, pathbreaking work

by Jeff Passel and colleagues produced the first estimates

of the number of illegal immigrants counted in the census.

This work was generally validated when data from the

Immigration Reform and Control Act (IRCA) produced

similar numbers of immigrants applying for legalization.

Although the 1980 PEP was not explicitly designed to

correct the census for measured undercount, it was the

first PES to be considered in this context. Increased use of

census results for congressional, state, and local redistricting, as well as for federal funds allocation highlighted the

importance of census accuracy. The voting rights cases of

the 1960’s (Baker v. Carr (1962), Reynolds v. Simms

(1964)) had greatly increased the importance of census

data in redistricting. General Revenue Sharing funds,

distributed in part based on census data, became an

important source of local government revenue in the mid

1970’s. The legal and statistical questions were discussed

in academic journals and as part of several lawsuits,

including influential suits by the City of Detroit and the

City of New York. The U.S. Census Bureau’s position was

that the 1980 PEP was not of sufficient accuracy for this

purpose, and this decision was upheld.

1990

Building on the knowledge gained in 1980, the Census

Bureau made major design changes for the 1990 PES.

Important changes included:

• Excluding institutional population and military

ships/barracks from the universe.

• The use of a block sample tied to census geographic

codes, with the same sample of blocks used for both

the P and the E sample.

• Repeated call-back to reduce nonresponse and missing

data.

• A computer and computer-assisted clerical matching

operation.

• A model to account for missing data taking into account

the important covariates.

The design of the estimation cells (post-strata) was completely changed. Following the advice of John Tukey and

others, the estimation cells were not restricted to a single

state, but allowed to cross state lines. Thus, Hispanics

living in Utah could be combined with Hispanics living in

Colorado and other mountain states to form one estimation cell, rather than being combined with non-Hispanics

living in Utah. A ‘‘smoothing model’’ was used to combine

information within Census Region.

The 1990 PES was explicitly designed so that it could be

used to adjust the census results. Specifically, modelbased methods were developed to carry the estimates

down to the smallest census geographic units (blocks) and

to include positive or negative whole person records to

account for the measured net undercount or overcount.

This complete file could then be aggregated to obtain data

that was consistent for all geographical levels.

Many lessons were learned in 1990, many having to do

with the need for tight operational control and testing.

One important statistical lesson concerned the use of the

statistical smoothing methods. These methods became

highly controversial and became the focus of much statistical analysis and debate. They were not well understood

and the U.S. Census Bureau decided to drop the use of

smoothing and instead recompute the results with fewer

and thus larger estimation cells.

Demographic analysis estimates went very smoothly in

1990 with birth registration and Medicare data covering

all but those age 55 to 65. The IRCA data and the work of

Jeff Passell and others (see Fay et al., 1988, Chapters 2

1–4 Section I—Chapter 1 Introduction to the A.C.E.

U.S. Census Bureau, Census 2000
and 3) provided an allowance for undocumented immigrants. Further, for the first time, the Census Bureau produced explicit allowances for the uncertainty in the demographic analysis estimates. This analysis showed that the

‘‘preferred’’ or ‘‘point’’ demographic analysis estimates

tended to fall at the lower end of the uncertainty range.

However, this method of expressing the uncertainty range

came under criticism from outside the Census Bureau.

Limitations of this method are documented in Robinson et

al. (1993) and Himes and Clogg (1992).

The 1990 Demographic Analysis estimates were in general

agreement with the results of the 1990 PES. At the

national level the two estimates were very close — 1.8

percent undercount for demographic analysis (later

revised to 1.7 percent) and 1.6 percent for the PES. At

more detailed levels, differences emerged, especially the

tendency for the PES to greatly underestimate the undercount for adult African-American males. Taking into

account what was known about the biases and uncertainties of each, it seemed clear that both were measuring a

real differential undercount even though PES was underestimating the amount for adult African-American males.

2000

In the early 1990s, task forces and National Academy of

Science Panels suggested that the differential undercount

in the census could not be reduced without elaborate

enumeration and matching procedures, which are too

costly to be carried out except on a sample of the population. In the 1995 and 1996 Census Tests, an alternative

‘‘Census Plus’’ methodology was compared to the DSE. The

performance of the DSE was better and subsequent

research efforts focused on improving the DSE. Consequently, most of the A.C.E. design can be seen as a

continuation and refinement of the 1990 PES design.

Among the important refinements are:

• Much larger and better designed block sample.

• Earlier interviewing, including the use of early telephone

interviewing.

• Computer-assisted (laptop) telephone and personal

interviewing.

• More refined estimation cells (post-strata).

• Explicit collapsing rules to account for small cell size.

• Explicit weight trimming rules in case of extraordinary

(outlier) cells.

The survey universe was restricted to the housing

unit/household population. All group quarters, not just

military and institutional, populations were excluded.

Consequently, the A.C.E. estimate of coverage error will

be underestimated to the extent there were errors in the

group quarters population.

Another concern is the treatment in the DSE of cases

involved in the Housing Unit Duplication Operation

(referred to as late census adds) and the level of whole

person imputations in the census. These records were

not included in the A.C.E. matching, processing, or

follow-up processes. They were also excluded from the

DSE, although properly accounted for in computing the

net undercount. It is possible that, had these records

been included in the A.C.E. and the DSE, the estimated

undercount would have differed. The number of

excluded records is much larger than it was in 1990. If

the ratio of matches to correct enumerations is the

same for the excluded and included cases, the DSE

expected value should be nearly the same. However, if

the people referred to in the correct cases were either

much more likely to have been included in the A.C.E. or

much less likely to have been included, then excluding

these cases from the A.C.E. would have changed the

level of correlation bias and affected the A.C.E. For

more detail, see Hogan (2001).

There was a change in the treatment of people who had

moved between April 1 and the time of the PES interview. In 1980 and 1990, these ‘‘movers’’ were sampled

at their current (i.e. PES Interview Day) address. In the

A.C.E., they were sampled at their Census Day, April 1,

address.

Although conceptually much the same, the implementation of the ‘‘search area’’ was very different. In 1990, the

entire search area was always to be searched for all

cases in order to find matches or duplicates, and all

cases were ‘‘map-spotted’’ to determine whether they

were inside the search area. In 2000, the search of the

surrounding blocks was restricted by both targeting and

sampling. First, the surrounding block was searched for

only certain kinds of cases, specifically cases where

there was a likelihood of geocoding error in the basic

census process. In addition, a stratified sub-sample was

taken for this search, with only some of the initial

sample blocks subjected to this extended search. This

process was known as Targeted Extended Search, or

TES.

Because of the difficulty in explaining and defending

the 1990 smoothing methods, smoothing models were

not employed. Instead, the A.C.E. relied upon a larger

sample size and a more refined set of estimation cells

to produce estimates.

Finally, although this was not a separate step, the A.C.E.

was subjected to much more exacting specification,

documentation and testing than any previous coverage

measurement study. Much of the operational success of

the A.C.E. can be traced to the care and attention given

to documentation and testing.

Introduction to the A.C.E. Section I—Chapter 1 1–5

U.S. Census Bureau, Census 2000
This document is then very much part of the overall

A.C.E. process. It attempts to document, concisely and

clearly as well as precisely and accurately, the A.C.E.

design.

1–6 Section I—Chapter 1 Introduction to the A.C.E.

U.S. Census Bureau, Census 2000
Chapter 2.

Accuracy and Coverage Evaluation Overview

INTRODUCTION

The Accuracy and Coverage Evaluation Survey (A.C.E.) was

designed primarily to measure the net undercoverage or

overcoverage in the census enumeration. The methodology used was dual system estimation that requires two

independent systems of measurement. The P sample or

‘‘Population sample’’ measured the housing unit population, as did the census, but was conducted independently

of the census. This was done by selecting a sample of

block clusters, geographically contiguous groups of

blocks, and interviewing housing units that were obtained

by independently canvassing each block cluster. The

results of the P sample were matched to census

enumerations to determine the omission rate in the

census. Additionally, a sample of census enumerations,

the E sample, was selected to measure the erroneous enumeration rate in the census. The E sample was comprised

of census enumerations in the same sample block clusters

as the P sample. These overlapping samples reduced

variance on the dual system estimator, reduced the

amount of field activities and their cost, and resulted in

efficient data processing.

There were considerable challenges in the implementation

of the A.C.E. One of the requirements of the A.C.E. was to

produce measures of net undercount or overcount shortly

after the census counts were compiled. This was a daunting task because the requirement for independence meant

that A.C.E. activities could not interfere, or in any way

affect the results of the census enumerations, or vice

versa. As with most surveys, the A.C.E. consisted of

designing a sample, creating a frame, selecting the

sample, conducting the interviews, dealing with nonresponses and missing information, as well as producing the

estimates. In addition, the A.C.E. had several matching

and field follow-up activities. In order to accomplish these

tasks and meet the goals of the A.C.E. in a timely manner,

its design was uniquely built around census operations.

Additionally, to ensure quality with such a compressed

time schedule, it was essential that software systems be

written and thoroughly tested prior to the start of an

activity.

One census operation that had major influence on the

A.C.E. design and estimation plan was the Housing Unit

Duplication Operation. As the census questionnaires were

being processed, the Census Bureau suspected that there

was a significant number of duplicate addresses in the

census files. To address the suspected housing unit

duplication, the Housing Unit Duplication Operation was

introduced in the fall of 2000. See Nash (2000) for further

details. The primary goal of this census operation was to

improve the quality of the census; however, its design

allowed the A.C.E. operations to proceed. Essentially, suspected duplicate housing units were temporarily removed

from the census files, while further analysis was done for

these cases. Approximately 5.9 million person records

were in these suspected duplicate housing units, which

were: 1) out-of-scope for the E-sample component of the

A.C.E., 2) not available for the person matching including

the identification of person duplicates in the E sample, and

3) excluded from the census component in the dual system estimates. Approximately 2.3 million person records

were reinstated into the census after the E sample was

selected and were reflected in the net coverage estimates.

Hogan (2001) showed that excluding these person records

from the A.C.E. would not affect the dual system estimates, if the number of P-sample matches was reduced

proportionately to the number of E-sample correct enumerations.

This chapter summarizes the major activities of the A.C.E.

and indicates their relationship to the census. Subsequent

chapters go into considerably greater detail about the

methodology of the A.C.E. and are organized as follows:

• Chapter 3. Design of the A.C.E. Sample

• Chapter 4. A.C.E. Field and Processing Activities

• Chapter 5. Targeted Extended Search

• Chapter 6. Missing Data Procedures

• Chapter 7. Dual System Estimation

• Chapter 8. Model-Based Estimation for Small Areas

The intent of this chapter is to provide a broad context for

the design of the A.C.E. Here we give a sequential

accounting of these activities. Table 2-1 gives the order in

which the A.C.E. activities occurred and maps the activities to the chapter where each is discussed in further

detail. This table shows the substantial integration of the

sampling and operational activities. Figure 2-1 shows the

flow of the major activities.

Accuracy and Coverage Evaluation Overview Section I—Chapter 2 2–1

U.S. Census Bureau, Census 2000
Table 2-1. Sequence of A.C.E. Activities

Activity Description Chapter(s)

1 First-phase sampling 3

2 Independent listing 4

3 Second-phase sampling 3

4 Initial housing unit matching/field follow-up 4

5 Targeted extended search 4 & 5

6 Subsampling within large block clusters 3

7 A.C.E. person interviewing 4

8 E-sample identification 3 & 4

9 Person matching and field follow-up 4

10 Missing data processing 6

11 Dual system estimation 7

12 Model-based estimation for small areas 8

Table 2-2 further illustrates the integration of the sampling

activities and operations by summarizing the sample size

at each phase of sampling and the operations for which

the sample is an input. The data collected from each

operation is input to the next sampling operation. For

example, the first phase of sampling resulted in 29,136

sample areas with almost 2 million housing units.

Independent address lists were created for these areas.

The results of the independent listing were used in the

second phase of sampling.

Activity 1. First-Phase Sampling

Timing: March through June, 1999; prior to the creation

of the census address list.

At the time of the January, 1999 Supreme Court ruling

against the use of sampling for apportionment, the

Census Bureau was heavily involved in the first phases of

sampling for the Integrated Coverage Measurement (ICM).

The goal of the ICM was to produce reliable estimates of

coverage of each state’s total population, and this required

a very large sample – a 750,000 housing unit sample was

planned. As a result of the Supreme Court ruling, state

population estimates for apportionment were no longer

key estimates of the coverage survey; instead, the goal

was to measure census coverage for national and subnational population domains having different census coverage properties. These estimates could be measured with

sufficient precision with a sample of about 300,000

housing units.

Rather than abandoning the effort, i.e., software development, etc., that had already been invested in the ICM, it

was more efficient, particularly from a software quality

perspective, to complete the sampling for the ICM, and

then select a subsample for the A.C.E. The infrastructure

for the field staff was being deployed in preparation for

the first field operation that started in September, 1999,

and the development of the sampling system that was

scheduled to begin production in March, 1999 was well

underway. There was not adequate time to redesign the

A.C.E. sample allocation entirely, select the sample,

produce the different listing materials including maps,

conduct the listing as scheduled, and ensure a high level

of quality in a revised software system. Consequently, the

A.C.E. sample design was derived from the ICM design

using a double sampling approach. The entire ICM sample

was selected as originally planned and then reduced

through various steps to yield the A.C.E. target housing

unit sample.

The first-phase sampling consisted of:

• Forming primary sampling units.

• Stratifying primary sampling units.

• Systematic sampling of primary sampling units.

The A.C.E. primary sampling unit was the block cluster, a

group of one or more geographically contiguous census

blocks. To make efficient field workloads, the target size

of block clusters was about 30 housing units, although

block clusters varied in size. Within each state, block

clusters were stratified by size using housing unit counts

from a preliminary census address list: small (0 to 2

housing units), medium (3 to 79 housing units), and large

(80 or more housing units). Some states included a separate sampling stratum for American Indian Reservations.

Within each sampling stratum, a systematic sample of

block clusters was selected with equal probability.

This phase of sampling yielded 29,136 block clusters with

an estimated 2 million housing units in the 50 states and

the District of Columbia.

Table 2-2. Sample Sizes by Sampling Phase and Operation

Sampling phase

Sample size

Operations

Areas Housing units

First-phase . . . ............................... 29,136 1,989,000 Independent listing

Second-phase ............................... 11,303 844,000 Initial housing unit matching/follow-up

Subsampling within large cluster (P-sample) . . . . 11,303 301,000 A.C.E. person interviewing, person matching/follow-up, dual

system estimation

E-sample identification . . ..................... 11,303 311,000 Person matching/follow-up, dual system estimation

2–2 Section I—Chapter 2 Accuracy and Coverage Evaluation Overview

U.S. Census Bureau, Census 2000
Activity 2: Independent Listing

Timing: September through early-December, 1999; well

before census enumeration began.

Field staff visited the sample block clusters and created an

independent address list of all housing units, including

housing units at special places. The goal of this operation

was to create an independent address frame of all the

housing units that were likely to exist on Census Day,

April 1, 2000. Since this operation occurred prior to

Census Day, any potential housing unit structures were

included on the independent address list. Later, during

housing unit follow-up, these structures were visited

to confirm that they actually contained housing units

on Census Day. Since housing units could not be added

to the independent address frame in this later operation,

but could be removed, it was important to include structures with questionable housing unit status during the

independent listing.

This listing consisted of approximately 2 million housing

units or potential housing units in the 50 states and the

District of Columbia.

Activity 3: Second-Phase Sampling

Timing: December, 1999 through February, 2000; prior

to mailing the census questionnaire.

The second phase of sampling selected block clusters

from the first phase to be the final A.C.E. sample areas.

Block clusters were stratified using two housing unit

counts: 1) a count from the independent listing operation,

and 2) a count from the updated census address list as of

January, 2000. It was important to reduce the first-phase

sample before the next operations, the housing unit

matching and field follow-up, to reduce the number of

clusters going into those operations. The stratification of

the block clusters was done separately by first-phase sampling strata: 1) medium and large strata, and 2) small

strata. All first-phase clusters from the American Indian

Reservation stratum were retained in the second-phase

sample.

Medium and large strata. The resulting national sample

allocation was roughly proportional to state population

with some differential sampling within states. The two

goals of the differential sampling were: 1) to provide

sufficient sample to support reliable estimates for several

sub-populations, and 2) to reduce the variance contribution due to clusters with the potential for high omission

or erroneous enumeration rates. These clusters were identified and put into separate sampling strata by comparing

the consistency of housing unit counts between the independent list and the updated census list for each cluster.

Small cluster stratum. Conducting interviews and

follow-up operations in small block clusters is much more

costly per housing unit than in medium or large block

clusters. Lower sampling rates were, therefore, used in

this stratum. However, two considerations were taken into

account in establishing the lower rates. One goal was to

avoid having small clusters with an overall probability of

selection much lower than the probability of selection of

other clusters in the sample. A second goal was to have

higher probabilities of selection for small clusters in which

the number of housing units was greater than the

expected 0 to 2 housing units. These two goals attempted

to reduce the contribution of small clusters to the variance

of the dual system estimates. Small block clusters with the

potential for high erroneous enumeration or nonmatch

rates were retained at higher rates. The second-phase

sample contained 11,303 block clusters for the 50 states

and the District of Columbia.

Activity 4: Initial Housing Unit Matching and Field

Follow-Up

Timing: February through April, 2000; prior to census

nonresponse follow-up.

The objectives of these operations were:

1. Create a list of confirmed A.C.E. housing units in order

to:

• obtain the best list of housing units to facilitate person interviewing in later activities.

• have better control of the final A.C.E. housing unit

sample size.

2. Establish a link between the A.C.E. and census housing units in order to:

• identify the A.C.E. housing units eligible for telephone interviewing.

• facilitate overlapping P and E samples.

3. Identify potential geocoding errors in order to:

• establish the targeted extended search sampling

frame.

• identify sample areas for which the creation of a new

independent address list, or relisting, was necessary.

Housing unit matching. The housing units on the census address list in January, 2000 were matched to the

A.C.E. independent address list. First, the addresses were

computer matched. The computer matching was followed

by a clerical review of the computer match results in an

automated environment intended to find additional

matches using supplemental materials. There was also a

clerical search, limited to the block cluster, for duplicate

housing units during this phase of the matching. Possible

duplicates in both the A.C.E. and the census were identified.

Accuracy and Coverage Evaluation Overview Section I—Chapter 2 2–3

U.S. Census Bureau, Census 2000
Housing unit follow-up. In some cases, the computer

and clerical matching were not able to determine the status of a housing unit. Field staff visited these cases to get

more information about these housing units. After matching, the cases which were not matched, possibly matched,

or possible duplicates were sent to the field for follow-up

interviews. Some of the matched cases were also sent for

additional information. The field follow-up was designed

to determine if a housing unit existed, if it existed in the

block cluster, or if different addresses were referring to

the same housing unit.

Activity 5: Targeted Extended Search

Timing: May, 2000.

The targeted extended search was designed to improve

the accuracy of the dual system estimate by searching for

matches, correct enumerations and duplicates one ring

beyond the sample block cluster. The operation was

implemented in a subset of A.C.E. block clusters selected

through a combination of certainty and probability

sampling.

There are census geocoding errors of exclusion and inclusion in the A.C.E. sample block clusters. Census geocoding errors of exclusion (i.e., housing units miscoded in the

census so they appear to be outside the A.C.E. block

cluster) affect the P-sample match rate. Census geocoding

errors of inclusion (i.e., housing units miscoded in the

census to appear inside the block cluster) affect the erroneous enumeration rate in the census or E sample. If the

census housing unit is omitted from the sample block

cluster, the P-sample household can not be matched. This

yields a lower match rate. On the E-sample side, if a housing unit is included in the sample block cluster due to a

geocoding error, the E-sample people will be considered

erroneously enumerated.

The primary motivation for using an extended search area

was to reduce the sampling variance of the dual system

estimates due to census geocoding error. Even though the

extended search allowed more P-sample people to be

matched and more E-sample people to be converted to

correct enumerations, the expected value of the dual system estimate should not be affected as long as the two

samples were treated equally with respect to the search

area. Another benefit is that the extended search makes

the dual system estimate more robust by protecting

against potential bias due to P-sample geocoding error.

Previous census evaluations have shown that geocoding

errors are highly clustered. The targeted extended search

was designed to take advantage of the distribution of

geocoding errors by focusing on those clusters that contain the most potential geocoding errors. The implementation of this operation resulted in dual system estimates

with more precision.

The initial housing unit matching results were used to

identify the A.C.E. housing unit nonmatches and census

housing unit geocoding errors. Clusters without A.C.E.

housing unit nonmatches or census geocoding errors were

out-of-scope for the targeted extended search sampling.

Changes to the census inventory of housing units after

January, 2000 were not reflected in the housing unit

matching used to identify targeted extended search

clusters.

Only whole households of nonmatched people were

eligible for the extended search during person matching.

Partial household nonmatches (i.e., some household members were matches) were not as likely to indicate that the

housing unit was a geocoding error.

Activity 6: Subsampling Within Large Block

Clusters

Timing: April and May, 2000; during census nonresponse

follow-up.

Subsampling was used in large block clusters for the final

selection of housing units to participate in the P sample.

The objective was to reduce costs and yield manageable

field workloads without seriously affecting the precision

of the A.C.E. by taking advantage of the high intra-class

correlation expected in large block clusters. Since the

large block clusters had a higher initial probability of

selection than medium block clusters, the reduction in

sample size had a fairly minor effect on the precision of

the A.C.E. estimates. The subsampling of housing units

within large clusters brought the overall probability of

selection of these housing units more in line with housing

units in the medium clusters.

Any block cluster with 80 or more confirmed A.C.E. housing units, based on the initial housing unit match, was

eligible for this housing unit reduction. The reduction of

housing units within a large block cluster was done by

forming groups of adjacent housing units, called segments, and selecting one or more segments for A.C.E.

person interviewing. The segments had roughly equal

numbers of housing units within a block cluster. Segments

of housing units were used as the sampling unit in order

to obtain compact interviewing workloads and to facilitate

the identification of an overlapping E sample. The A.C.E.

housing units that were retained after all of the subsampling comprise the P sample.

After the reduction of housing units within large block

clusters was completed, the A.C.E. interview sample size

for the 50 states and the District of Columbia was approximately 300,000 housing units.

Activity 7: A.C.E. Person Interviewing

Timing: April through mid-June, 2000 for the telephone

phase; Mid-June through mid-September, 2000 for the personal visit phase; after census enumeration was complete.

2–4 Section I—Chapter 2 Accuracy and Coverage Evaluation Overview

U.S. Census Bureau, Census 2000
The goal of the A.C.E. person interview was to provide a

list of persons who lived at the sample address on Census

Day, as well as those who lived at the address at the time

of A.C.E. interviewing. The A.C.E. person interview was

conducted using a Computer Assisted Personal Interview

(CAPI) instrument.

To get an early start on interviewing, a telephone interview was conducted at households for which the census

questionnaire was data-captured and included a telephone

number. Both households with mail returns and

enumerator-filled questionnaires were eligible for telephone interviews. Certain types of housing units, such as

those without house number and street name, were not

eligible for a telephone interview. All remaining interviews

following the telephone operation were conducted in person. However, some nonresponse conversion operation

interviews and interviews in gated communities or

secured buildings were conducted by telephone.

The person interview was conducted only with a household member during the first 3 weeks of interviewing. If

an interview with a household member was not obtained

after 3 weeks, an interview with a nonhousehold member

was attempted. This was called a proxy interview. Proxy

interviews were allowed during the remainder of the interviewing period. During the last 2 weeks of interviewing a

nonresponse conversion operation was attempted for the

noninterviews using interviewers who were considered to

be the best available.

Activity 8: E-Sample Identification

Timing: October, 2000.

The E sample consisted of the census enumerations in the

same sample areas as the P sample. All data-defined census person records in the A.C.E. block clusters were eligible to be in the E sample.1 To be a census data-defined

person, the person record must have two 100-percent

data items filled. Name was not required for the person

record to be considered data-defined, but could be one

of the two items required to be data-defined. Like the

P sample, it was sometimes necessary to subsample the

census housing units in a cluster when it contained a large

number of census housing units. The goal of the E-sample

identification was to create overlapping P and E samples in

an effort to reduce person follow-up workloads. An overlapping P and E sample is not necessary, but improves

both the cost effectiveness of the subsequent operation

and the precision of the dual system estimates.

If a block cluster had fewer than 80 census housing units,

then all of the census housing units in the block cluster

were in the E sample. For block clusters with 80 or more

census housing units, the within-cluster segments of adjacent housing units defined for the P-sample reduction

were mapped on to the census records. This was possible

when a link between the census and A.C.E. housing unit

was established during the initial housing unit matching.

Using specific rules, census housing units that did not

have this link were assigned to a segment. The segment

selected for the P sample was selected for the E sample. If

the sample segment contained 80 or more census housing

units with no established link to an A.C.E. housing unit,

then a systematic sample of these housing units was

selected to reduce the E-sample person follow-up workloads.

This resulted in approximately 311,000 census housing

units in the E sample for the 50 states and the District of

Columbia.

Activity 9: Person Matching and Field Follow-Up

Timing: October and November, 2000.

Insufficient information for matching. Rules were

established for determining which person records had

sufficient information for matching. These rules were

established and applied before the start of the matching

operation to avoid introducing potential bias into the

matching results. Both the P and E samples used the same

rules. Each person record required a complete name and

two other characteristics.

Person matching. All P-sample persons who lived at

each sample housing unit on Census Day were matched to

the people enumerated in the census to estimate the

match rate. Census persons in the E sample who matched

to the P sample were considered to be correctly enumerated. The E-sample person records that did not match to

the P sample were interviewed during field follow-up

operations to classify them as correctly or erroneously

enumerated. This matching was a computer operation

with clerical review. Variables such as name, address, date

of birth, age, sex, race, Hispanic origin, and relationship

were used to identify matches between the P sample and

census enumerations. Duplicates were identified in both

the P sample and E sample. If a case qualified for targeted

extended search, the search for matches and duplicates

was extended to the ring beyond the sample block cluster.

Person follow-up. The person follow-up interview collected additional information that was sometimes necessary for the accurate coding of the residence status of the

nonmatched P-sample people and the enumeration status

of the nonmatched E-sample people. The goal of this

operation was to confirm that ambiguous P-sample nonmatches actually lived in the sample block cluster on

Census Day. Thus, follow-up interviews for P-sample nonmatched cases were carried out when there was a possibility the residence status was not correct. Similarly,

1

Excludes data-defined person records temporarily removed

from the census.

Accuracy and Coverage Evaluation Overview Section I—Chapter 2 2–5

U.S. Census Bureau, Census 2000
E-sample nonmatch cases were subject to follow-up interviews to determine if they were correctly or erroneously

enumerated in the block cluster. Possible matches were

interviewed to resolve their match status. There were also

other cases sent to follow-up, such as matched people

with unresolved residence status and other types of cases

considered to have the potential for geographic errors in

the P sample. The person follow-up interview used a

paper questionnaire. Interviewers gathered information

that permitted each person to be coded as a matched

resident/nonresident or a nonmatched resident/

nonresident of the block cluster on Census Day. There was

considerable emphasis on obtaining a knowledgeable

respondent before the follow-up questions were asked.

After the follow-up interview was completed, the results

were reviewed by clerks who assigned final status to these

cases using an automated system.

Activity 10: Missing Data Processing

Timing: December, 2000 through the early part of

January, 2001.

Since the results of the matching operation were to be

used in the estimation phase of the A.C.E., it was necessary to determine the match, correct enumeration and

residence status of all sample cases. When these could not

be resolved through computer and clerical matching or

through field follow-up interviews, the match, correct enumeration, or residence probabilities were imputed based

on the distribution of outcomes of the resolved follow-up

interviews. Also, as in the census, some respondents did

not answer all the questions in the A.C.E. interview which

were needed for estimation. If the variables tenure, sex,

race, Hispanic origin, or age were blank for P-sample individuals, the missing information was imputed based on

the distribution of the variable within the household, the

overall distribution of the variable, or using hot-deck

methods, depending on the variable. Imputation for missing information in the E sample was resolved in the census

processing. Finally, a noninterview adjustment was made

to account for the weights of households that should have

been interviewed in A.C.E., but were not.

Activity 11: Dual System Estimation

Timing: Late January, 2001.

Dual system estimation was used to estimate the net

undercount or overcount of the household population

included in the census. Coverage estimates of persons

living in group quarters or in Remote Alaska areas were

not made.

The term dual system estimation is used because data

from two independent systems are combined to measure

the same population. After matching to the census, the

P sample was used to measure the omission rate in the

census. The E sample was used to measure the erroneous

enumeration rate in the census. The dual system estimator

assumes that all persons have the same probability of

being captured in the census. This is obviously an oversimplification of the existing situation. Post-stratification

sharply reduced the likelihood that this assumption would

bias the results, since it only requires equal capture probabilities within post-strata.

Post-stratification. Dual system estimation was used to

calculate the proportion of persons missed in each of a

number of relatively homogeneous population groups

called post-strata. The post-strata for the Census 2000

A.C.E. were defined by the variables: race/Hispanic origin

domain, age/sex, tenure, census region, metropolitan

statistical area size/type of enumeration area, and census

return rate. A complete cross-classification of these variables would have unnecessarily increased the variances of

the estimates due to small expected sample sizes in many

of the post-strata. Consequently, many of the detailed

cells were combined. In the United States, there were 448

potential post-strata which were collapsed to 416 poststrata on the basis of small observed sample sizes or high

coefficients of variation.

The dual system estimate. The dual system estimate

(DSE) for each post-stratum was defined by:

DSˆE DD 

CE

Ne



Np

M

where DD was the number of data-defined persons in the

census at the time of A.C.E. matching,2 CE was the

weighted estimate of the number of people in the census

who were correctly enumerated, Ne was the weighted

estimate of the number of people in the census, Np was

the weighted estimate of the number of people found by

the independent A.C.E. collection procedures, and M was

the weighted estimate of the number of persons found by

the independent A.C.E. collection procedures who were

matched to persons enumerated in the census.

Activity 12: Model-Based Estimation for Small

Areas

Timing: February, 2001.

Activities 1 through 11 were designed to provide estimates of net coverage for Census 2000. These estimates

can serve two purposes. One purpose was to provide

information on the quality of the census so that analysts

can make more intelligent use of the data, and to help the

Census Bureau improve procedures for future censuses.

The second purpose was to have a basis for adjusting the

census counts for net coverage, if deemed appropriate.

The sample sizes used in the A.C.E. provided adequate

2

The data-defined persons term excludes cases temporarily

removed from the census.

2–6 Section I—Chapter 2 Accuracy and Coverage Evaluation Overview

U.S. Census Bureau, Census 2000
reliability for such estimates for the U.S. as a whole, and

for major geographical areas. However, the sample sizes

were too small to provide reliable estimates for most

states, counties, cities, and the thousands of other municipalities that normally make use of census data. As a

result, model-based estimation was used in these areas.

Model-based estimation treats the coverage correction

factors as uniform within a given post-stratum. Another

way of saying this is that the coverage error rate for a

given post-stratum is assumed to be the same within all

geographic areas. This assumption is obviously an oversimplification, and small errors are introduced. However,

the model-based estimates provide a consistent set of estimates in which the sum of the population counts for small

areas are equal to the dual system estimates of much

larger areas (e.g., the U.S. total, regions, etc.).

Coverage correction factors were obtained by dividing the

dual system estimates by the census counts of persons in

housing units. Persons in group quarters were not

adjusted for net coverage. Coverage correction factors for

population groups that generally had good coverage were

close to 1.00. Population groups with poor coverage had

coverage correction factors higher than 1.00, while coverage correction factors less than 1.00 in a post-stratum

occurred when erroneous enumerations rates in the

census exceeded omission rates.

A coverage correction factor was calculated for each

post-stratum. If a post-stratum was estimated to have

more persons than the census count, within each block a

random sample of the appropriate size of census people

in the post-stratum was selected. The data of the selected

people were replicated in their blocks with a weight of

+1. If a post-stratum was estimated to have fewer people

than the census count, within each block a random sample

of the appropriate size of people in the post-stratum was

selected. The data of the selected people were replicated

in their blocks with a weight of -1. Under this procedure

no reported data for any individual was removed from the

Census 2000 data files. A controlled rounding procedure

was used to produce integer-valued model-based estimates at various geographic levels.

Estimates were made at various levels by aggregating the

data from the appropriate blocks and/or post-strata.

Accuracy and Coverage Evaluation Overview Section I—Chapter 2 2–7

U.S. Census Bureau, Census 2000
	


	

	



	
		
	

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Chapter 3.

Design of the A.C.E. Sample

INTRODUCTION

The A.C.E. sample design was a multiphase, national

sample of 301,000 housing units. Its development was

heavily influenced by its planned predecessor, the Integrated Coverage Measurement survey (ICM). Initial plans

for Census 2000 were for a one-number census corrected

for coverage based on the ICM. A primary purpose of the

ICM was to produce direct state estimates of coverage

with sufficient reliability for apportionment population

counts. This called for a state-based design and a much

larger overall national sample of 750,000 housing units.

The January 1999 Supreme Court ruling against the use of

sampling for apportionment resulted in a change of plans

for the Census 2000 coverage survey for which the primary goal became the production of reliable national census coverage estimates, and of selected sub-populations.

This did not require as large a sample.

The A.C.E. sample design was derived from the ICM

sample design. By the time the change of plans for the

Census 2000 coverage survey occurred, many operational

plans for the ICM were too far advanced to make significant changes required for a newly conceived sample

design plan. The implementation plans and software systems for creation of the sampling frame and selection of

the ICM sample were moving along and almost ready to

start. Much of the field office infrastructure and staffing

was being put in place for the first field operation under

the ICM sample plan. It was critical to proceed as planned

in order to meet schedules.

The A.C.E. sampling plan was thus developed as a multiphase design. The much larger ICM sample was first

selected. Field staff canvassed the sample areas to create

an independent address list. Then, using updated measures of size from the field canvass, the ICM sample was

re-stratified and reduced with differential probabilities of

selection to create the A.C.E. sample design.

Sections on the A.C.E. sample and its design are directed

to a general audience. They provide results of the A.C.E.

sample along with a broad overview of the sample design.

Later sections of this chapter provide a more in-depth

description of the A.C.E. design and are available for readers who desire greater detail.

A.C.E. SAMPLE OVERVIEW AND RESULTS

The A.C.E. consisted of two parts. The Population Sample,

P sample, and the Enumeration Sample, E sample, have

traditionally defined the samples for dual system estimation. Both the P sample and the E sample measured the

same household population. However, the P-sample operations were conducted independent of the census. The E

sample consists of census enumerations in the same

sample areas as the P sample. After matching with the

census lists and reconciliation, the P sample yields an estimated rate at which the population was missed in the census whereas the E sample yields an estimated rate at

which enumerations were erroneously included in the census. Combining them yields an A.C.E. estimate of net census coverage of the household population.

The Accuracy and Coverage Evaluation had three sampling

phases:

1. First-phase sample. The selection of the ICM

sample, comprising a large number of sample areas

for which a list of housing unit addresses was created

independent of the census.

2. Second-phase sample. The reduction of the firstphase sample which resulted in the A.C.E. sample

areas.

3. Third-phase sample. The reduction of housing units

by subsampling within unusually large A.C.E. sample

areas.

Table 3-1 summarizes the A.C.E. sample size after each

phase of sampling for the United States. The dates given

in the table are the production dates. The housing unit

counts are approximate, based on the best known information at the time of the particular sampling phase.

Design of the A.C.E. Sample Section I—Chapter 3 3–1

U.S. Census Bureau, Census 2000
Table 3-1. Census 2000 A.C.E. Sample Sizes by Sampling Phase

Start and finish date Sampling phase Sample areas Estimated housing units

March, 1999 thru June, 1999 First-phase 29,136 1,989,000

December, 1999 thru February, 2000 Second-phase 11,303 844,000

April, 2000 thru May, 2000 Third-phase 11,303 301,000

within-cluster reduction 3,153 106,000

no within-cluster reduction 8,150 195,000

SURVEY CHARACTERISTICS AND THE A.C.E.

SAMPLE DESIGN

Main Characteristics of the A.C.E. Sample

The A.C.E. sample:

• Is a probability sample of 301,000 housing units in

11,303 sample areas for the United States.

• Yields estimates of net census coverage of persons in

households and housing units for the nation excluding

Remote Alaska.

• Has independent samples in each state and the District

of Columbia, but there are no state-based design

criteria.

• Has total state sample sizes roughly proportional to

population size with the exception that the smaller

states have additional sample; these smaller states have

similar sample sizes.

• Uses some differential sampling within states for areas

that may contribute disproportionately to total variance

or have higher concentrations of historically undercounted population groups.

• Has a separate sample of American Indian Reservation

and other associated trust lands.

• Uses updated measures of size at each phase of

sampling.

• Balances operational limitations such as field workloads

and statistical issues such as weight variation.

Overview of the Design

The A.C.E. uses a multiphase sample to measure the net

coverage for the household population in Census 2000.

The national sample, 301,000 housing units in 11,303

sample areas, was distributed among the 50 states and

the District of Columbia roughly proportional to population size except for the smaller states that had their

samples increased.

Primary sampling unit. The block cluster was the Primary Sampling Unit (PSU) for the A.C.E. Each block cluster

consisted of one or more geographically contiguous census blocks. Each block cluster contained on average 30

housing units, which was an efficient interviewer workload. An important block cluster characteristic was welldefined, physical boundaries. Ambiguous block cluster

boundaries could potentially lead to errors of omission or

erroneous inclusion in the A.C.E. sample.

Phases of the A.C.E. sample. Three phases of the

A.C.E. sampling were:

1. Selection of an initial sample of approximately 30,000

block clusters for which the field staff developed an

independent list of housing unit addresses.

2. Selection from the initial sample results of a subsample of block clusters for the A.C.E. sample based

on the results of the independent list.

3. Selection of a subsample of housing units within large

block clusters.

First phase consisted of the selection of a systematic sample in each state. In the first phase of the

A.C.E. sampling, block clusters in each state were classified by size into four mutually exclusive groups known as

sampling strata: (1) clusters with 0 to 2 housing units

(small stratum), (2) clusters with 3 to 79 housing units

(medium stratum), (3) clusters with 80 or more housing

units (large stratum), and (4) clusters on American Indian

Reservations with three or more housing units (American

Indian Reservation stratum). Block clusters with 80 or

more housing units were selected with higher probability

than medium clusters in this phase because housing units

in large clusters were subsampled in a later operation,

bringing the overall probability of selection−the inverse of

the sampling weight−for housing units in these clusters

more in line with the overall selection probabilities of

housing units in medium clusters. Within each sampling

stratum, clusters were sorted and a systematic sample

was selected with equal probability.

Second phase involved the reduction of the ICM

first-phase sample to the level desired for the

A.C.E. In the second phase, the block clusters from the

medium and large sampling strata were re-stratified based

on the estimated demographic composition of the block

clusters and the relationship between the housing unit

count from the independent list and the January 2000

updated census address list. This was done separately for

3–2 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
the medium and large strata within each state. These substrata are referred to as ‘‘reduction strata.’’ Within each

reduction stratum, the clusters were sorted, and a systematic sample was selected with equal probability within

each reduction stratum. This reduction used different

selection probabilities across the reduction strata within a

state and across states.

Next, using housing unit counts from the independent list

and the January 2000 updated census address list, the

small block clusters were stratified within each state by

size, and systematic samples were selected from each

stratum with equal probability. All clusters from the small

sampling stratum with 10 or more housing units based on

the updated information were retained. All clusters from

the small sampling stratum that were on American Indian

land as well as List/Enumerate clusters were also retained.

The second phase of sampling was not done for the

American Indian Reservation sampling stratum.

The third phase consisted of the sample reduction

of housing units within large block clusters. In the

third phase of A.C.E. sampling, a subsample of housing

units was selected within large clusters. If a cluster contained 79 or fewer housing units, all the housing units

were included in the A.C.E. sample. In clusters with 80 or

more housing units, a subsample was selected to reduce

the cost of data collection. This phase of sampling

resulted in lower variation of selection probabilities for

housing units within the same reduction stratum because

the large clusters had a higher probability of selection at

the first phase. This subsampling was done by forming

groups of adjacent housing units, called segments. A systematic sample of segments within each cluster was

selected. All housing units in the selected segments were

included in the A.C.E. sample.

The P sample and the E sample. The P sample consisted of the households used for the A.C.E. interviews

that were conducted in these selected block clusters and

block cluster segments. The E sample was the set of

census enumerations in these same block clusters and

block cluster segments.

Measures of Size

As stated earlier, the A.C.E. sample design used updated

measures of size at each phase of sampling.

First-phase sample. The block cluster measure of size

for the first-phase sample was based on preliminary census files existing in the spring of 1999. Ideally, the source

of the block cluster measure of size would have been the

Decennial Master Address File, the base file of census

addresses for the decennial programs. However, the first

version of this file was not available until the summer of

1999, too late for use in the block clustering. Instead, the

first-phase measure of size was typically the higher of the

preliminary census housing unit count or the 1990 census

address count for a block cluster containing city-style

addresses, house number and street name. For block clusters with non-city-style addresses, the measure of size

was the preliminary 2000 census housing unit count. The

rules for determining which housing units on the preliminary 2000 census files would eventually move forward to

the Decennial Master Address File had not been defined,

so the block cluster measure of size was based on a reasonable set of criteria, but not the final set.

Second-phase sample. For the second phase of sampling, the block cluster measure of size was the count of

housing units on the list of housing unit addresses created

independently of the census in the fall of 1999. The reduction of the medium and large block clusters used a preliminary count of these housing units, which was a clerical

tally of housing units from the listing sheets. The small

block cluster reduction used the count of housing units

from the independent listing sheets after the addresses

had been keyed. For the most part, the preliminary and

the keyed counts for each block cluster were identical, but

for some clusters there were differences. Using a preliminary count was necessary because the medium and large

cluster reduction had to be completed before the keying

of the independent listing sheets was done.

Third-phase sample. For the third phase of A.C.E. sampling, the block cluster measure of size was the housing

unit count resulting from the housing unit matching and

follow-up operation. This operation confirmed the count

resulting from the independent listing and removed any

nonexistent addresses from the sampling frame.

FIRST PHASE OF THE A.C.E. SAMPLE DESIGN

The sample selection during the first phase consisted of

three major steps:

1. Definition of the primary sampling units.

2. Stratification and allocation of the primary sampling

units within each state.

3. Selection of the primary sampling units within each

state.

Defining the Primary Sampling Unit

The Primary Sampling Units (PSUs) for the A.C.E. were

block clusters. The PSUs were delineated in such a way

that they encompass the entire land area of the United

States, except for extremely remote areas of Alaska. Each

block cluster consisted of a census block or several geographically contiguous census blocks. They contained an

average of 30 housing units. The land area for each PSU

was made reasonably compact so it could be traversed by

an interviewer in the field without incurring unreasonable

costs.

Design of the A.C.E. Sample Section I—Chapter 3 3–3

U.S. Census Bureau, Census 2000
Why the block cluster? A basic design decision, which

was a continuation from the 1990 Post-Enumeration Survey, was that the PSU would be a block cluster, a single

block or a group of adjacent blocks established for the

collection of Census 2000 information. These blocks may

be standard city blocks or irregularly shaped areas with

identifiable political or geographic boundaries. Using

block clusters as PSUs, instead of counties or county

groups that are more commonly used in national surveys,

improved the precision considerably with only a modest

increase in costs.

An alternative sample design was considered that would

have defined PSUs by segmenting whole blocks into

smaller components (roughly one-half of a block.) The

alternative design would likely have resulted in reduced

sampling error, but was rejected because it would increase

costs (primarily due to increased matching workloads and

interviewer travel) and probably would have resulted in

matching errors due to problems in identifying (spatially)

the PSU boundaries.

Goals of block clustering. Block clusters were formed

to meet both statistical and operational goals. In the Census 2000 Dress Rehearsal, a small census block was by

definition a single block cluster. This rule led to a large

number of small block clusters that could potentially exert

undue influence on the final population and variance estimates. One feature of block clustering under the Census

2000 A.C.E. procedure was to combine small census

blocks with adjacent census blocks, if the neighboring

block contained one or more housing units. This change in

the treatment of small census blocks had an enormous

impact on the number of small block clusters, which was

reduced by approximately 65 percent as seen in Table 3-2.

Still, many block clusters contained zero housing units.

Roughly 70 percent of the zero housing unit blocks

occurred in sparsely populated areas. Without populated

neighboring blocks, these zero housing unit blocks

remained stand-alone zero block clusters.

The two operational goals of forming block clusters were

to increase listing efficiency and to reduce the chance of

listing error. The first goal was met by collapsing census

blocks to produce block clusters that were geographically

compact and which averaged about 30 housing units, a

manageable workload. The second goal was to create

block clusters that were well defined to minimize the

chance that the cluster would be listed incorrectly. For

example, a listing error may result when a census block

has an invisible or nonphysical boundary such as city limits making it unclear where the block boundary was. As a

result, census blocks separated by invisible boundaries

were always combined.

Limitations. As mentioned earlier, the block cluster

measure of size for the first phase was based on preliminary census address counts. Some census operations that

helped build the census address list were not available at

the time block clustering started. Instead, a snapshot of

the best known information was used. This presented

some limitations with the data used for block clustering.

• Address limitations: The results of the Block Canvassing

and Local Update of Census Addresses (LUCA) operations were not incorporated into the census address list

in time for block clustering. Block Canvassing was a

Census 2000 field operation in mailout/mailback areas

(mostly city-style addresses). The Census Bureau sent

staff into the field to canvass their assignment areas

and provide updates to the address list such as corrections, adds, or deletes. Local Update of Census

Addresses was also a Census 2000 program that provided an opportunity for local and tribal governments to

review and update address information in the census

address list.

Table 3-2. Accuracy and Coverage Evaluation: Block Cluster Summary Statistics1

Preliminary number of housing units

0 - 2 3 - 79 80+ Total

Number of census blocks2 ........................ 2,969,000 4,009,000 245,000 7,223,000

Number of block clusters.......................... 1,029,000 2,486,000 252,000 3,767,000

Number of blocks per cluster3 . . . . . . . . . . . . . . . . . . . . . 1.3 2.2 1.5 1.9

Number of housing units per cluster . . . . . . . . . . . . . . . . 0.3 29.2 181.9 31.5

1

The United States and Puerto Rico are included in these summary statistics.

2

Count of census collection blocks before clustering and before block suffixing. Does not include water blocks or census

blocks in Remote Alaska. 3

These numbers are not the first row divided by the second row. They are the number of census blocks in each block cluster

size category divided by the number of block clusters in each category. For example, if two census blocks with 40 housing units

collapse to form an 80 housing unit block cluster, those two census blocks are counted in the 80+ category for the number of

blocks per cluster computation. Block clustering can combine across categories; therefore, the first and second rows are not

consistent.

3–4 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
• Geographic limitations: Each block in the census

address list had a Type of Enumeration Area (TEA)

assignment. For Census 2000, TEA is a classification

that identified both the census enumeration method and

the method used to compile the census address list. The

block clustering operation occurred concurrently with

the census review of TEA assignments to ensure the

most complete coverage of the area. This review process sometimes changed the TEA assignment of blocks

after the block cluster was defined. On a few occasions,

this resulted in a block cluster consisting of blocks that

had different methods for compiling the census address

list. For example, a block cluster consisted of three

blocks, and all three blocks had a TEA assignment of

‘‘Block Canvassing and Mailout/Mailback’’ at the time of

block clustering. After the census TEA review, one of

those blocks was converted to an ‘‘Address Listing and

Update/Leave’’ TEA assignment. For a complete list of

TEAs for Census 2000, see the attachment or visit

http://www.geo.census.gov/mob/homep/teas.html.

General rules for defining block clusters.

• Block clusters were formed by combining neighboring

Census 2000 blocks.

• Block clusters did not cross specific geographical

boundaries. Among these were county, interim census

tract, Local Census Office, TEA group, military area, and

American Indian Country. For ‘‘TEA groups,’’ blocks from

certain TEAs could be clustered together if the TEAs had

the same method for compiling the address list. American Indian Country refers, collectively, to lands that are

American Indian Reservation or other trust lands, tribal

jurisdiction statistical areas (now known as Oklahoma

Tribal Statistical Areas), tribal designated statistical

areas, and Alaska native village statistical areas.

• Blocks separated by an invisible boundary, a city line,

for example, were clustered except for the situations

described above.

• Whenever possible, small census blocks, those with

fewer than three housing units, were clustered with

neighboring census blocks containing housing units to

reduce the total number of small block clusters. If there

were no neighboring census block with housing units,

the small census block was a cluster by itself.

• To prevent block clusters from becoming too large with

respect to housing unit size, census blocks with 80 or

more housing units were generally not clustered with

other census blocks.

• In addition to the criteria of unit size, any block larger

than 15 square miles was generally a block cluster by

itself.

These rules produced 3.8 million block clusters, about half

the 7.2 million non-suffixed census blocks. The block clusters had an average of 29.2 housing units per medium

block cluster and an average of 31.5 overall. The number

of small block clusters also decreased from nearly three

million to about one million, an approximate 65 percent

reduction from the Census 2000 Dress Rehearsal rules of

defining a small block to be a cluster by itself. However,

since about 70 percent of small blocks occurred in less

populated areas with little or no population to combine,

many single zero-housing unit block clusters were formed.

Stratifying and Allocating the Primary Sampling

Units

Stratifying the first-phase sample. Prior to sampling,

block clusters were stratified according to the expected

number of housing units and the American Indian Reservation (AIR) status of the block cluster. The four sampling

strata and their definitions are presented in Table 3-3.

Allocating the first-phase sample. As stated earlier,

the Census Bureau was preparing to conduct the ICM, a

much larger coverage measurement survey of 750,000

housing units, when the use of sampling for apportionment counts was disallowed by the Supreme Court in

January, 1999. To keep the coverage measurement survey

on schedule, the Census Bureau went ahead with the plans

to select the ICM sample and create independent address

lists. This was followed by the subsampling of the firstphase sample to produce the A.C.E. sample design.

The first-phase sampling plan was a national sample of

30,000 block clusters: 25,000 medium and large block

clusters and 5,000 small block clusters. Included in the

25,000 block clusters was a separate sample of block

clusters for American Indian Reservations.

It is important to point out that the allocation of the

25,000 medium and large block clusters was dependent

on the ICM sample design and under the assumption of

roughly 30 housing units per block cluster. The allocation

of the 5,000 small block clusters to the states and the

separate American Indian Reservation sample to the states

was done prior to defining block clusters for all states,

since the first-phase sampling was done on a state-bystate flow-basis. This means that the first-phase sample

was selected for some states before the block clusters had

been defined for other states. As a result, we used the

best information we had at the time to carry out the

allocation.

Medium and large block clusters. The 25,000

medium and large block clusters were allocated to the

states to meet the ICM sample requirements (Schindler,

1998) with some minor modifications. Most states had

between 300 to 500 block clusters and the very largest

states had an allocation of between 1,000 and 2,000 block

clusters.

Design of the A.C.E. Sample Section I—Chapter 3 3–5

U.S. Census Bureau, Census 2000
Table 3-3. First-Phase Sampling Strata

First-phase sampling stratum Definition

Small 0 to 2 housing units

Medium 3 to 79 housing units

Large 80 or more housing units

American Indian Reservation 3 or more housing units and on American Indian Reservations

Within each state, the block cluster sample was proportionally allocated to the medium and large sampling strata

based on the number of housing units in the sampling

stratum:

cstate,k  Cstate 

Hstate,k

Hstate

where,

k = medium or large sampling stratum;

cstate,k = target number of clusters in sampling

stratum k within state;

Cstate = target number of A.C.E. first-phase

medium and large sample clusters for

state;

Hstate,k = number of housing units in sampling stratum k within state;

Hstate = number of housing units in the medium

and large strata in state.

As an example, let’s say that 402 total medium and large

block clusters were allocated to a particular state. Assuming that there are an expected 9,000 housing units in all

clusters in the medium sampling stratum and 12,060

housing units in both the medium and large sampling

strata, the target number of clusters from the medium

sampling stratum for the state is calculated as follows:

Cstate, medium  402 

9,000

12,060  300.

The target number of clusters from the large sampling

stratum would then be 102.

Small block clusters. Because of cost considerations,

small block clusters were generally sampled at a lower

rate than either medium or large clusters. An overall allocation of 5,000 small block clusters was chosen because a

total of 30,000 block clusters was deemed manageable for

creating independent address lists. The high weights

resulting from the lower sampling rates were not expected

to have a serious impact on the estimates or variances for

most clusters selected from the small block cluster sampling stratum. However, for clusters that were initially

classified as small, but were observed to have a larger

number of housing units, there was concern about high

sampling weights disproportionately contributing to variance. In an attempt to avoid the problems associated with

the high weights, a larger number of small clusters was

initially selected, followed by an independent address list,

followed by a subsample to remain in sample. Using

updated measures of size for those 5,000 small block

clusters in the small cluster reduction helped to target

clusters that could have contributed disproportionately to

the variance. These initial 5,000 small clusters were allocated to states proportionately to their estimated total

number of housing units in small blocks.

Ideally, we would have allocated the 5,000 block clusters

proportionally to states based on the number of small

block clusters in the state. This was not possible because

the first-phase sampling was done on a flow basis.

American Indian Reservation block clusters. To

ensure sufficient sample for calculating reliable coverage

estimates for American Indians living on reservations, we

allocated 355 block clusters to American Indian Reservations nationwide. The 355 clusters were allocated to 26

states proportional to the 1990 population of American

Indians living on reservations. Small block clusters on

American Indian Reservations were not included in these

355 block clusters. These clusters were eligible for selection in the small cluster stratum. Block clusters within

states containing little or no American Indian population

on reservations were represented in the medium and large

strata.

This sample allocation resulted in variable first-phase

selection probabilities across the states despite our goal of

having proportional allocation of the American Indian Reservation (AIR) sample. This occurred because the average

number of housing units per American Indian Reservation

block cluster varied across states. To get similar firstphase selection probabilities, we needed to have all of the

block clustering completed before allocating the sample.

However, the first-phase sampling was done on a flow

basis.

3–6 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
Selecting the Primary Sampling Units Within Each

State

Calculation of the sampling parameters. The block

cluster probability of selection (PS) for each of the four

sampling strata in each state is the ratio of the target

sample size to the number of clusters in the stratum. It

takes the following form:

PSstate,k  cstate,k L state

Cstate,k

,

where,

PSstate,k = probability of selection (sampling rate) in

sampling stratum k within state;

Cstate,k = number of clusters in sampling stratum k

within state;

cstate,k = target number of clusters in sampling stratum k within state;

Lstate = the factor to reduce the number of clusters

to select for the state, if the expected listing

workload exceeded the planning estimate.

L state  { 1 for small, medium and AIR sampling stratum

0< L  1 for large sampling stratum

The large block cluster sampling rate was reduced if the

expected number of housing units to list was greater than

the planning estimate of the listing workload. A second

step of sampling was necessary in Missouri and Indiana

because the selected sample of clusters resulted in a

greater number of housing units to list than was expected.

To meet operational constraints, a subsample of the firststep selected block clusters was selected. The second step

of sampling only occurred in the large sampling stratum,

since that stratum disproportionately contributed to the

listing workload. The second step occurred only if the estimated number of housing units in the medium and large

strata was at least ten percent larger than the planning

estimate of the number of housing units to be listed.

For states needing the second step of sampling, the sampling rate took the following form:

PS2state  PWstate

Wstate

where,

PS2state = second-step sampling rate for the large

sampling stratum in state,

Wstate = resulting workload estimate from sample

selection for the large sampling stratum

in state,

PWstate = planning workload estimate for the large

sampling stratum in state.

Sorting the PSUs. The first-phase clusters were sorted

within each sampling stratum as follows:

• American Indian Country Indicator

• Demographic/Tenure Group

• 1990 Urbanization

• County code

• Block cluster identification number

Although there was no differential sampling within the

four first-phase sampling strata, the clusters were sorted

by several variables in an attempt to improve the representativeness of the sample of block clusters. The first

variable was the American Indian Country Indicator, which

separated the block clusters into three American Indian

categories:

1. American Indian Reservation or other trust land,

2. tribal jurisdiction statistical area, Alaska native village

statistical area or tribal designated statistical area, and

3. all other areas.

The second sort variable was the demographic/tenure

group. Block clusters containing similar demographic/

tenure proportions, based on 1990 census data, were

grouped. To aid in selecting a sample that was well represented by the six major race/origin groups, as well as

owners and renters, block clusters were classified into 12

demographic/tenure groups. Although many block clusters tend to have a large proportion of one demographic/

tenure group, rarely were they entirely composed of only

one, thus many clusters fit well in two or more categories.

To ensure that each cluster was assigned to only one

group, a hierarchical assignment rule was developed so

that when a cluster exceeded the first group threshold, it

was assigned to that group. These thresholds were based

on a multivariate clustering method applied to 1990 census blocks. Table 3-4 lists these threshold values. The hierarchy gives the smaller demographic groups priority over

the larger ones and renters priority over owners. For

example, if the approximate distribution of a block cluster

population was 20 percent Asian Renter, 40 percent Asian

Owner, and 40 percent White and other Renter, then the

block cluster was assigned to the Asian Renter

demographic/tenure group.

Design of the A.C.E. Sample Section I—Chapter 3 3–7

U.S. Census Bureau, Census 2000
Table 3-4. Demographic/Tenure Group

Thresholds (50 States and the

District of Columbia)

Order Demographic/Tenure Group Threshold

1 Hawaiian and Pacific Islander renters 10%

2 Hawaiian and Pacific Islander owners 10%

3 American Indian and Alaska Native renters 10%

4 American Indian and Alaska Native owners 10%

5 Asian renters 20%

6 Asian owners 20%

7 Hispanic renters 20%

8 Hispanic owners 20%

9 Black renters 25%

10 Black owners 25%

11 White and other renters 30%

12 All others all others

A third sort variable was the estimated level of urbanization based on 1990 data for each block cluster. Each block

cluster was categorized either as an urbanized area with

250,000 or more people, an urbanized area with less than

250,000 people, or a non-urban area. And finally, the clusters were sorted geographically using county and cluster

number.

General sampling procedure. A systematic sample of

block clusters was selected from each sampling stratum

with each block cluster having the same probability of

selection within a sampling stratum. The method used to

select systematic samples follows:

1. Sampling units were sorted using the PSU sort criteria

described at each sampling phase.

2. Each successive PSU was assigned an index number 1

through N within each sampling stratum where N is

the number of PSUs in the stratum.

3. A random number (RN) between zero and one,

0 < RN ≤ 1, was generated.

4. A random start (RS) for the sampling stratum was calculated. The random start was the random number

multiplied by the inverse of the probability of selection, RS = RN 1/PS, such that 0 < RS ≤ 1/PS.

5. Sampling sequence numbers were calculated. Given N

PSUs, sequence numbers were:

RS, RS + 1 (1/PS), RS + 2 × (1/PS),...,RS + n (1/PS)

where n was the largest integer such that

[RS + (n-1) 1/PS] ≤ N. Sequence numbers were

rounded up to the next integer. An integer

number rounded to itself.

6. Sampling sequence numbers were compared to the

index numbers assigned to PSUs. The PSU with the

index number corresponding to the rounded sequence

number was selected. All PSUs without corresponding

index numbers were not in sample.

First-Phase Sample Results

Table 3-5 lists the block cluster sample sizes and the number of housing units by sampling stratum for each state,

the District of Columbia, and the nation.

3–8 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
Table 3-5. State First-Phase Sample Results by First-Phase Stratum

State

First-phase housing units1 First-phase block clusters

Small Medium Large AIR Total Small Medium Large AIR Total

Alabama . . . . . . . . . . . . . . . . . . . . . . 60 7,900 19,000 0 26,960 116 286 109 0 511

Alaska . . . . . . . . . . . . . . . . . . . . . . . . 20 5,200 23,200 20 28,440 20 190 137 1 348

Arizona . . . . . . . . . . . . . . . . . . . . . . . 20 7,800 44,700 2,600 55,120 86 269 180 113 648

Arkansas . . . . . . . . . . . . . . . . . . . . . 40 9,600 15,900 0 25,540 90 353 101 0 544

California . . . . . . . . . . . . . . . . . . . . . 50 45,000 227,600 230 272,880 184 1,442 1,311 11 2,948

Colorado . . . . . . . . . . . . . . . . . . . . . . 20 8,000 25,600 60 33,680 83 293 157 2 535

Connecticut . . . . . . . . . . . . . . . . . . . 10 6,100 25,600 0 31,710 20 211 159 0 390

Delaware . . . . . . . . . . . . . . . . . . . . . 20 7,200 28,700 0 35,920 20 243 156 0 419

District of Columbia . . . . . . . . . . . . 10 4,800 50,500 0 55,310 20 132 247 0 399

Florida . . . . . . . . . . . . . . . . . . . . . . . . 50 7,500 50,100 30 57,680 145 259 230 1 635

Georgia . . . . . . . . . . . . . . . . . . . . . . . 70 6,100 30,300 0 36,470 154 220 162 0 536

Hawaii . . . . . . . . . . . . . . . . . . . . . . . . 10 3,000 42,400 0 45,410 20 103 161 0 284

Idaho . . . . . . . . . . . . . . . . . . . . . . . . . 10 8,200 10,900 140 19,250 54 312 75 6 447

Illinois . . . . . . . . . . . . . . . . . . . . . . . . 100 8,600 22,300 0 31,000 185 281 140 0 606

Indiana . . . . . . . . . . . . . . . . . . . . . . . 80 6,100 9,700 0 15,880 140 202 51 0 393

Iowa . . . . . . . . . . . . . . . . . . . . . . . . . 120 6,800 9,500 0 16,420 147 242 53 0 442

Kansas . . . . . . . . . . . . . . . . . . . . . . . 110 6,400 11,100 30 17,640 193 237 63 1 494

Kentucky . . . . . . . . . . . . . . . . . . . . . 60 7,200 22,300 0 29,560 96 268 135 0 499

Louisiana . . . . . . . . . . . . . . . . . . . . . 10 11,300 24,900 0 36,210 65 407 155 0 627

Maine . . . . . . . . . . . . . . . . . . . . . . . . 20 5,800 11,000 10 16,830 38 226 79 1 344

Maryland . . . . . . . . . . . . . . . . . . . . . 20 5,300 38,000 0 43,320 36 177 175 0 388

Massachusetts . . . . . . . . . . . . . . . . 20 6,400 22,000 0 28,420 38 229 140 0 407

Michigan . . . . . . . . . . . . . . . . . . . . . . 50 7,900 15,100 150 23,200 122 268 104 5 499

Minnesota . . . . . . . . . . . . . . . . . . . . 70 6,000 14,000 270 20,340 141 208 83 10 442

Mississippi . . . . . . . . . . . . . . . . . . . . 40 8,400 11,700 120 20,260 81 303 77 3 464

Missouri . . . . . . . . . . . . . . . . . . . . . . 110 5,700 14,500 0 20,310 162 200 71 0 433

Montana . . . . . . . . . . . . . . . . . . . . . . 10 8,400 9,700 840 18,950 67 333 67 24 491

Nebraska . . . . . . . . . . . . . . . . . . . . . 80 6,800 7,700 70 14,650 142 245 55 3 445

Nevada . . . . . . . . . . . . . . . . . . . . . . . 10 6,400 57,800 190 64,400 46 225 230 5 506

New Hampshire . . . . . . . . . . . . . . . 20 5,700 15,400 0 21,120 25 201 106 0 332

New Jersey . . . . . . . . . . . . . . . . . . . 10 8,700 30,100 0 38,810 39 282 178 0 499

New Mexico . . . . . . . . . . . . . . . . . . . 10 9,300 24,800 1,640 35,750 108 335 136 70 649

New York . . . . . . . . . . . . . . . . . . . . . 80 17,600 124,700 70 142,450 143 603 631 5 1,382

North Carolina . . . . . . . . . . . . . . . . . 100 6,700 20,700 80 27,580 143 236 121 4 504

North Dakota . . . . . . . . . . . . . . . . . . 100 5,900 9,100 340 15,440 121 236 64 12 433

Ohio . . . . . . . . . . . . . . . . . . . . . . . . . 110 7,800 24,000 0 31,910 132 268 133 0 533

Oklahoma . . . . . . . . . . . . . . . . . . . . . 60 9,000 17,300 270 26,630 142 314 101 8 565

Oregon . . . . . . . . . . . . . . . . . . . . . . . 10 5,200 15,400 70 20,680 86 195 90 3 374

Pennsylvania . . . . . . . . . . . . . . . . . . 110 12,900 22,600 0 35,610 180 427 146 0 753

Rhode Island . . . . . . . . . . . . . . . . . . 10 7,600 18,000 0 25,610 20 256 108 0 384

South Carolina . . . . . . . . . . . . . . . . 40 8,200 19,100 0 27,340 95 285 112 0 492

South Dakota . . . . . . . . . . . . . . . . . 50 5,800 9,200 450 15,500 106 242 57 27 432

Tennessee . . . . . . . . . . . . . . . . . . . . 90 7,800 25,400 0 33,290 133 285 137 0 555

Texas . . . . . . . . . . . . . . . . . . . . . . . . 70 34,700 148,500 30 183,300 349 1,222 681 1 2,253

Utah . . . . . . . . . . . . . . . . . . . . . . . . . 10 9,100 23,900 120 33,130 38 312 144 7 501

Vermont . . . . . . . . . . . . . . . . . . . . . . 20 5,600 12,000 0 17,620 21 201 88 0 310

Virginia . . . . . . . . . . . . . . . . . . . . . . . 60 5,600 31,900 0 37,560 98 96 166 0 460

Washington . . . . . . . . . . . . . . . . . . . 20 5,600 21,400 480 27,500 73 187 120 17 397

West Virginia . . . . . . . . . . . . . . . . . . 30 5,000 13,100 0 18,130 46 189 79 0 314

Wisconsin . . . . . . . . . . . . . . . . . . . . . 80 6,200 8,200 220 14,700 119 211 58 10 398

Wyoming . . . . . . . . . . . . . . . . . . . . . 10 8,700 9,200 90 18,000 72 346 69 5 492

Total U.S. ..................... 2,400 438,600 1,539,800 8,620 1,989,420 5,000 15,393 8,388 355 29,136

1

Preliminary census address list housing unit counts from spring 1999.

SECOND PHASE OF THE A.C.E. SAMPLE DESIGN

The second phase, often referred to as the A.C.E. reduction phase, linked the first-phase sample selection to the

A.C.E. sampling plan. The A.C.E. reduction was the first of

several operations that reduced the number of housing

units from the nearly two million housing units in the

independent listing to the approximately 300,000 housing

units that were sent for interview. Since not all of the firstphase block clusters were required for A.C.E., the reduction subsampled those clusters, with the selected clusters

retained for the A.C.E. operations.

Following the selection of the A.C.E. first-phase sample,

field staff visited the block clusters and created an independent address list for A.C.E. These updated housing

Design of the A.C.E. Sample Section I—Chapter 3 3–9

U.S. Census Bureau, Census 2000
unit counts were used in the cluster subsampling phase.

The cluster subsampling was done separately for:

• medium and large cluster reduction, and

• small block cluster reduction.

Medium and Large Cluster Reduction

The medium and large cluster reduction was the transition

to the A.C.E. sampling plan. The resulting national sample

allocation was roughly proportional to state population

with some differential sampling within states. Only block

clusters from the medium and large first-phase sampling

strata in the 50 states and the District of Columbia were

subsampled in this phase. As part of the sample reduction, two other objectives of the A.C.E. sample were implemented.

One objective of the medium and large cluster reduction

design was to stratify the first-phase clusters based on the

relationship of current housing unit counts from the A.C.E.

independent listing and the updated census address list as

of January, 2000. Clusters were sampled with different

selection probabilities in order to reduce the variance contribution due to inconsistent housing unit counts between

the updated census list and the independent list. Clusters

with significant differences between the counts were

expected to have high erroneous enumeration and high

omission rates. The objective of differentially sampling

these types of clusters was to reduce the sampling

weights associated with clusters having relatively high

numbers of missed persons or those enumerated in error,

and, thus, having potentially high variance contributions.

A second objective of the medium and large cluster reduction design was to differentially sample clusters based on

the estimated demographic composition of the cluster.

Clusters with a high proportion of persons of Hispanic origin or persons belonging to a census race group other

than White were classified into a minority stratum. These

types of clusters were sampled at a higher rate than predominantly non-Hispanic White clusters, in order to

increase the sample size and improve the reliability of the

A.C.E. population estimates for these historically undercounted subgroups.

Stratifying second-phase clusters. Each block cluster

was put into two categories for the medium and large

cluster reduction: a demographic group and a consistency

group. Block clusters were put into reduction strata based

on the combination of these two groups.

Demographic groups were based on the demographic/

tenure groups created in the first-phase sample selection.

The demographic/tenure groups represented a classification of block clusters, using the information of race/

Hispanic origin and tenure of each block reported in the

1990 census. The demographic/tenure groups were used

as a sort variable in the selection of the first-phase

sample. For this reduction, clusters were put into two

demographic groups by combining the 12 demographic/

tenure groups in Table 3-4. The two demographic groups

are:

1. Minority: block clusters from one of the ten minority

demographic/tenure groups

2. Non-minority: block clusters from one of the two

other demographic/tenure groups

For this reduction, two updated cluster housing unit

counts were used: the independent listing housing unit

count and the housing unit count from the updated census

address list as of January 2000. The two housing unit

counts were compared, and clusters were placed into consistency groups based on the relationship of the housing

unit counts. Large differences between the counts indicated that coverage problems might occur; thus, the sampling weights for such clusters were controlled to avoid

serious variance effects.

Clusters were placed into three consistency groups as

shown in Table 3-6.

Table 3-6. Second-Phase Sampling Consistency

Groups

Relationship Consistency group

Independent list is at least 25 percent lower than

census . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Low inconsistent

Independent list is at least 25 percent greater than

census ...................................... High inconsistent

Independent list is within ± 25 percent of census . . Consistent

For List/Enumerate clusters (see attachment), the

census housing unit count was not known at the time

of the reduction since this census operation had not

started. Thus, all such clusters were classified as high

inconsistent.

3–10 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
Based on the demographic group, the consistency group,

and the independent listing housing unit count, block

clusters were assigned to one of five reduction strata:

1. Minority (low inconsistent, high inconsistent,

consistent)

2. Non-minority low inconsistent

3. Non-minority high inconsistent

4. Non-minority consistent

5. Medium stratum jumper

Medium stratum jumper clusters were selected from the

medium sampling stratum for the first-phase sample, but

had 80 or more independent listing housing units.

Medium clusters were sampled at lower rates than large

clusters in the first-phase sample since large clusters

eventually were to undergo within-cluster housing unit

subsampling, an operation that increases sampling

weights. Medium stratum jumper clusters also went

through within-cluster housing unit subsampling, meaning

the already higher sampling weights of these clusters

became even larger. Retaining all of the medium stratum

jumper clusters in this reduction avoided introducing significant weight variation in the sample.

Allocating sample to strata. The first step was to allocate the national sample of 300,000 housing units to the

50 states and the District of Columbia, in most cases proportional to 1998 population estimates, with a minimum

of 1,800 housing units in each state. Hawaii was allocated

approximately 3,750 housing units due to its concentration of Hawaiian and Pacific Islanders for which separate

population coverage estimates were planned.

Within each state, the second-phase selection probabilities

varied somewhat among the strata. First, all clusters in the

medium stratum jumper reduction stratum were retained.

For the remaining four reduction strata, higher retention

rates were used in the minority, non-minority low inconsistent and the non-minority high inconsistent reduction

strata than the non-minority consistent stratum. The stratum differential sampling factor is the ratio of the probability of selection for the stratum to the probability of

selection for the consistent stratum.

The following statements describe how the stratum differential sampling factors were set to yield the overall state

sample size. These are not exact rules, but give a sense of

how much differential sampling within states was done.

• The maximum expected sampling weight after all subsampling, the inverse of the overall probability of selection, was 650 for the non-minority consistent reduction

stratum.

• The maximum differential sampling factor was 3 for the

two inconsistent reduction strata.

• The differential sampling factor was around 2 for the

minority reduction stratum, except in small states

where all of the minority clusters were retained.

The differential sampling factors were assigned using

guidelines designed to achieve the two objectives of the

reduction, while also controlling the size of the sampling

weights and the amount of differential sampling. This led

to the design of the differential sampling factors summarized in Table 3-7.

Using the stratum differential sampling factors and the

estimated number of housing units, the sample allocation

for each reduction stratum was derived as follows:

Tg  T 

DSFg H

ˆ

g



g  1

4

DSFg H

ˆ

g

where,

g = A.C.E. second-phase sampling stratum,

Tg = Target number of sample housing units

allocated to reduction stratum g,

T = State target number of sample housing

units modified for medium stratum jumper

clusters,

H

ˆ

g = Estimated number of housing units in the

reduction stratum based on the independent listing housing unit counts, and

DSFg = Differential Sampling Factor for reduction

stratum g.

Design of the A.C.E. Sample Section I—Chapter 3 3–11

U.S. Census Bureau, Census 2000
Table 3-7. A.C.E. Second-Phase Sample Design Parameters for Large and Medium Clusters

State

Differential Sampling Factors1

Target

sample

size6

First-phase

sample

size Minority2 7

Low

inconsistent3

High

inconsistent4 Consistent5

Alabama .................................... 1.78 1.78 1.78 1.00 4,470 26,960

Alaska ...................................... 6.20 3.00 3.00 1.00 1,800 28,440

Arizona ..................................... 1.78 1.78 1.78 1.00 4,800 55,120

Arkansas . . . ................................ 2.00 3.00 3.00 1.00 2,610 25,540

California ................................... 2.00 3.00 3.00 1.00 33,510 272,880

Colorado . . ................................. 1.99 2.93 2.93 1.00 4,080 33,680

Connecticut ................................. 2.00 3.00 3.00 1.00 3,360 31,710

Delaware ................................... 2.91 3.00 3.00 1.00 1,800 35,920

District of Columbia . . ........................ 2.00 3.00 3.00 1.00 1,800 55,310

Florida ..................................... 1.00 1.00 1.00 1.00 15,300 57,680

Georgia .................................... 2.01 2.01 2.01 1.00 7,830 63,470

Hawaii ...................................... 2.00 3.00 3.00 1.00 3,750 45,410

Idaho ....................................... 2.71 3.00 3.00 1.00 1,800 19,250

Illinois . ..................................... 1.19 1.19 1.19 1.00 12,360 31,000

Indiana ..................................... 1.68 1.68 1.68 1.00 6,060 15,880

Iowa . . ..................................... 2.00 3.00 3.00 1.00 2,940 16,420

Kansas . .................................... 2.00 3.00 3.00 1.00 2,700 17,640

Kentucky ................................... 2.00 3.00 3.00 1.00 4,050 29,560

Louisiana ................................... 1.89 3.00 3.00 1.00 4,470 36,210

Maine ...................................... 6.55 3.00 3.00 1.00 1,800 16,830

Maryland . . ................................. 1.87 2.46 2.46 1.00 5,280 43,320

Massachusetts .............................. 2.33 2.33 2.33 1.00 6,300 28,420

Michigan .................................... 1.25 1.25 1.25 1.00 10,080 23,200

Minnesota . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11 2.11 2.11 1.00 4,860 20,340

Mississippi .................................. 1.96 2.83 2.83 1.00 2,820 20,260

Missouri .................................... 2.25 2.25 2.25 1.00 5,580 20,310

Montana . . .................................. 1.57 3.00 3.00 1.00 1,800 18,950

Nebraska ................................... 2.44 3.00 3.00 1.00 1,800 14,650

Nevada ..................................... 1.95 2.76 2.76 1.00 1,800 64,400

New Hampshire . ............................ 6.84 3.00 3.00 1.00 1,800 21,120

New Jersey ................................. 2.24 2.24 2.24 1.00 8,340 38,810

New Mexico ................................. 1.73 1.73 1.73 1.00 1,800 35,750

New York . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.00 3.00 3.00 1.00 18,660 142,450

North Carolina ............................... 1.83 1.83 1.83 1.00 7,740 27,580

North Dakota ................................ 2.14 3.00 3.00 1.00 1,800 15,440

Ohio . . ..................................... 1.22 1.22 1.22 1.00 11,490 31,910

Oklahoma .................................. 2.00 3.00 3.00 1.00 3,420 26,630

Oregon ..................................... 1.94 2.76 2.76 1.00 3,360 20,680

Pennsylvania . . .............................. 1.70 1.70 1.70 1.00 12,300 35,610

Rhode Island . . .............................. 2.94 3.00 3.00 1.00 1,800 25,610

South Carolina .............................. 1.60 1.60 1.60 1.00 3,930 27,340

South Dakota ............................... 1.83 3.00 3.00 1.00 1,800 15,500

Tennessee .................................. 1.99 2.86 2.86 1.00 5,580 33,290

Texas . ..................................... 1.86 2.36 2.36 1.00 20,280 183,300

Utah . . ..................................... 2.00 3.00 3.00 1.00 2,160 33,130

Vermont .................................... 6.91 3.00 3.00 1.00 1,800 17,620

Virginia . . . .................................. 1.90 1.90 1.90 1.00 6,960 37,560

Washington ................................. 2.23 2.23 2.23 1.00 5,850 27,500

West Virginia ................................ 2.00 3.00 3.00 1.00 1,860 18,130

Wisconsin .................................. 1.75 1.75 1.75 1.00 5,370 14,700

Wyoming . . . ................................ 1.99 3.00 3.00 1.00 1,800 18,000

1

The observed or actual sampling factors differed from the design sample rates. See the section on ‘‘Selecting a subsample.’’

2

Clusters with high concentrations of minorities.

3

Clusters where the independent listing housing unit count is at least 25 percent lower than the updated census list count.

4

Clusters where the independent listing count is at least 25 percent higher than the updated census list.

5

Clusters where the independent listing count and the updated census list do not differ by more than 25 percent.

6

Target state housing unit interview sample size, excluding American Indian Reservation sample.

7

First-phase preliminary census address list housing unit counts from Spring, 1999.

3–12 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
Sorting the PSUs. The first-phase clusters within each

second-phase stratum by first-phase sampling stratum

were sorted as follows:

• Consistency group

• List/Enumerate indicator

• American Indian Country Indicator

• Demographic/Tenure Group

• 1990 Urbanization

• County code

• Block cluster identification number

Selecting a subsample. Since the first-phase sample

utilized different sampling rates for the medium and large

sampling strata, separate samples were drawn for each

second-phase stratum within the first-phase sampling

strata. Selecting the sample required calculating the sampling rates, sorting the clusters, and drawing a systematic

sample of clusters.

All of the medium stratum jumpers were retained in the

sample. The sampling rates for the remaining four reduction strata were computed so that an integer number of

block clusters was selected. This required computing a

sampling rate based on the ratio of housing units which

resulted in a non-integer expected number of clusters,

determining an integer number of clusters to select, and

calculating the final sampling rate based on the ratio of

clusters. The medium and large cluster reduction followed

the sampling procedure discussed earlier.

This resulted in a total of 9,765 out of 24,136 medium

and large clusters retained in the A.C.E. sample for the 50

states and the District of Columbia.

Medium and large cluster reduction sample results.

Table 3-8 lists the number of housing units and clusters in

sample.

Small Cluster Reduction

The first-phase sample contained 5,000 small clusters in

the United States. Small clusters were expected to have

between zero and two housing units based on an early

census address list. Conducting interviewing and

follow-up operations in clusters of this size was not as

cost effective as in larger clusters. Therefore, to allocate

A.C.E. resources more efficiently, only a subsample of

these small clusters was retained in the A.C.E. sample.

This subsampling operation attempted a balance among

three goals. One goal was to prevent any small clusters

from having sampling weights that were extremely high

compared to other clusters in the sample. Second, sampling weights should be lower on clusters where the number of housing units was different than expected. These

first two goals attempted to reduce the contribution of

small clusters to the variance of the dual system estimates. The third goal was to improve operational efficiency by reducing the number of clusters and future field

visits. To achieve these goals, differential sampling was

used.

Stratifying first-phase clusters. The first-phase small

clusters were classified into nine possible reduction strata

within each state. These strata were defined using three

cluster characteristics: Size, American Indian Country status, and List/Enumerate status.

The size of a cluster was based on the greater of the independent listing housing unit count or the updated census

address list housing unit count as of January 2000. For

List/Enumerate clusters the size was always based on the

actual independent listing count since the List/Enumerate

operation had not yet started by the time of this reduction. The American Indian Country status had three categories as described in the first-phase of sampling.

Table 3-9 contains the reduction strata for small block

clusters.

Table 3-8. Second-Phase Results−Medium and Large Block Cluster and Housing Unit Counts

Number of....

Minority

Low

inconsistent

High

inconsistent Consistent

Stratum

jumpers

American

Indian

reservations Nation

Housing units1 .......................... 230,529 49,086 94,850 403,806 32,064 9,251 819,586

Clusters . . . ............................. 2,553 971 842 4,801 243 355 9,765

1

Independent Listing counts as of December, 1999.

Design of the A.C.E. Sample Section I—Chapter 3 3–13

U.S. Census Bureau, Census 2000
Table 3-9. Small Block Cluster Second-Phase Strata

Second-phase

stratum

Housing

units

American

Indian country

List/Enumerate

status

1 0 to 2 No No

2 3 to 5 No No

3 6 to 9 No No

4 10+ - -

5 0 to 2 No Yes

6 3 to 9 No Yes

7 0 to 9 Reservation/Trust land -

8 0 to 2 TJSA/TDSA/ANVSA1 -

9 3 to 9 TJSA/TDSA/ANVSA -

1

Tribal Jurisdiction Statistical Area/Tribal Designated Statistical Area/Alaska Native Village Statistical Area

Determining target sampling rates. Using independent listing housing unit counts, target sampling rates

were determined. These rates attempted to satisfy the previously discussed statistical and operational goals.

Generally, the small clusters were stratified into four

groups based on the number of housing units in the cluster. All clusters with ten or more housing units, on American Indian land, or classified as List/Enumerate were

retained in sample. For the remaining three reduction

strata, some differential sampling was introduced.

To determine the sampling rates for these strata, two conditions were imposed. One of these conditions was that, if

possible, the number of weighted housing units in a cluster did not exceed 2,400 housing units. Through computer simulations, a number of different limits were tried

until a cap of 2,400 yielded a sample of appropriate size.

The second condition was a minimum sampling rate,

which varied among the three strata. Table 3-10 contains a

summary of the sampling conditions. Table 3-11 illustrates

the process for determining the second-phase sampling

rate for each stratum.

The overall target selection probability was based on the

maximum number of housing units within a stratum and

the previously mentioned cap of 2,400 housing units. For

example, the maximum number of housing units in stratum group one was two. Hence, the overall target selection probability was 1 in (2,400/2) or 1 in 1,200. The sampling rate for each second-phase stratum was then set at

the rate required to attain these overall target probabilities

of selection.

Sorting the PSUs. The first-phase clusters were sorted

in the following order in each second-phase stratum:

• 1990 urbanization

• county code

• A.C.E. cluster identification number

Table 3-10. Small Cluster Reduction Sampling Conditions

Second-phase

stratum

Cluster

size (HUs)

Overall target

selection probability

Minimum second-phase

sampling rate

1 0 to 2 1/1,200 1/10

2 3 to 5 1/480 1/4

3 6 to 9 1/267 1/2.22

Table 3-11. Second-Phase Sampling Rate Criterion

If . . . Then, the second-phase sampling rate equals...

Overall target selection probability ≥ Minimum second-phase sampling rate First-phase sampling rate

Overall target selection probability

First-phase sampling rate

Overall target selection probability < Minimum second-phase sampling rate First-phase sampling rate

Minimum second-phase sampling rate

3–14 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
Selecting a subsample. Separate samples were selected

from each second-phase stratum within each state and the

District of Columbia. This required calculating the actual

sampling rate for the stratum, sorting the clusters and

drawing a systematic sample of clusters.

All clusters with 10 or more housing units that were classified as List/Enumerate, or were in American Indian Country, were retained in sample. The sampling rates for the

remaining three strata were computed to achieve an integer number of block clusters drawn from each stratum,

similar to procedures used for the medium and large cluster reduction. This required computing a sampling rate,

which resulted in a noninteger expected number of clusters determining an integer number of clusters to select,

and calculating the final sampling rate based on the ratio

of clusters. The small cluster reduction followed the sampling procedure discussed earlier.

This resulted in a total of 1,538 out of 5,000 small clusters retained in the A.C.E. sample for the 50 states and the

District of Columbia.

Small cluster reduction results. Table 3-12 gives the

distribution of block clusters and housing units after small

block cluster reduction. As mentioned earlier, the larger of

the independent listing housing unit count and the housing unit count from the updated census address list as of

January 2000 was used to stratify the clusters. In Table

3-12, only the independent listing housing unit count is

used in these tallies. Hence, with 55 clusters, as seen in

the ‘‘6-9’’ cluster size, the number of housing units does

not achieve the minimum of 330.

Second-Phase Sampling Results

Table 3-13 lists the block cluster sample sizes and

the number of housing units in each state, the

District of Columbia, and the nation after the second

phase of A.C.E. sampling.

Table 3-12. Second-Phase Results—Small Block Cluster and Housing Unit Counts

Cluster size

(HUs)1

American Indian

country

List/enumerate

status

Number of

housing units2

Number of

clusters

0-2 No No 209 692

3-5 No No 358 117

6-9 No No 325 55

10+ - - 4,532 112

0-2 No Yes 59 290

3-9 No Yes 76 16

0-9 Reservation/Trust land - 43 128

0-2 TJSA/TDSA/ANVSA3 - 40 121

3-9 TJSA/TDSA/ANVSA - 30 7

Total 5,672 1,538

1

The size of a cluster was based on the higher of the independent listing housing unit count or the January, 2000 census address list. For

List/Enumerate clusters the size was always based on the actual independent listing count since the List/Enumerate operation had not yet been

started by the time of this reduction. 2

Keyed independent listing housing unit counts as of January, 2000.

3

Tribal Jurisdiction Statistical Area/Tribal Designated Statistical Area/Alaska Native Village Statistical Area.

Design of the A.C.E. Sample Section I—Chapter 3 3–15

U.S. Census Bureau, Census 2000
Table 3-13. State Second-Phase Sample Results by First-Phase Stratum

State

Second-phase housing units1 Second-phase block clusters

Small Medium Large AIR Total Small Medium Large AIR Total

Alabama . . . . . . . . . . . . . . . . . . . . . . 54 3,599 7,531 0 11,184 14 104 43 0 161

Alaska . . . . . . . . . . . . . . . . . . . . . . . . 24 1,401 3,099 16 4,540 7 40 22 1 70

Arizona . . . . . . . . . . . . . . . . . . . . . . . 140 3,082 17,185 2,826 23,233 69 79 61 113 322

Arkansas . . . . . . . . . . . . . . . . . . . . . 16 2,077 3,566 0 5,659 13 71 24 0 108

California . . . . . . . . . . . . . . . . . . . . . 401 19,124 77,913 204 97,642 93 528 469 11 1,101

Colorado . . . . . . . . . . . . . . . . . . . . . . 19 2,722 9,248 52 12,041 24 85 55 2 166

Connecticut . . . . . . . . . . . . . . . . . . . 37 1,699 6,718 0 8,454 5 59 47 0 111

Delaware . .................... 7 1,572 2,979 0 4,558 3 40 23 0 66

District of Columbia ............ 0 1,251 5,403 0 6,654 2 25 31 0 58

Florida . . . . . . . . . . . . . . . . . . . . . . . . 265 7,976 54,986 20 63,247 43 259 230 1 533

Georgia . . . . . . . . . . . . . . . . . . . . . . . 211 4,095 21,195 0 25,501 27 138 111 0 276

Hawaii . . . . . . . . . . . . . . . . . . . . . . . . 11 1,200 22,252 0 23,463 6 40 75 0 121

Idaho . . . . . . . . . . . . . . . . . . . . . . . . . 12 1,632 2,714 152 4,510 32 53 16 6 107

Illinois . . . . . . . . . . . . . . . . . . . . . . . . 51 7,527 20,041 0 27,619 25 247 131 0 403

Indiana . . . . . . . . . . . . . . . . . . . . . . . 125 4,141 7,431 0 11,697 24 141 46 0 211

Iowa . . . . . . . . . . . . . . . . . . . . . . . . . 161 2,338 3,705 0 6,204 21 79 22 0 122

Kansas . . . . . . . . . . . . . . . . . . . . . . . 33 2,193 3,488 31 5,745 24 70 22 1 117

Kentucky . . . . . . . . . . . . . . . . . . . . . 92 2,329 9,621 0 12,042 14 92 52 0 158

Louisiana ..................... 7 3,332 6,574 0 9,913 40 109 50 0 199

Maine . . . . . . . . . . . . . . . . . . . . . . . . 38 1,447 2,020 1 3,506 24 53 16 1 94

Maryland . . . . . . . . . . . . . . . . . . . . . 22 3,288 17,041 0 20,351 6 77 82 0 165

Massachusetts . . . . . . . . . . . . . . . . 105 3,467 11,471 0 15,043 10 120 80 0 210

Michigan . . . . . . . . . . . . . . . . . . . . . . 64 6,612 13,581 148 20,405 19 227 92 5 343

Minnesota . . . . . . . . . . . . . . . . . . . . 79 3,210 7,275 286 10,850 28 116 49 10 203

Mississippi . . . . . . . . . . . . . . . . . . . . 84 2,499 2,957 96 5,636 20 76 25 3 124

Missouri . . . . . . . . . . . . . . . . . . . . . . 269 3,229 11,558 0 15,056 24 113 51 0 188

Montana . . . . . . . . . . . . . . . . . . . . . . 15 1,880 2,365 905 5,165 41 60 14 24 139

Nebraska . . . . . . . . . . . . . . . . . . . . . 25 1,685 1,317 91 3,118 31 53 13 3 100

Nevada ....................... 1 1,361 8,506 204 10,072 38 28 30 5 101

New Hampshire . . . . . . . . . . . . . . . 50 1,658 2,535 0 4,243 11 46 19 0 76

New Jersey . . . ................ 4 4,883 14,960 0 19,847 8 147 103 0 258

New Mexico . . . . . . . . . . . . . . . . . . . 29 1,813 2,666 1,854 6,362 76 47 19 70 212

New York . . . . . . . . . . . . . . . . . . . . . 582 8,256 62,616 93 71,547 34 271 317 5 627

North Carolina . . . . . . . . . . . . . . . . . 300 5,149 18,901 136 24,486 28 151 93 4 276

North Dakota . . . . . . . . . . . . . . . . . . 35 1,332 2,076 394 3,837 34 58 17 12 121

Ohio . . . . . . . . . . . . . . . . . . . . . . . . . 146 6,906 22,631 0 29,683 22 230 127 0 379

Oklahoma . . . . . . . . . . . . . . . . . . . . . 96 2,557 5,142 267 8,062 104 89 31 8 232

Oregon . . ..................... 7 2,165 7,231 124 9,527 52 70 44 3 169

Pennsylvania . . . . . . . . . . . . . . . . . . 203 8,622 15,227 0 24,052 28 293 107 0 428

Rhode Island .................. 6 1,517 2,517 0 4,040 4 47 18 0 69

South Carolina . . . . . . . . . . . . . . . . 113 3,540 9,094 0 12,747 15 88 39 0 142

South Dakota . . . . . . . . . . . . . . . . . 22 1,307 2,613 453 4,395 40 55 14 27 136

Tennessee . . . . . . . . . . . . . . . . . . . . 381 4,000 10,436 0 14,817 24 125 58 0 207

Texas . . . . . . . . . . . . . . . . . . . . . . . . 714 13,473 47,011 30 61,228 149 405 238 1 793

Utah . . . . . . . . . . . . . . . . . . . . . . . . . 112 2,583 4,061 134 6,890 29 48 23 7 107

Vermont . . . . . . . . . . . . . . . . . . . . . . 16 1,191 3,237 0 4,444 10 45 20 0 75

Virginia . . . . . . . . . . . . . . . . . . . . . . . 62 3,443 20,872 0 24,377 15 131 112 0 258

Washington . . . . . . . . . . . . . . . . . . . 225 3,320 12,976 438 16,959 33 106 76 17 232

West Virginia . . . . . . . . . . . . . . . . . . 24 1,263 4,666 0 5,953 10 46 23 0 79

Wisconsin . . . . . . . . . . . . . . . . . . . . . 164 4,380 5,909 219 10,672 24 138 39 10 211

Wyoming . . . . . . . . . . . . . . . . . . . . . 13 1,778 1,186 89 3,066 61 62 11 5 139

Total U.S. ..................... 5,672 187,104 642,303 9,263 844,342 1,538 5,880 3,530 355 11,303

1

Keyed independent listing housing unit counts as of January 2000. ‘‘Keyed’’ implies these counts went through a quality control review. Consequently, small discrepancies may exist between these independent listing housing unit counts and those from Table 3-8.

3–16 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
THIRD PHASE OF THE A.C.E. SAMPLE DESIGN

In very large block clusters, the housing units within the

cluster were subsampled. This achieved manageable field

workloads for A.C.E. interviewing and person follow-up

without having a big impact on reliability. The strategy of

the A.C.E. large block cluster sampling plan was to

increase the number of clusters in sample, while still

attaining the targeted number of housing units for interview. Because housing units in a block cluster are often

similar, interviewing all of them is not the most efficient

use of resources. Instead, interviewing a manageable fraction of several different clusters provides a more geographically diverse sample.

In the first-phase sampling, large block clusters had a

higher selection probability than medium block clusters to

take into account this anticipated, subsequent housing

unit reduction. The A.C.E. second-phase reduction maintained the differential selection probabilities between the

large and medium block clusters. After the reduction of

housing units in large block clusters, the housing unit

selection probabilities in medium and large block clusters

in the same second-phase sampling stratum were similar.

Another important goal of this housing unit reduction was

to geographically overlap the P and E samples to reduce

the E-sample person follow-up workload. An overlapping P

and E sample was not necessary, but improved the precision of dual system estimates, the cost-effectiveness of

the succeeding operation, and the data processing

efficiency.

Identifying the P-Sample Housing Units

The source of the P-sample housing units, which were

subject to person interviewing by the field staff, was the

independently listed housing units that were confirmed to

exist following the housing unit matching and follow-up

operations. (See Chapter 4.) In block clusters that had

fewer than 80 of these housing units, all of the housing

units were designated to be in the P sample. In addition,

all housing units in a block cluster selected from the

American Indian Reservation stratum were in the P

sample, regardless of how many housing units were in the

block cluster. Most block clusters from this stratum were

expected to have fewer than 80 housing units and it was

desirable to avoid introducing weight variation to the

sample cases for this stratum. For block clusters with 80

or more housing units, the housing units were subsampled and the selected housing units were in the P

sample.

The reduction of housing units within a large block cluster

was done by forming groups of adjacent housing units

called segments and selecting one or more segments of

housing units to participate in the P sample. The segments

had approximately equal numbers of housing units within

a block cluster. Segments of housing units were used as

the sampling units in order to obtain compact interviewing workloads and to facilitate overlapping P and E

samples to reduce E-sample person follow-up workloads.

Flow of operations. A complication of this project was

that large block clusters were ready for the housing unit

subsampling on a flow basis as the preceding operations,

housing unit matching and follow-up, were completed. To

remain on schedule, it was essential that the P-sample

housing units were selected and prepared for interview as

quickly as possible. This meant that sampling parameters

were computed based on the housing unit counts from the

independent listing. If scheduling had not been an issue,

the housing unit counts from the housing unit matching

and follow-up would have been used. The time schedule

constraints did not permit the entire country to be processed prior to subsampling. Further, there was no prespecified order in which block clusters were ready for

housing unit subsampling. Thus, following the flow of

block clusters from the preceding operations, the housing

unit subsampling was performed daily.

Stratifying third-phase clusters. Before selecting the

sample of segments, block clusters were divided into

seven strata within each state. The first five strata were

the same strata used for the second phase of sampling for

the medium and large first-phase strata. The sixth stratum

was the small to large stratum jumpers, block clusters

from the small stratum observed to have more than 80

housing units during the independent listing. The seventh

stratum was equivalent to the first-phase American Indian

Reservation stratum, for which no housing unit reduction

was done.

Allocating the sample. Nationally, the target distribution of the 300,000 P-sample housing unit sample was

roughly proportional to population size, except for

increases in sample size in the smaller states, which had

roughly equal sizes. The second-phase introduced differential sampling within each state and generated overall

target sample sizes for each reduction stratum in the

state, the Tg in the earlier section. Based on these targets

and the observed second-phase sample block clusters, the

sample was allocated to each stratum to provide approximately equal overall probabilities of selection for housing

units from the same stratum.

Determining sampling parameters. Separate sampling parameters were computed for each stratum within a

state. For each stratum, the selection probability was the

ratio of the target number of housing units from large

block clusters over the number of housing units from the

independent listing in large block clusters.

Within-cluster sampling rate =

Target housing unit sample size in large block clusters

Number of listed housing units in large block clusters

Design of the A.C.E. Sample Section I—Chapter 3 3–17

U.S. Census Bureau, Census 2000
The target housing unit sample size was derived by subtracting the number of housing units in medium block

clusters based on the independent list from the target

stratum sample size. When tallying the housing unit

counts from the independent list, any housing units classified as future construction were omitted from the count.

Although some of this future construction was probably

going to be built by Census Day, it was expected to be a

rare occurrence.

Within a particular stratum in a state, a fixed number of

segments was formed in each block cluster. This number

was a function of the within-cluster sampling rate. This

method yielded different size segments across block clusters within the same stratum. This method is a trade-off

between having fewer segments to reduce nonsampling

error and having more segments of a fixed size to reduce

sample size variation. Nonsampling error was reduced by

having fewer segment boundaries to identify. If the withincluster sampling rate was less than or equal to 0.5, then

Number of segments  1

within-cluster sampling rate

rounded up to the nearest integer. When the within-cluster

sampling rate was greater than 0.5, the above formula

results in only two segments resulting in increased sample

size variation with the larger segment size. To better control sample size variation when the sampling rate was

greater than 0.5, the number of segments was calculated

as

Number of segments  1

(1 - within-cluster sampling rate)

Forming the segments. Within each block cluster the

housing units were sorted by census block and geographic location within the block. Then based on the number of segments, approximately equal numbers of housing

units were assigned to each segment.

Selecting a subsample. Within-cluster subsampling was

done daily as the clusters completed the housing unit

matching and follow-up operations. Despite the daily processing, the subsampling was equivalent to a one-time

sample, since the results of the previous day were carried

over to the next and continued. The one difference with

the daily operation was the inability to control the block

cluster sort across all block clusters in the stratum due to

the flow of the block clusters. So, each day the block clusters that were to be subsampled were sorted by block

cluster number within each stratum.

A sample of segments was selected by taking one systematic sample across all large block clusters in each stratum

within a state. Selecting one systematic sample per sampling stratum, rather than a separate sample from each

large cluster, reduced sample size variability. This allowed

an observed sample size close to the target housing unit

sample size to be achieved.

P-Sample Results

Following within-cluster subsampling, the sample for

the 50 states and the District of Columbia was 11,303

block clusters containing about 301,000 housing units.

Table 3-14 displays the results for each state.

3–18 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
Table 3-14. State Third-Phase Sample Results for the P Sample

State

Housing unit counts1 by cluster size2 Block cluster counts by cluster size2

0 - 79 80+ AIR Total 0 - 79 80+ AIR Total

Alabama ........................... 2,947 1,503 0 4,450 115 46 0 161

Alaska . . ........................... 1,152 587 16 1,739 48 21 1 70

Arizona . . . .......................... 5,193 2,474 2,661 7,667 154 55 113 322

Arkansas . . ......................... 1,795 921 0 2,716 86 22 0 108

California ........................... 18,608 14,919 192 33,527 675 415 11 1,101

Colorado . .......................... 2,662 1,491 50 4,153 113 51 2 166

Connecticut ......................... 1,971 1,272 0 3,243 72 39 0 111

Delaware ........................... 1,077 693 0 1,770 42 24 0 66

District of Columbia .................. 1,106 1,084 0 2,190 29 29 0 58

Florida ............................. 8,736 6,518 20 15,254 329 203 1 533

Georgia ............................ 4,690 3,072 0 7,762 183 93 0 276

Hawaii ............................. 1,156 2,447 0 3,603 47 74 0 121

Idaho . . ............................ 1,653 342 146 1,995 86 15 6 107

Illinois .............................. 8,510 3,855 0 12,365 292 111 0 403

Indiana ............................. 4,172 1,773 0 5,945 169 42 0 211

Iowa ............................... 2,162 829 0 2,991 101 21 0 122

Kansas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2,114 552 29 2,666 101 15 1 117

Kentucky ........................... 2,607 1,372 0 3,979 111 47 0 158

Louisiana ........................... 3,031 1,386 0 4,417 153 46 0 199

Maine .............................. 1,571 361 1 1,932 80 13 1 94

Maryland ........................... 2,574 2,713 0 5,287 91 74 0 165

Massachusetts ...................... 4,500 1,893 0 6,393 151 59 0 210

Michigan ........................... 7,224 2,756 147 9,980 259 79 5 343

Minnesota .......................... 3,734 1,420 261 5,154 151 42 10 203

Mississippi . . ........................ 2,332 602 96 2,934 97 24 3 124

Missouri ............................ 3,389 2,120 0 5,509 141 47 0 188

Montana ............................ 2,146 654 863 2,800 100 15 24 139

Nebraska ........................... 1,736 225 79 1,961 86 11 3 100

Nevada . ........................... 1,141 973 189 2,114 70 26 5 101

New Hampshire ..................... 1,156 609 0 1,765 53 23 0 76

New Jersey ......................... 5,369 2,902 0 8,271 175 83 0 258

New Mexico . . . ..................... 2,600 988 1,736 3,588 119 23 70 212

New York . . . . . . . . . . . . . . . . . . . . . . . . . . . 9,301 9,390 88 18,691 332 290 5 627

North Carolina . . . ................... 4,405 3,438 93 7,843 177 95 4 276

North Dakota . . . .................... 1,780 404 381 2,184 95 14 12 121

Ohio ............................... 7,369 3,973 0 11,342 262 117 0 379

Oklahoma .......................... 2,696 970 260 3,666 193 31 8 232

Oregon ............................. 1,866 1,606 124 3,472 127 39 3 169

Pennsylvania ....................... 9,463 2,801 0 12,264 344 84 0 428

Rhode Island ....................... 1,200 574 0 1,774 49 20 0 69

South Carolina ...................... 2,505 1,994 0 4,499 103 39 0 142

South Dakota ....................... 1,657 520 439 2,177 95 14 27 136

Tennessee . . . ....................... 4,071 1,748 0 5,819 156 51 0 207

Texas .............................. 13,031 7,331 29 20,362 588 204 1 793

Utah ............................... 1,640 846 122 2,486 73 27 7 107

Vermont ............................ 1,345 571 0 1,916 57 18 0 75

Virginia . . ........................... 3,765 3,122 0 6,887 156 102 0 258

Washington ......................... 4,064 2,043 416 6,107 147 68 17 232

West Virginia . . . ..................... 1,108 769 0 1,877 56 23 0 79

Wisconsin .......................... 4,323 1,186 209 5,509 164 27 10 211

Wyoming . . ......................... 1,391 527 83 1,918 121 13 5 139

Total U.S. . .......................... 184,155 108,028 8,730 300,913 7,774 3,174 355 11,303

1

The source of the P-sample housing unit counts was the independent list that was confirmed to exist following the housing unit matching and

follow-up operations. 2

Cluster size was based on number of confirmed A.C.E. housing units after housing unit matching and follow-up.

Identifying the E-Sample Housing Units

The E sample consisted of the census enumerations in the

same sample areas as the P sample. The source of the

E-sample housing units was the unedited census files. Like

the P sample, all housing units in block clusters that had

fewer than 80 census housing units or in block clusters

selected from the American Indian Reservation stratum

were designated to be in the E sample. For block clusters

with 80 or more housing units, the housing units were

reduced and the selected housing units were in the E

sample.

Design of the A.C.E. Sample Section I—Chapter 3 3–19

U.S. Census Bureau, Census 2000
The reduction of housing units within a large block cluster

was done by mapping the P-sample segments onto the

census housing units. This was possible because when

there was a match between an A.C.E. independently listed

address and a census address during the housing unit

matching, the census identification number was linked to

the A.C.E. unit. Then the same segment selected for the P

sample was selected for the E sample.

The census inventory of housing units changed between

the housing unit matching operation and the identification

of the E sample. Therefore, some census housing units did

not have a link with an A.C.E. unit. These cases were

assigned to a segment using pre-specified rules. Sometimes there were a large number of these cases in the segment selected to be in sample. If there were more than 80

of these, then an additional subsample was drawn from

these census housing units without a link to an A.C.E.

unit.

The data-defined census person enumerations in the

E-sample housing units were in the E sample. To be a census data-defined person, the person record had two

100-percent data items filled. Name was not required for

the person record to be considered data-defined, but

could be one of the two items required to be data-defined.

Census housing units not available for the

E sample. Not all housing units on the unedited census

file were eligible to be in the E sample. As the census enumerations were being processed, the Census Bureau suspected that there was a significant number of duplicate

addresses in the census files. As such, a new census

operation, the Housing Unit Duplication Operation, was

introduced in the fall of 2000. The primary goal of this

operation was to improve the quality of the census; however its design allowed the A.C.E. operations to proceed.

Essentially, suspected duplicate housing units were set

aside and analyzed further. These housing units and the

corresponding census person enumerations were not eligible for the E-sample component of the A.C.E. nor available for person matching and were excluded from the

dual-system estimation calculation. Some of these setaside housing units and the corresponding census enumerations were later put back into the final census counts.

Subsampling criteria. If a block cluster contained 80 or

fewer available census housing units, then all available

census housing units were in the E sample. If the block

cluster was from the American Indian Reservation stratum,

all available housing units were in the E sample. If the

block cluster had 80 or more available census housing

units, the housing units were subsampled.

Assigning housing units to segments. Within a block

cluster, the census housing units were assigned to a segment based on the link to an A.C.E. housing unit address.

If there was a link with an A.C.E. unit, then the census

housing unit was assigned to the same segment as the

A.C.E. unit. This helped to create overlapping P and E

samples. Sometimes a census housing unit did not have a

link with an A.C.E. housing unit. When this happened, all

the available census housing units were sorted and then

each census housing unit without a link was assigned to

the same segment as the preceding census housing unit.

When the block cluster contained city-style addresses, the

census housing units were sorted by census block number, street name, house number, and unit designation.

When the block cluster contained non-city-style addresses,

the census housing units were sorted by census block

number and geographic location within the block. For citystyle census addresses, geographic location was not available.

Selecting the E-sample housing units. Once all the

census housing units within a block cluster were assigned

to a segment, then the census housing units in the segment or segments selected for the P sample were in the E

sample. Occasionally, the selected segment or segments

within the block cluster contained more than 80 census

housing units that did not link to an A.C.E. housing unit.

When this occurred, an additional step of subsampling

was done to reduce the E sample follow-up workload,

since the census housing units without this link were

more likely to contribute to the follow-up workload than

census housing units with this link.

A systematic subsample of census housing units without a

link to an A.C.E. housing unit was drawn. Using the same

sort used for assigning housing units to a segment, a subsample of 40 housing units was selected if the resulting

subsampling rate was greater than 0.25. However, to

avoid excessive sampling weight variation, the minimum

subsampling rate was set to 0.25, resulting in more than

40 census housing units without a link to an A.C.E. housing unit being in the E sample from the particular block

cluster.

Special case block clusters. There were special case

block clusters when none of the census housing units in a

block cluster linked to an A.C.E. housing unit address at

the time of the housing unit matching. One example of a

special case was a List/Enumerate cluster, since the

List/Enumerate operation had not been conducted by the

time that the housing unit matching was done. None of

the housing units in a List/Enumerate cluster could be

assigned to a segment. Instead of selecting a compact

segment of housing units to be in the E sample, a systematic subsample of the housing units was drawn using the

same method as discussed above. This prevented overlapping the P and E samples when these block clusters were

large. This did not happen often.

3–20 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
E-Sample Results

Following E-sample identification and subsampling, the E

sample for the 50 states and the District of Columbia was

11,303 block clusters containing about 311,000 housing

units. Table 3-15 displays the results for each state.

Table 3-15. State Third-Phase Sample Results for the E Sample

State

Housing unit1 counts by cluster size2 Block cluster counts by cluster size2

0 - 79 80+ AIR Total 0 - 79 80+ AIR Total

Alabama ........................... 2,776 1,793 0 4,569 113 48 0 161

Alaska . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925 926 16 1,867 44 25 1 70

Arizona . . . .......................... 2,819 2,521 2,521 7,861 152 57 113 322

Arkansas . . ......................... 1,838 1,118 0 2,956 85 23 0 108

California ........................... 17,906 16,228 271 34,405 658 432 11 1,101

Colorado . .......................... 2,623 1,587 49 4,259 114 50 2 166

Connecticut ......................... 2,074 1,241 0 3,315 73 38 0 111

Delaware ........................... 1,270 659 0 1,929 45 21 0 66

District of Columbia .................. 1,144 1,216 0 2,360 29 29 0 58

Florida ............................. 8,108 7,037 26 15,171 320 212 1 533

Georgia ............................ 4,373 3,346 0 7,719 179 97 0 276

Hawaii ............................. 1,323 2,653 0 3,976 49 72 0 121

Idaho . . ............................ 1,243 850 155 2,248 72 19 6 107

Illinois .............................. 8,190 4,302 0 12,492 288 115 0 403

Indiana ............................. 4,082 1,870 0 5,952 170 41 0 211

Iowa ............................... 2,237 907 0 3,144 102 20 0 122

Kansas ............................. 2,097 734 27 2,858 100 16 1 117

Kentucky ........................... 2,360 1,692 0 4,052 107 51 0 158

Louisiana ........................... 3,078 1,809 0 4,887 152 47 0 199

Maine .............................. 1,595 429 1 2,025 80 13 1 94

Maryland ........................... 2,651 2,786 0 5,437 92 73 0 165

Massachusetts ...................... 4,249 2,736 0 6,985 146 64 0 210

Michigan ........................... 6,682 3,311 146 10,139 253 85 5 343

Minnesota .......................... 3,183 1,720 260 5,163 148 45 10 203

Mississippi . . ........................ 2,374 647 114 3,135 99 22 3 124

Missouri ............................ 3,231 2,098 0 5,329 141 47 0 188

Montana ............................ 1,480 521 866 2,867 98 17 24 139

Nebraska ........................... 1,637 258 68 1,963 86 11 3 100

Nevada . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907 1,175 133 2,215 67 29 5 101

New Hampshire ..................... 1,426 467 0 1,893 57 19 0 76

New Jersey ......................... 4,952 3,666 0 8,618 170 88 0 258

New Mexico . . . ..................... 1,136 754 1,536 3,426 121 21 70 212

New York . . . . . . . . . . . . . . . . . . . . . . . . . . . 9,114 11,071 84 20,269 326 296 5 627

North Carolina . . . ................... 4,510 3,253 101 7,864 182 90 4 276

North Dakota . . . .................... 1,401 482 358 2,241 95 14 12 121

Ohio ............................... 7,223 4,016 0 11,239 263 116 0 379

Oklahoma .......................... 2,366 1,038 265 3,669 193 31 8 232

Oregon ............................. 1,644 2,378 125 4,147 122 44 3 169

Pennsylvania ....................... 9,143 3,449 0 12,592 336 92 0 428

Rhode Island ....................... 1,194 556 0 1,750 50 19 0 69

South Carolina ...................... 2,502 1,968 0 4,470 105 37 0 142

South Dakota ....................... 1,278 495 433 2,206 95 14 27 136

Tennessee . . . ....................... 4,022 2,429 0 6,451 157 50 0 207

Texas .............................. 12,412 9,213 27 21,652 574 218 1 793

Utah ............................... 1,434 818 123 2,375 75 25 7 107

Vermont ............................ 1,263 640 0 1,903 56 19 0 75

Virginia . . ........................... 3,555 3,731 0 7,286 152 106 0 258

Washington ......................... 3,371 2,609 411 6,391 144 71 17 232

West Virginia . . . ..................... 1,173 724 0 1,897 57 22 0 79

Wisconsin .......................... 4,067 1,159 211 5,437 167 34 10 211

Wyoming . . ......................... 1,337 554 84 1,975 121 13 5 139

Total U.S. . .......................... 178,978 123,640 8,411 311,029 7,690 3,258 355 11,303

1

Available housing unit counts from the unedited census file.

2

Cluster size was based on available census housing unit tallies.

Design of the A.C.E. Sample Section I—Chapter 3 3–21

U.S. Census Bureau, Census 2000
Third-Phase Sampling Results

Table 3-16 gives the state weighted and unweighted

P-sample and E-sample housing units. Also displayed are

the average P-sample and E-sample weights, prior to

weight trimming, TES adjustment, and nonresponse

adjustments. The average weights ranged from approximately 100 to 500.

In Table 3-16, for most of the states, the average E-sample

weight is smaller than the average P-sample weight.

Nationally, despite the P- and E-sample sizes differing by

about 10,000 housing units, after applying the weight, the

weighted number of P-sample housing units is less than

one percent larger than the weighted number of E-sample

housing units.

Table 3-16. P-Sample and E-Sample Housing Unit Sampling Results

State

Weighted housing unit estimates Housing unit sample sizes Average weight

P sample E sample P/E P sample E sample P/E P sample E sample

Alabama ........................... 1,967,703 1,953,559 1.007 4,450 4,569 0.974 442 428

Alaska . . ........................... 186,971 187,657 0.996 1,739 1,867 0.931 108 101

Arizona . . . .......................... 2,291,735 2,419,098 0.947 7,667 7,861 0.975 299 308

Arkansas . . ......................... 1,204,014 1,214,878 0.991 2,716 2,956 0.919 443 411

California ........................... 12,255,066 12,129,849 1.010 33,527 34,405 0.974 366 353

Colorado . .......................... 1,633,980 1,579,070 1.035 4,153 4,259 0.975 393 371

Connecticut ......................... 1,262,197 1,249,792 1.010 3,243 3,315 0.978 389 377

Delaware ........................... 282,962 285,557 0.991 1,770 1,929 0.918 160 148

District of Columbia .................. 295,972 295,099 1.003 2,190 2,360 0.928 135 125

Florida ............................. 7,350,667 6,958,799 1.056 15,254 15,171 1.005 482 459

Georgia ............................ 3,178,003 3,101,337 1.025 7,762 7,719 1.006 409 402

Hawaii ............................. 446,780 467,582 0.956 3,603 3,976 0.906 124 118

Idaho . . ............................ 475,978 494,377 0.963 1,995 2,248 0.887 239 220

Illinois .............................. 4,752,616 4,723,175 1.006 12,365 12,492 0.990 384 378

Indiana ............................. 2,565,559 2,611,248 0.983 5,945 5,952 0.999 432 439

Iowa ............................... 1,286,159 1,303,393 0.987 2,991 3,144 0.951 430 415

Kansas ............................. 1,054,277 1,085,066 0.972 2,666 2,858 0.933 395 380

Kentucky ........................... 1,738,637 1,688,359 1.030 3,979 4,052 0.982 437 417

Louisiana ........................... 1,690,093 1,767,498 0.956 4,417 4,887 0.904 383 362

Maine .............................. 606,684 580,671 1.045 1,932 2,025 0.954 314 287

Maryland ........................... 2,240,463 2,237,811 1.001 5,287 5,437 0.972 424 412

Massachusetts ...................... 2,637,732 2,652,699 0.994 6,393 6,985 0.915 413 380

Michigan ........................... 3,945,568 3,948,348 0.999 9,980 10,139 0.984 395 389

Minnesota .......................... 1,976,410 1,940,302 1.019 5,154 5,163 0.998 383 376

Mississippi . . ........................ 1,067,393 1,065,495 1.002 2,934 3,135 0.936 364 340

Missouri ............................ 2,678,909 2,576,545 1.040 5,509 5,329 1.034 486 483

Montana ............................ 463,607 459,884 1.008 2,800 2,867 0.977 166 160

Nebraska ........................... 684,874 667,586 1.026 1,961 1,963 0.999 349 340

Nevada . ........................... 895,050 862,509 1.038 2,114 2,215 0.954 423 389

New Hampshire ..................... 558,641 523,562 1.067 1,765 1,893 0.932 317 277

New Jersey ......................... 3,377,908 3,338,768 1.012 8,271 8,618 0.960 408 387

New Mexico . . . ..................... 708,714 667,620 1.062 3,588 3,426 1.047 198 195

New York . . . . . . . . . . . . . . . . . . . . . . . . . . . 7,573,292 7,706,526 0.983 18,691 20,269 0.922 405 380

North Carolina . . . ................... 3,857,166 3,748,539 1.029 7,843 7,864 0.997 492 477

North Dakota . . . .................... 294,040 288,677 1.019 2,184 2,241 0.975 135 129

Ohio ............................... 4,785,461 4,687,680 1.021 11,342 11,239 1.009 422 417

Oklahoma .......................... 1,461,163 1,465,046 0.997 3,666 3,669 0.999 399 399

Oregon ............................. 1,411,681 1,431,030 0.986 3,472 4,147 0.837 407 345

Pennsylvania ....................... 5130,010 5,179,175 0.991 12,264 12,592 0.974 418 411

Rhode Island ....................... 408,426 401,022 1.018 1,774 1,750 1.014 230 229

South Carolina ...................... 2,274,389 2,332,485 0.975 4,499 4,470 1.006 506 522

South Dakota ....................... 300,952 297,492 1.012 2,177 2,206 0.987 138 135

Tennessee . . . ....................... 2,489,607 2,609,919 0.954 5,819 6,451 0.902 428 405

Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8,116,215 8,098,923 1.002 20,362 21,652 0.940 399 374

Utah ............................... 885,164 823,255 1.075 2,486 2,375 1.047 356 347

Vermont ............................ 307,822 296,414 1.038 1,916 1,903 1.007 161 156

Virginia . . ........................... 2,714,879 2,797,836 0.970 6,887 7,286 0.945 394 384

Washington ......................... 2,496,269 2,435,145 1.025 6,107 6,391 0.956 409 381

West Virginia . . . ..................... 917,901 916,552 1.001 1,877 1,897 0.989 489 483

Wisconsin .......................... 2,274,773 2,268,976 1.003 5,509 5,437 1.013 413 417

Wyoming . . ......................... 190,271 194,844 0.977 1,918 1,975 0.971 99 99

United States ....................... 115,650,803 115,016,729 1.006 300,913 311,029 0.967 384 370

3–22 Section I—Chapter 3 Design of the A.C.E. Sample

U.S. Census Bureau, Census 2000
Attachment.

Census 2000 Type of Enumeration Areas (TEAs)1

The term ‘‘TEA’’ has been used for several decennial censuses. For Census 2000, it reflects not only the type of

enumeration, but also the method of compiling the census

address list that controls the enumeration process.

The Census Bureau defines TEA codes at the census collection block level. Each block must have a TEA code, and no

block may have more than one TEA code.

TEA 1 - Block Canvassing and Mailout/Mailback

• Contains areas with predominantly city-style (house

number/street name) addresses used for mail delivery.

• Census address list is created from USPS, 1990 census,

local/tribal, and other potential supplementary address

sources.

• Blocks are included in both Block Canvassing and the

Postal Validation Check.

• Blocks are included in local/tribal program to identify

‘‘new construction.’’

Mailout/mailback is the most efficient, cost-effective enumeration method in heavily populated areas in which mail

is delivered to city-style addresses in virtually all cases

(there may be scattered non-city-style mailing addresses in

use in these areas). In most instances, a census enumerator visits a residence once—during Block Canvassing. A

subsequent visit is sometimes necessary during Nonresponse Follow-up.

The mailing list used for this operation is derived initially

from automated address files (the USPS Delivery Sequence

File and the 1990 Census Address Control File), and

updated through various operations, including Address

List Review (LUCA1998), ongoing DSF updates, Block Canvassing, the Postal Validation Check, and the New Construction Program.

TEA 2 - Address Listing and Update/Leave

• Contains areas with some number of non-city-style (e.g.,

P.O. Box or Rural Route) mailing addresses.

• Census address list is created from Address Listing, and

updated from Address List Review (LUCA) 1999 Recanvassing (in selected areas) and Update/Leave

• Blocks are NOT included in Block Canvassing, the Postal

Validation Check, or the New Construction Program

• Puerto Rico, including its military bases, is completely in

TEA 2

Address Listing and Update/Leave are implemented in

areas where mail often is delivered to non-city-style

addresses. In these areas, it is difficult to obtain an up-todate mailing address list and then ‘‘geocode’’ each address

(that is, assign it to a collection block code), because of

the constantly changing residential location/mailing

address relationship (especially for P.O. Box addresses).

The census address list therefore is compiled through a

door-to-door independent listing operation (Address Listing) that is implemented in all TEA 2 blocks.

During Address Listing, enumerators knock on each residence door to obtain the occupant’s name, phone number,

residential address (or location description), and mailing

address. (Enumerators do NOT revisit residences whose

occupants are not present. This is why the census address

list frequently does NOT contain a mailing address, and

why the location description is the ONLY ‘‘address’’ in the

census address list for many residences.) Enumerators

identify the location of each building (containing living

quarters) they encounter with a uniquely numbered map

spot that they enter on their map and record in their

address register; this number is linked to all residential

units in the building, and stored in both the census

address list and the TIGER data base. These areas will be

included in Address List Review (LUCA) 1999.

At census time, enumerators deliver census questionnaires to all housing units compiled during Address Listing and that remain in TEA 2. In the course of delivering

these questionnaires, the enumerators also update the

census address list and map spotted map to reflect housing units that were not previously listed, and to eliminate

residences that they cannot locate. (This operation is

called Update/Leave, because the enumerators UPDATE

the census address list and maps and LEAVE questionnaires.) Update/Leave enumerators use the residential

address/location description in conjunction with the map

spot location to determine the correct delivery point for all

questionnaires.

Most housing units in TEA 2 areas are visited at least twice

by enumerators — once during Address Listing, and again

during Update/Listing. Respondents must mail their completed census questionnaires to the Census Bureau, and so

some residences also will be visited a third time, during

Nonresponse Follow-up.

1

This documentation is reproduced from the Geography

Division, U.S. Census Bureau, Web site located at

http://www.geo.census.gov/mob/homep/teas.html.

Design of the Accuracy and Coverage Evaluation Sample Section I—Chapter 3 3–23

U.S. Census Bureau, Census 2000
TEA 3 - List/Enumerate

• Contains areas that are remote, sparsely populated, or

not easily accessible

• Census address list is created and enumeration conducted concurrently

• Blocks are not included in Block Canvassing, the Postal

Validation Check, the New Construction Program, or

Address Listing

• Includes all military bases in TEA 3 areas

• All island areas (except Puerto Rico), including their military bases, are TEA 3

Some areas are remote, sparsely populated, and/or not

easily visited. Many of the residences in these areas do not

have city-style mail delivery. It is inefficient and expensive

to implement Address Listing, Update/Listing, and Nonresponse Follow-up operations involving multiple visits.

Instead, the creation of the address list and the

delivery/completion of the census questionnaire are

accomplished during a single operation, List/Enumerate.

Enumerators visit residences in TEA 3 blocks, LIST them

for inclusion in the census address list, mark their location

on their map with a map spot and number, enter that map

spot number in their address register, and ENUMERATE the

residents on-site. They collect the same address information as in Address Listing, and include a map spot to

reflect each building that contains one or more living quarters. These areas will NOT be included in any Address List

Review (LUCA) program, because there is no address list

for them in advance of the census.

TEA 4 - Remote Alaska

• Similar to List/Enumerate, but conducted earlier, before

ice breakup/snow melt

• These areas will NOT be included in any Address List

Review (LUCA) program, because there is no address list

for them in advance of the census

TEA 5 - ‘‘Rural’’ Update/Enumerate

• Contains blocks initially in TEA 2, with map spots for all

structures containing at least one housing unit

• In some instances, blocks initially in TEA 3 will be converted to TEA 5. These blocks were not included in

Address Listing and LUCA 1999, and therefore lack

structures and map spots in the MAF and TIGER at the

times that LUCA 1999 and ‘‘Rural’’ Update/Enumerate

are conducted

• Self-enumeration (through Update/Leave) is thought to

be unlikely or problematic

• Census address list is updated, and enumeration is conducted, concurrently

• Blocks are NOT included in the Postal Validation Check

or the New Construction Program

• The term ‘‘rural’’ reflects Address Listing as the initial

source of the census address list, and does NOT reflect

the official census definition of the term ‘‘rural’’

• These areas will be included in Address List Review

(LUCA) 1999 materials, as the MAF was compiled initially from Address Listing

In some areas that otherwise meet the criteria for inclusion in TEA 2, the Census Bureau has decided that having

respondents enumerate themselves and return their questionnaires via the mail is not the best way to conduct the

enumeration. Some targeted populations may be less

likely to return their questionnaires in the mail, and more

likely to respond to an enumerator. In other areas, housing

units may be vacant because they are occupied seasonally.

In these and comparable situations, enumerators visit all

residences on the census address list and complete the

enumeration on-site. In the course of delivering these

questionnaires, they also update the census address list to

1) reflect housing units that were not previously listed

(including a map spot to reflect each building that contains one or more living quarters), and 2) eliminate housing units that they cannot locate. (This operation is called

‘‘Rural’’ Update/Enumerate, because the enumerators work

in areas that were Address Listed, UPDATE the census

address list [and assign map spots as well], and ENUMERATE the residents.)

TEA 6 - Military

• Contains blocks within TEA 2 that are on military bases

• Mailout/Mailback for family housing

• Separate enumeration procedures for barracks, hospitals, etc.

• Blocks are included in both Block Canvassing and the

Postal Validation Check

• These blocks are included in Address List Review (LUCA)

1998 materials, as the MAF was compiled initially in the

same manner as TEA 1 areas

The Department of Defense has advised the Census

Bureau that virtually all family housing (that is, individual

residences as opposed to barracks, hospitals, and jails) are

assigned city-style addresses to which the Postal Service

delivers mail. The Census Bureau therefore implements

Mailout/Mailback methods to enumerate the population of

these individual residences. Within TEA 1 areas, blocks on

military bases are assigned a TEA code of 1. Within TEA 2

areas, blocks on military bases are assigned a TEA code of

6. There is no difference between TEA 1 blocks on military

3–24 Section I—Chapter 3 Design of the Accuracy and Coverage Evaluation Sample

U.S. Census Bureau, Census 2000
bases and TEA 6 blocks in terms of either compiling the

census address list or enumerating the population. Blocks

within military bases in List/Enumerate areas (TEA 3) also

are TEA 3.

TEA 7 - ‘‘Urban’’ Update/Leave

• Contains blocks initially in TEA 1

• Census address list is updated, and questionnaires are

delivered concurrently, by Census Bureau staff (following procedures employed in TEA 2 areas, but without

assigning map spots)

• Blocks ARE included in the Postal Validation Check and

the New Construction Program

• The term ‘‘urban’’ reflects the predominance of city-style

addresses, and does NOT reflect official census definition of the term ‘‘urban’’

• These blocks are included in Address List Review (LUCA)

1998 materials, as the MAF was compiled initially in the

same manner as TEA 1 areas

In many areas where mail is delivered mostly to city-style

addresses, older apartment buildings are common. In

many of these buildings, unit designators (that is, apartment numbers), often do not exist. Further, the subdivision of existing units into multiple units, and the conversion of non-residential space to living quarters, may be

frequent. Mail, therefore, often is not delivered to individual apartments (or individual mail boxes), but instead

left at common drop points.

In some other areas with mostly city-style addresses,

many residents have elected to receive their mail at post

office boxes. The Census Bureau is concerned that the

city-style addresses of these residents may not appear in

the census address list.

To ensure questionnaire delivery to the largest number of

residences, Update/Leave procedures are employed. As

these residences have city-style addresses, there is no

need for enumerators to assign map spots to assist enumerators in identifying these residences in subsequent

operations.

TEA 8 - ‘‘Urban’’ Update/Enumerate

• Contains blocks initially in TEA 1, without map spots for

any addresses; maps generated for TEA 8 areas will not

include map spots

• Contains mostly blocks on those American Indian reservations that initially were included in both TEA 1 and

either TEA 2 or 3

• Same enumeration procedures as TEA 5

• The term ‘‘urban’’ reflects the initial inclusion of the

block in TEA 1 due to the predominance of city-style

mailing addresses

• These areas are included in Block Canvassing and the

Postal Validation Check

Most American Indian Reservations will be enumerated

using a single enumeration procedure (Mailout/Mailback,

Update/Leave, or Update/Enumerate). Some of these initially contained blocks with a mixture of TEA codes. In

these instances, the reservations will be enumerated using

Update/Enumerate methods (see TEA 5). However, for

affected blocks initially in TEA 1, the MAF and TIGER do

not include map spots for structures containing at least

one housing unit. Instead of converting these blocks to

TEA 5 (‘‘Rural’’ Update/Enumerate) and determining map

spot locations, the blocks are being distinguished by a

separate TEA.

TEA 9 - Additions to Address Listing Universe of

Blocks

• Contains groups of blocks (assignment areas) initially

assigned to TEA 1

• Converted to Address Listing before Block Canvassing is

conducted

• Blocks are NOT included in Block Canvassing, the Postal

Validation Check, or the New Construction Program

Some blocks that are in TEA 1 contain a significant number of living quarters with non-city-style addresses. These

blocks should not be included in Block Canvassing, which

is an operation that is designed to confirm and correct the

existence and/or location of city-style addresses. The

Geography and Field Divisions are identifying Block Canvassing assignment areas (AAs) that likely contain blocks

with significant numbers of non-city-style addresses.

Some of these AAs will be removed from Block Canvassing, and included in Address Listing. The blocks in these

AAs will be assigned a TEA code of 9, and the census

address list compilation and census enumeration activities

in TEA 9 blocks will be virtually identical to those in TEA 2

blocks (for instance, they will be included in Update/Leave

and Nonresponse Follow-up).

Because most of these blocks had few, if any, addresses in

the MAF from the USPS, the entities the blocks are in

mostly had nothing to review during Address List Review

(LUCA) 1998. For this reason, most of these blocks will

have their Address List Reviewed during a new phase of

LUCA, often called ‘‘LUCA 99 1/2 .’’

Design of the Accuracy and Coverage Evaluation Sample Section I—Chapter 3 3–25

U.S. Census Bureau, Census 2000
Chapter 4.

A.C.E. Field and Processing Activities

INTRODUCTION

This chapter describes the operational aspects of the

A.C.E. which consisted of four major activities: housing

unit listing, housing unit matching, person interviewing,

and person matching. Housing unit listing and person

interviews were conducted as field activities, whereas

housing unit matching and person matching were processing activities carried out in the National Processing Center

(NPC) in Jeffersonville, Indiana. As described earlier, all of

these activities were completed prior to estimation. Once

the sample clusters were selected, interviewers visited the

clusters and independently listed all housing units. The

A.C.E. and census housing units were then matched and,

for those for which a match was not found, a follow-up

interview was conducted to determine the status of the

housing unit at the time of the census.

Following the resolution of the housing unit nonmatches,

interviews were conducted with residents of the A.C.E.

sample household (P sample) to obtain the roster of

household residents and the detail required for matching.

The P-sample persons were then matched to the list of

persons enumerated in the census in the sample clusters.

The search area was expanded to include one ring of surrounding blocks for those clusters identified as containing

potential census geocoding errors. This operation was

called the targeted extended search (TES) because it targeted clusters with high rates of A.C.E. housing unit nonmatches and census housing unit geocoding error. A further follow-up interview was conducted for selected

mismatched people for whom additional information was

required. Based on these activities, each person in the

sample clusters, whether interviewed in the A.C.E. sample

(P sample) or found in the census (E sample) was assigned

a final match status code.

It is important to point out some key improvements of the

A.C.E. 2000 operations over the 1990 Post-Enumeration

Survey (PES). The 2000 A.C.E. improved on 1990 PES in

several ways for interviewing and clerical matching.

• One problem in 1990 was the misreporting of Census

Day addresses, with an estimated 0.7 percent of the P

sample being erroneously reported as nonmovers (West

1991). The Computer Assisted Personal Interview (CAPI)

instrument improved the quality of the reporting of

mover status because it was a more automated process.

In 2000, the Census Day household consisted of nonmovers and outmovers. The nonmovers lived in the

housing unit at the time of the interview and on Census

Day. The outmovers lived in the housing unit on Census

Day, but moved before the A.C.E. interview. Nonmovers

and outmovers in the P sample were matched to census

people in their block cluster. In 1990, each inmover

household (those that moved into PES block clusters

after Census Day) had to be matched to a Census Day

address, which was usually outside the cluster. In 2000,

the reconstructed Census Day household was matched

to the census enumerations in the sample block cluster.

• A study of clerical error in the 1990 PES found error in

coding matches (Davis 1991) and erroneous enumerations (Davis 1991b). In 1990, codes were entered into a

computer system, but the actual matching and duplicate

searches were done using paper. In the 2000 A.C.E., the

matching was better controlled and more efficient than

1990 because the clerical matching and quality assurance were automated and coded directly into the automated system. The automated interactive system did

not prevent all matching error, but reduced the chances

for error significantly. Software allowed searching for

matches in the census based on first names, last names,

characteristics, and addresses. For example, the system

allowed searching for all people named George, all

people whose last name begins with an H, all people on

Elm Street, or everyone in the age 30 to 40 range. The

software controlled the match codes that were relevant

to the situation. For example, only P-sample nonmatch

codes could be assigned to a P-sample nonmatch.

• The electronic searches for duplicates reduced the

tedious searching through paper lists of census people.

The searching in 1990 was limited to printouts in two

sorts: last name and household by address. In 2000, the

clerks had the capability to filter on name, characteristics, and address to help identify duplicates. The system

monitored whether the matcher had completed all the

necessary searches, such as looking for duplicates.

• There were built-in edits to ensure consistency of coding. For example, codes that applied to a household,

such as geographic codes, were assigned to all people

in the household. The system automatically assigned

certain codes, reducing coding error.

• Clerical matchers could use a code indicating the case

needed review at the next level of matching. This code

allowed them to flag unusual cases to be examined by a

person with more experience.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–1

U.S. Census Bureau, Census 2000
• All quality assurance for the clerical matching was automated.

• Clerical matching was centralized at the NPC instead

of having separate groups of matchers in the seven

processing offices, as was done in 1990. Forty-six technicians were hired in August, 1999 and were thoroughly

trained in the design of the A.C.E. and methods of

matching people and housing units. These technicians

were responsible for quality assurance of the clerical

matchers. Additionally, ten analysts who were among

the most experienced matchers conducted quality

assurance for the technicians and handled the most

difficult cases.

• The computer matcher identified matches and possible

matches within a block cluster. Additional computer

programs were used to check the matching on cases

after the before follow-up clerical matching to identify

matches and duplicates in the expanded search area

that were not identified by the clerical matchers. Consistency checks were also performed between housing unit

and person match codes.

• Keying error in the data capture of the 1990 PES was

reduced because the 2000 interview used a CAPI instrument. A more accurate capture of the data increased the

efficiency of the computer matching.

HOUSING UNIT LISTING

The first stage of sampling was the selection of A.C.E.

block clusters. Then, in September through December of

1999, a listing of the addresses of all the housing units in

the A.C.E. sample clusters was conducted. The listing was

independent of the census. Training in how to list both

city-style and non-city-style areas lasted 3 days and

included a review of the first completed cluster assigned

to each lister. There were 29,136 sampled block clusters

in the 50 states and the District of Columbia. This list of

housing units recorded in the Independent Listing Books

(ILB) became the frame of A.C.E. housing units from which

the P sample was later selected. Besides listing each housing unit in the cluster, the listers inquired about housing

units present at each special place and commercial structure.

The housing unit listing was by basic street address. Each

basic street address was assigned a map spot number and

the map spot number was recorded on the A.C.E. map to

identify the location of the basic street address. The

address and coverage questions about the structure were

asked for each basic street address. The number of housing units at the basic street address was obtained from a

household member at the address, by proxy, from the

apartment manager, or by observation. This contact

helped to improve the coverage of housing units in the

A.C.E. A page in the listing book for single and multiunit

structures is shown in Figure 4-1. The individual housing

units within a basic street address were listed on the

pages of the listing book reserved for multiunits. Also, the

A.C.E. lister recorded the number of units within a basic

street address on the map in parentheses to conform with

census methodology.

Mobile homes that were not in mobile home parks were

listed like single units. Each mobile home was assigned a

unique map spot number and each mobile home was

listed on a separate line in the listing book. If the mobile

homes were in a park, the park was listed in the housing

unit section of the listing book, and each individual mobile

home and vacant site was listed in the mobile home park

section of the listing book. Each individual mobile home

was assigned a unique map spot number, whether the

mobile home was in a park or not. The location of the

mobile home was identified by placing the map spot number for the mobile home on the map. This was the same

procedure that was used in the census.

The following items were collected and recorded in the

listing book for each basic street address:

• City-style addresses (house number and street names)

• Non-city-style addresses (route numbers, route and box

numbers, or any other type of address that was not a

city-style address)

• Householder names (rural areas only)

• Description of addresses (for only nonhouse number

addresses in both urban and rural areas)

• Number of housing units in a basic street address

• Type of basic street address (single unit, multiunit,

mobile home not in a mobile home park, mobile home

in a mobile home park, housing unit in special place,

multiunit in a special place, or other)

• Unit status for single units (occupied or intended for

occupancy, under construction, future construction,

unfit for habitation, boarded up, storage of household

goods, and other)

The following items were also collected and recorded in

the listing book for each unit within a multiunit basic

street address:

• Unit designation

• Unit status for multi units (occupied or intended for

occupancy, under construction, future construction,

unfit for habitation, boarded up, storage of household

goods, and other)

The following items were also collected and recorded in

the listing book for each mobile home in a mobile home

park:

• House number, lot number, or physical description

• Street name

4–2 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
• Rural address

• Unit status (intended for occupancy, unfit for habitation,

boarded up, storage of household goods, vacant trailer

site in a mobile home park, and other)

After the listing books were received in NPC, they were

checked in and the data keyed into a computer file. The

keying quality assurance was 100 percent. Keying rejects

were reviewed clerically to correct errors before the

matching began. A data file of the A.C.E. housing units

was created to be used as input to the housing unit

matching.

HOUSING UNIT MATCH

The housing unit matching consisted of four steps: computer matching, clerical matching, housing unit follow-up,

and after follow-up coding. The A.C.E. housing units were

compared to the census housing units within cluster by

computer, and then, clerically. Housing units that did not

match, possible matches, and possible duplicates were

followed up by field inspection and interview. The results

of the follow-up interview were recorded during the after

follow-up coding.

The purpose of housing unit matching was to create a list

of addresses that existed as housing units in the block

cluster on Census Day to use in the P-sample interviewing.

The housing unit listing was conducted in the Fall of

1999. Addresses that had a chance to be housing units on

Census Day, such as under construction, future construction, and vacant trailer sites, were listed. After the housing

unit matching and follow-up, only the housing units originally listed and confirmed to exist as housing units were

included in the P sample for CAPI interviewing. Housing

units with unresolved status were also included in the

interviewing.

Computer matching was conducted after the second

phase of sampling, which consisted of sample reduction

and small block subsampling. The results of the computer

matching were reviewed clerically. All matching was conducted within the sample block clusters. The census

addresses were the ones contained in the January, 2000

version of the Decennial Master Address File (DMAF). This

was not the final version of the inventory of census

addresses, because of later operations. The inventory of

census housing units was final after the Hundred Percent

Census Unedited File (HCUF) was completed.

As noted earlier, the P and E samples were located in the

same block clusters. The advantages of linking the A.C.E.

and census housing units were:

• The link of A.C.E. and census addresses allowed an

overlapping P sample and E sample, (i.e., the housing

units selected for the P sample were mostly the same as

those in the E sample) eliminating the error prone clerical E-sample identification required to achieve the overlapping samples in the 1990 Post Enumeration Survey.

• The linking of addresses also allowed the person interviewing to begin earlier on the telephone using the census telephone number for the census questionnaire

returned by mail. The telephone number from the census questionnaire was not available without the link

between the A.C.E. housing unit and the census questionnaire for that housing unit.

After sample reduction of clusters, there were 11,303 clusters in the 50 states and the District of Columbia. See

Chapter 3 for a discussion on the sample reduction. The

420 clusters in list/enumerate areas were not matched,

because their census addresses were not available in the

Spring of 2000. Therefore, 10,883 clusters were matched

in the housing unit phase. Table 1 contains the number of

housing units and clusters in housing unit matching for

the A.C.E. The census numbers were preliminary; these

were the addresses prior to mailing the census questionnaires. Subsequent census operations added and removed

addresses from this list. Even though this census list contains more housing units than the A.C.E., this was not

indicative of coverage differences due to the preliminary

nature of the census numbers. See Chapter 3 for a discussion of the final P-sample and E-sample housing units and

how they compare.

Table 4-1. Sample Sizes for the A.C.E. Housing

Unit Matching

Clusters

Housing

units

Clusters with housing units ............. 10,157

A.C.E. housing units.................. 838,427

Census housing units................. 859,296

Clusters without housing units . . . . . . . . . . . 726

Total clusters in housing unit matching.... 10,883

Computer Match

The census housing units included on the DMAF in

January, 2000, in the block clusters retained in the A.C.E.

after sample reduction and small block subsampling, were

used in the housing unit matching. The housing unit data

from the independent listing book file and the DMAF

extract went through a series of data preparation steps,

including address standardization. Addresses from either

file that were blank or could not be standardized were

matched clerically. The results of the computer matching

and images of the A.C.E. and census maps with map spots

in rural areas were inputs into an automated review and

coding software for clerical matching.

Clerical Match

The clerical matchers used the results of the computer

matching to aid in their matching of addresses from the

A.C.E. Field and Processing Activities Section I—Chapter 4 4–3

U.S. Census Bureau, Census 2000
A.C.E. and the census. There were 115 clerks, 46 technicians, and ten analysts involved in the matching operation. The clerks carried out the matching. The technicians

applied quality control to the matching performed by the

clerks. The analysts carried out quality control on the

work of the technicians. The clerks and technicians used a

‘‘review’’ code when they saw something unusual or something that should have been looked at by the next level of

matcher. The technicians and analysts examined the cases

coded for review in the previous stage of matching, in

addition to cases selected for quality control. The clerks

used in the housing unit matching were given 4 weeks of

training. The technicians were hired in August, 1999 and

given extensive training on the background of coverage

measurement and the design of the A.C.E. allowing them

to make more informed decisions. The analysts were our

most experienced people. The analysts have worked on

coverage measurement for many years and were quite

knowledgeable about the A.C.E. The three levels of staff

produced a high quality of matching with a cost-efficient

operation.

The clerical matching was conducted in the housing unit

matching phase of the A.C.E. only for clusters expected to

benefit from further examination. Since clerical matching

was labor intensive, the amount of clerical work performed for the 2000 A.C.E. was reduced by an automated

identification of clusters for follow-up interviewing without clerical review. These clusters had only a few nonmatches or nonmatches on only one side. For example,

there could be 25 A.C.E. nonmatches and no census nonmatches, so there was nothing the clerical matchers could

do. The clerical matchers were thus able to concentrate on

the more difficult clusters where the review was beneficial. In 2000, 3,267 clusters were sent to the field for the

follow-up phase without clerical review.

Supplemental materials were provided to facilitate the

clerical matching, such as the maps with spots to identify

the location of A.C.E. and census addresses in rural areas.

The A.C.E. and census addresses that could not be

matched by the computer were identified for the clerical

matching. The matched addresses were not targeted for

review, because experience in studies preparatory to the

2000 Census indicated a very high quality of the matches

assigned by the computer. However, clerks were allowed

to correct any errors in the computer matching that they

noticed, while they were attempting to match the housing

units that were not computer matched.

The clerical matchers used all housing unit information

available to match housing units. The urban areas were

almost totally city-style addresses. In rural areas, the

addresses were more difficult to match, mainly because of

the non-city-style addresses. The matchers had householder names and location descriptions to help in matching the A.C.E. and census addresses in rural areas. The

spotted maps for the A.C.E. and the census were also used

in the final determination of which housing units matched

in rural areas. Computer images of the A.C.E. and census

spotted maps that were used in the housing unit matching

were accessed via the matching software and viewed on

the screen.

There was also a clerical search, limited to the block cluster, for duplicate housing units during this phase of the

matching. The possible duplicates were linked in the database for both the A.C.E. and the census. A follow-up interview was conducted to determine if the two addresses

referred to the same housing unit.

One goal for the 2000 A.C.E. was not to use any paper in

the clerical matching. Almost all materials needed for

clerical matching were available on the computer. Paperless matching reduced the time needed for clerical matching, because the time spent waiting for an assignment and

associated material was eliminated. There was thus no

need for a large staff to maintain an A.C.E. library. Paper

maps were available to use for cases where the image of

the map was not available or was not easy to view in the

software.

The quality assurance was applied as follows: all of the

work done by each clerical matcher was reviewed initially

until the matcher was determined to be performing at an

acceptable level of quality. The number of records to be

reviewed before a clerical matcher was classified as

acceptable was 200, after which an ‘‘acceptable clerk’’ had

a systematic sample of clusters reviewed for quality assurance. There was a computer record of the level of quality

of each clerk’s work. If the work in the sample of reviewed

clusters fell below the acceptable level of quality, all of the

subsequent work of that clerk was reviewed by technicians, until the clerk achieved an acceptable level of quality, then sampling was resumed. The analysts performed

the same type of quality assurance on the technicians.

Table 4-2 contains the results of before follow-up clerical

matching. These numbers include only the housing units

in clusters that were processed in the housing unit matching. The list/enumerate clusters are therefore not

included. The relisted clusters described at the end of this

section are also not included in Table 4-2. The census had

more possible duplicates and housing units not matching

than the A.C.E. The follow-up interview resolved the housing unit status and determined if the possible duplicates

were in fact duplicated.

4–4 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
Table 4-2. Housing Unit Matching Results Before Follow-Up

Interviewing

A.C.E. Census

Housing units Percent Housing units Percent

Matched ..................... 681,385 81.6 681,385 79.7

Possible match ............... 29,231 3.5 29,231 3.4

Possible duplicate . . . . . . . . . . . . 735 0.1 5,775 0.7

Not matched ................. 123,469 14.8 138,657 16.2

Remove from A.C.E. . . . . . . . . . . 10 0.0

Total ........................ 834,830 100.0 855,048 100.0

Housing Unit Follow-Up

All of the cases coded as not matched, possibly matched,

or possibly duplicated were sent for a follow-up interview,

regardless of the type of basic street address code.

Selected matched cases were also sent to follow-up to

collect additional information. Specifically, the cases

identified for field follow-up were:

• A.C.E. addresses with a before follow-up code of

not matched. Information was obtained to determine

whether the addresses were housing units within the

sample cluster.

• Census addresses with a before follow-up code of

not matched. Information was obtained to determine

whether the addresses were housing units within the

sample cluster.

• Possible matches. The possible matches were sent to

the field to determine if the A.C.E. and census addresses

referred to the same housing unit. If they did not, they

were identified as an A.C.E. nonmatch and a census

nonmatch during the housing unit follow-up and information was obtained to determine whether the

addresses were housing units within the sample cluster.

• Possible census duplicates. Census housing units

that were identified as possible duplicates were followed up to determine if the two census addresses

referred to the same housing unit.

• Possible A.C.E. duplicates. A.C.E. housing units that

were identified as possible duplicates were followed up

to determine if the two A.C.E. addresses referred to the

same housing unit.

• Matched housing units with a code of under construction, future construction, unfit for habitation, vacant trailer site in a mobile home park,

other. These matches were followed up to determine if

they fit the definition of a housing unit at the time of

the follow-up interview.

An A.C.E. housing unit with unit status indicating something other than an occupied or vacant housing unit that

was intended for occupancy needed a follow-up interview

to determine its status at the time of the follow-up interview. The address was either classified as a housing unit

or removed from further processing. For example, a unit

that was under construction or future construction at the

time of listing may have fit the definition of a housing unit

at the time of the follow-up interview. If the unit fit the

definition of a housing unit, it was included in the A.C.E.

housing unit processing. If construction had not progressed enough for it to fit the definition of a housing

unit, it was coded as removed from the A.C.E. housing

unit inventory.

The housing unit follow-up forms were computer generated. The questions for housing units requiring a

follow-up interview were printed. In addition, all housing

units in the block cluster were printed for reference. The

questions for the A.C.E. nonmatches are in Figure 4-2. The

same questions were asked for the census nonmatches.

The questions on the follow-up form were not designed to

be read to respondents, but were intended to be used as a

guide for an interviewer. Indeed, many questions were

answered by observation. The answer to one question

may have been the result of asking several other questions. The follow-up interviewer appropriately modified

the questions, when necessary, to the situation that was

encountered in the field and recorded the appropriate

answers on the follow-up form. This approach was

adopted because there were many situations that could

occur and a form to cover every possible situation would

be cumbersome to handle. It was necessary to find out if

the housing unit satisfied the census housing unit definition at the time of the follow-up interview. There was no

attempt to gather information about reasons for being

something other than a housing unit.

For example, the follow-up interviewer determined if the

address for an A.C.E. independent listing nonmatch or a

census nonmatch existed as a housing unit. This was not

a question meant for a respondent. There were several

reasons why an address might not fit the definition of a

housing unit, such as it burned, it was a mobile home that

moved, it was converted to fewer housing units, it was

group quarters, it was used for storage of farm machinery,

it was the laundry room in an apartment complex, it was a

A.C.E. Field and Processing Activities Section I—Chapter 4 4–5

U.S. Census Bureau, Census 2000
Table 4-3. After Follow-Up Housing Unit Matching Results

A.C.E. Census

Housing units Percent Housing units Percent

Matched ................................................. 719,013 86.1 719,013 84.1

Not matched, but existed in the block cluster . ............... 76,418 9.2 28,874 3.4

Did not exist as a housing unit . . . .......................... 30,770 3.7 48,684 5.7

Geocoded outside the cluster .............................. 6,316 0.8 45,053 5.3

Duplicate ................................................ 1,157 0.1 12,296 1.4

Unresolved .............................................. 1,156 0.1 1,128 0.1

Total . . .................................................. 834,830 100.0 855,048 100.0

business, and so forth. The interviewer appropriately

modified the questions, as necessary, to the situation that

was encountered in the field. Furthermore, the interviewer

could identify matches or duplicates in the field that had

not been identified in the clerical matching.

Additional matches were also identified between the

A.C.E. and census addresses during the follow-up interview, when the interviewer realized the two different

addresses in the A.C.E. and census referred to the same

unit. Corrections and updates to the addresses were also

recorded on the follow-up form. The address updates

were keyed into the database to accurately identify A.C.E.

housing units for the person interviewing. The follow-up

interviewers were instructed not to add housing units

missed by both the A.C.E. and census for the 2000 A.C.E.

After Follow-Up Coding

After the field follow-up, the completed forms were

returned to the processing office. Using the information

obtained during the field work, an after follow-up match

code was assigned by the clerical matchers for cases sent

to the field. The technicians and analysts reviewed the

clusters containing housing units with a review code and

carried out quality assurance for the clusters processed in

the after follow-up housing unit matching.

The follow-up forms were reviewed clerically and codes

were assigned to the A.C.E. and census housing units.

Table 4-3 provides housing unit matching results for all

A.C.E. and census housing units after the follow-up interview codes were assigned. A.C.E. housing units classified

as existing in the block cluster and housing units with

unresolved housing unit status were eligible for person

interviewing. This included both matched and not

matched units. A.C.E. addresses classified as not housing

units, duplicates, and geocoding errors were removed

from the A.C.E. universe, and therefore, were not eligible

for person interviewing. The numbers in Table 4-4 are the

A.C.E. housing units that were eligible for person interviewing before sample reduction. These numbers do not

include the relisted clusters and clusters in list/enumerate

areas. Census housing units with codes of not matched

and unresolved statuses were not eligible to be included

in the P sample for interviewing because they were not

listed in the A.C.E. independent listing.

Table 4-4. A.C.E. Housing Units Eligible for

Person Interviewing

A.C.E.

Housing

units Percent

Matched .............................. 719,013 90.3

Not matched, but existed in the block

cluster .............................. 76,418 9.6

Unresolved ........................... 1,156 0.1

Total ................................. 796,587 100.0

Relisting for Clusters with A.C.E. Geocoding Errors

The follow-up operation also examined potential geocoding errors in the original A.C.E. housing unit listings. If a

large proportion of the A.C.E. housing units in the cluster

had wrong geocodes, the cluster was relisted. Clusters

were identified for relisting when the after follow-up coding described in the previous section was completed. The

decision to relist was automated. If 80 percent of the

housing units in a cluster had geocoding error, the cluster

was relisted. There were 62 relisted clusters in the 50

states and the District of Columbia. The field lister for

relisted clusters had no previous contact with this cluster.

The relisting operation was carried out independently of

the list of census housing units. To assure independence,

the A.C.E. housing unit listings (both the original listing

and the relisting) were done without the A.C.E. lister seeing the census inventory of housing units.

There was no housing unit matching in the relisted clusters during the housing unit matching phase of A.C.E. The

addresses listed for A.C.E. during the relisting operation

were the addresses used to conduct person interviewing.

These clusters were treated in the same way as the

list/enumerate clusters in 2000.

An unresolved code was assigned to all of the A.C.E. housing units in the relisted clusters and in the list/enumerate

clusters. The census housing units in these clusters were

assigned a blank housing unit code.

PERSON INTERVIEW

Prior to person interviewing there was another stage of

sampling, the within block subsampling of large block

4–6 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
clusters. See Chapter 3 for more details. The resulting

housing units from A.C.E. comprised the P-sample housing

units assigned for interviewing. There were 11,303 clusters selected for interviewing, and they contained 300,913

P-sample housing units. The person interview training

lasted five days.

A.C.E. mover and residence status codes necessary to

identify P-sample people from the person interview are

assigned within the interview instrument. These codes are

described in Figure 4-3.

The goal of the interview was to obtain a household roster

for everyone living at the housing unit at the time of the

interview and on Census Day, April 1, 2000. Procedure C

was used for the 2000 A.C.E. With Procedure C, each

A.C.E. person was assigned an A.C.E. mover code, an

A.C.E. born since Census Day code, an A.C.E. group quarters code, and an A.C.E. other residence code. The A.C.E.

status code combined all of the information from these

codes to identify the people for whom matching was necessary. Attachment 1 contains the definitions for codes for

the movers, those born since Census Day, members of

group quarters, other residence code, and the A.C.E.

status code. See the Chapter 7 attachment for more on

Procedure C.

Group quarters were not listed in the A.C.E. and A.C.E.

interviews were not conducted in group quarters. See

Attachment 2 for a discussion of the treatment of group

quarters in A.C.E.

Mode of Interview

The A.C.E. person interview was conducted using a CAPI

instrument on laptop computers. Attachment 3 contains a

description of the procedures followed in the person

interview. Some person interviews were conducted by telephone and some by personal visit.

To get an early start for the interviewing, a telephone

interview was conducted at households where the census

questionnaire included a telephone number and was

received at a census processing office early enough for

computer processing, before the start of person interviewing. The telephone number came from the census questionnaire of the matching census housing unit. The person

interviews conducted by telephone were conducted from

April 24, 2000 until June 13, 2000. See Byrne et al. (2001)

for more details. A total of 88,573 interviews or 29.4 percent of the total workload were conducted by telephone.

The following cases were excluded from the A.C.E. telephone interviewing:

• Housing units in census large household and census

coverage edit follow-up

• Questionnaires that were not returned by mail

• Housing units without house number and street name

addresses

• Housing units in small multiunit structures (i.e., less

than 20 units)

Large multiunits were able to be included in the telephone

interviewing, because they tended to have unique unit

designations. Many small multiunit structures and rural

areas did not have addresses that allow the telephone

interviewer to distinctly identify the address. Since there

was no housing unit matching in relisted and

list/enumerate clusters, all person interviewing in relisted

and list/enumerate clusters was by personal visit.

All remaining interviews after the end of the telephone

operation were conducted in person, except for some nonresponse conversion operation (NRCO) interviews and

interviews in gated communities or secured buildings. The

person interviews conducted by personal visit were conducted from June 18 until September 11, 2000. Crew

leaders and supervisors conducted telephone interviews

to give them experience in interviewing.

Table 4-5 contains the number of interviewers, crew leaders, and supervisors used during production interviewing

and during the interviewing for person follow-up after the

clerical matching.

Table 4-5. Field Interview Personnel

Telephone

interview

Personal

interview

Person

follow-up

Interviewers . . . . . . . . . . . . . . . . . . . . 450 4,502 4,470

Crew leaders . . . . . . . . . . . . . . . . . . . 794 836 712

Supervisors . . . . . . . . . . . . . . . . . . . . 189 186 184

For the first 3 weeks of interviewing, the person interview

was conducted only with a household member. If an interview with a household member could not be carried out

within 3 weeks, an interview with a knowledgeable nonhousehold member was attempted, called a proxy interview. The proxy interviewing was allowed during the

remainder of the interviewing period. During the last 2

weeks of interviewing for a cluster, a nonresponse conversion operation was conducted for the noninterviews using

the best interviewers. This noninterview conversion

attempted to obtain an interview with a household member or a knowledgeable proxy respondent, but not a last

resort interview1. The nonresponse conversion operation

converted 9,518 of the 9,735 total noninterviews to interviews.

1

Last resort interviews were ones with minimal information,

such as names like ‘‘White Female.’’ The last resort interview is

usually not from a knowledgeable proxy respondent. Last resort

interviews were conducted in the census at the end of nonresponse follow-up, after all attempts to contact a knowledgeable

respondent have not obtained an interview. Last resort interviews

were not conducted for A.C.E.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–7

U.S. Census Bureau, Census 2000
The Questionnaire

There were three paths or sections within the person interview. An interview was conducted using the first two

paths, when at least one of the household members, for

whom information was required, currently lived at the

housing unit when the interview was conducted. One path

collected data from a household member, and another

path collected data from a nonhousehold member (i.e.,

proxy respondent) for these people. There were two

paths, because the questions were worded differently for

interviews with household members and with proxy

respondents. The interviews from the first two paths were

in housing units containing:

• Whole household nonmovers

• Whole household inmovers

• Households with a mixture of nonmovers, inmovers,

and outmovers

The third path was for whole household outmovers. The

data for outmovers was obtained by proxy with the current resident in the sample household or with other proxy

respondents, when necessary. When there was an interview with whole household inmovers, there was also an

interview using the third path for whole household

outmovers.

When there were multiple interviews for the same housing

unit, the CAPI data from the last interview was selected for

processing. If there was also a quality assurance interview

that replaced the original interview, the quality assurance

interview was selected over any other interview.

After the interviewers obtained the names and characteristics of household members, they established the residence

status on Census Day. For nonmovers and outmovers,

mover status in addition to questions about group quarters and other residences on Census Day established the

residence status.

College students living elsewhere in dormitories were not

part of the A.C.E. universe. However, they were inadvertently included as inmovers in the A.C.E. instrument. To

correct for this, an edit was performed for partial household inmovers who were in group quarters on Census Day.

If the inmover was in group quarters on Census Day and

was between the ages of 18 and 22, inclusive, the

inmover was given an A.C.E. status code of removed.

Quality Assurance of Person Interviewing

The quality assurance plan for the A.C.E. Person Interview

operation consisted of a reinterview of a sample of the

original A.C.E. interviews. The workload consisted of a

preselected random sample of 5 percent of the total person interview caseload and another sample consisting of

cases targeted by the supervisors in the regional offices

using specially designed targeting reports. The targeting

was based on various indicators likely to predict poor data

quality or potential fabrication. The targeted sample was

another 5 percent of the total workload.

A separate CAPI questionnaire was designed for the quality assurance interviews. The quality assurance questionnaire contained separate paths for telephone and personal

visit quality assurance interviews. The questionnaire also

included a complete version of the original interview to

allow quality assurance interviewers to conduct the

household interview on cases suspected of fabrication.

Consequently, it was not necessary to assign another field

representative at a later date to conduct the household

interviews for such cases.

Quality assurance interviews were conducted either by

telephone or personal visit. The interview determined

whether or not the original respondent was contacted by

an interviewer. If, after an initial set of questions, it

appeared that the respondent had not been previously

contacted, the quality assurance interview continued with

a full household interview that replaced the original interview in all future processing.

The quality assurance plan centered on whether the original interviewer actually contacted the person who was

reported to have been interviewed. When this was the

case, the interview itself was assumed to be correct

because, the person interview questionnaire was designed

to ensure data quality using data edits and automated

questionnaire skip patterns. When this was not the case

(i.e., the proper household was not contacted), a full reinterview was conducted.

The quality assurance plan was designed to be most effective for the few interviewers who blatantly include data

from fictitious interviews. This occurs in practice in similar

surveys. Therefore, discrepant results were targeted by

looking for inconsistent or conspicuous results identified

using the targeting reports. Examples of inconsistent or

conspicuous results include using the same name for

respondents across cases, using famous names for household members, or completing cases too late in the day to

really have been interviewing at someone’s house.

Effectively identifying an interviewer with only one or two

errors in a large workload of cases would require a prohibitively large random sample. Because, later A.C.E.

operations such as the person follow-up interview were

expected to identify such cases, the quality assurance

plan did not attempt to identify these situations beyond

what falls in the 5 percent random sample.

Preliminary Estimation Outcome Codes

Preliminary P-sample estimation outcome codes were

assigned to each P-sample housing unit before the computer and clerical matching. This outcome code was

4–8 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
assigned to the housing unit based on Census Day for

nonmovers and outmovers. Only people with the

following A.C.E. status codes were used in the matching

operations:

• N = nonmover resident

• O = outmover resident

• U = unresolved residence status

The preliminary estimation outcome codes identified

interviews and noninterviews in occupied housing units,

vacant housing units, and housing units that were

removed from the P sample. The interview outcomes

described in this section were Census Day interview

outcomes after data editing, which converts whole households of Census Day residents with insufficient information for matching to noninterviews and whole households

of Census Day residents, who should not have been

counted at the housing unit on Census Day to vacant

housing units.

Interviews

• Complete interviews. Interviews conducted with a

household member.

• Proxy interviews. Interviews conducted with someone

outside the household.

• Sufficient partial interviews. Interviews with household

members or proxies that did not collect all required

data, but did collect enough information to be considered as interviews.

Noninterviews

• Field noninterview.

• Whole households of people with insufficient information to permit matching and follow-up.

Vacant on Census Day

• Housing units identified as vacant on Census Day by the

interviewer.

• Whole households of people who should have been

counted elsewhere on Census Day (i.e., whole household nonresidents).

Not a Housing Unit on Census Day

• The housing units identified during the person interview

as not a housing unit on Census Day were removed

from the P sample.

Table 4-6 contains the number of each category of preliminary outcome codes and the number and percentages of

total occupied and vacant housing units for the preliminary outcome codes grouped into interview, noninterview,

and vacant. The percentages of interview and noninterview for occupied housing units were also included. The

noninterview rate for occupied housing units was 1.9 percent based on the preliminary outcome codes before

clerical matching. The interviewers identified 10,206

addresses or 3.4 percent of the A.C.E. addresses as not

being housing units on Census Day. The A.C.E. housing

units identified as something other than housing units

were not in the P sample. For more details see Childers et

al. (2001).

Table 4-6. Preliminary Census Day Estimation Outcome for A.C.E. Housing Units (Unweighted)

Outcome code

Total housing units Occupied housing units

Number Percent Number Percent

Interview ............................................................ 257,624 88.6 257,624 98.1

Complete interview with a household member . ........................ 235,632

Complete interview with a proxy respondent .......................... 19,380

Sufficient partial interview ........................................... 2,612

Noninterview ........................................................ 4,988 1.7 4,988 1.9

Field noninterview ................................................. 2,667

All people have insufficient information for matching and follow-up ....... 2,321

Total occupied housing units ........................................... 262,612 100.0

Vacant . ............................................................. 28,095 9.7

No Census Day residents ........................................... 4,184

Vacant on Census Day . ............................................ 23,911

Total occupied and vacant housing units ................................ 290,707 100.0

Not a housing unit on Census Day ..................................... 10,206

Total interviewed housing units ........................................ 300,913

A.C.E. Field and Processing Activities Section I—Chapter 4 4–9

U.S. Census Bureau, Census 2000
The percent noninterview was calculated for the

unweighted numbers of noninterviews divided by the

occupied interviews, which was the interviews plus the

noninterviews. Tables of preliminary noninterview rates

are presented for respondent type and interview mode in

Tables 4-7 and 4-8.

Table 4-7. P-Sample Preliminary Percent

Noninterview in Before Follow-Up

by Respondent Type

Respondent type P-sample preliminary

percent noninterview

Household member . . . . . . . . . . . . . . . . . . . . . . . 0.9

Proxy . . . ................................ 13.8

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9

Of all interviews at occupied housing units, 33.5 percent

were completed by telephone, 66.1 percent were completed by personal visit, and 0.3 percent, which was 910

interviews, were completed by a quality assurance

replacement interview. The percent noninterview of occupied housing units for each interview mode is shown in

Table 4-8.

Table 4-8. P-Sample Preliminary Percent

Noninterview Before Follow-Up by

Interview Mode

Interview mode P-sample preliminary

percent noninterview

Telephone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.9

Personal visit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2

Quality assurance replacement ............. 36.0

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9

While telephone interviews were more likely than personal

visit interviews to have insufficient information because

neighbors could not be contacted, this was offset by the

straightforward nature of the telephone interviews. These

were cases where the respondent completed and returned

the census form in a timely manner and provided a telephone number on the form. Conversely, personal visit

cases tended to be the more difficult situations (such as

movers or reluctant respondents), and were therefore,

much more likely to result in noninterviews.

There were several reasons for a high noninterview rate

for the quality assurance replacement interviews. These

were difficult interviews, because they failed the quality

assurance check and needed a reinterview. Many of the

noninterviews were refusals. Additionally, because the

instrument was monitoring both the quality assurance

case and the replacement interview, it was difficult to

obtain the Census Day residents in mover cases so that

many of these were noninterviews. There was also a problem with the instrument in cases where the quality assurance interviewer could not find the address on the day of

the QA interview. When this occurred, the case failed the

quality assurance check, but no data were collected to

replace the original interview since the QA interviewer

could not find the address. However, unlike in personal

visit cases, no attempt was made by the QA interviewer to

determine if the sample address also did not exist on Census Day. Therefore, these cases were considered to be

Census Day noninterviews. There were 108 such cases.

PERSON MATCHING

After both the CAPI interviewing and the HCUF were completed, the E sample was identified from the HCUF and

person matching began. People with incomplete names

were identified by computer for both the P and E sample,

because they did not contain sufficient information for

matching and follow-up. See Attachment 4 for more information about census data-defined and insufficient information for matching and follow-up.

The P-sample people and those in the HCUF, within the

sample clusters, were computer matched. The possible

matches, P-sample nonmatches, and E-sample nonmatches

were clerically reviewed using an automated matching and

review system. Additional matches and possible matches

were identified by the clerical staff. Duplicates on both

lists were also identified clerically. After the matching was

completed, field follow-up was conducted and the results

of the field interview were coded in the matching database.

Within Block Cluster Computer and Clerical

Matching

With procedure C, the people in P-sample housing

units, who were initially matched to the E-sample and

non-E-sample census enumerations were:

• nonmovers and outmovers identified as residents (i.e.,

A.C.E. status equal to N and O), or

• people with unresolved residence status (i.e., A.C.E.

status equal to U)

The matching within the sample clusters was done by the

computer matcher followed by a computer assisted clerical review. The computer compared the nonmovers and

outmovers to the E-sample census enumerations in sample

clusters and when necessary to the non-E-sample enumerations. These non-E-sample enumerations were census

people in housing units that were not included in the E

sample after the subsampling of census housing units.

The clerical matchers also searched among people enumerated in the census in group quarters. A match was

assigned when the name and characteristics in the P

sample for a person were found in the census data within

the block cluster.

During computer matching, the P sample was matched to

the census. However, this matching was prioritized; first

4–10 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
the P sample was matched to the E sample, then any leftover nonmatches from the P sample were matched to the

non-E-sample people in housing units. The matching

occurred in two steps:

• Record Pair Ranking. The standardized names from

the P-sample person and the census person were compared along with the person characteristics using a

string comparison (Winkler, 1994). A ranking score was

assigned to each pair of people and the optimal pairs

were identified.

• Determination of Match Cutoffs. The optimal pairs

in the cluster were reviewed to determine the cutoffs for

matches and nonmatches. All pairs above the match

cutoff were identified as a match. All pairs between the

match cutoff and nonmatch cutoff were identified as

possible matches. All pairs below the nonmatch cutoff

were classified as not matched. Match cutoffs were

assigned conservatively to prevent false matches.

The goal of the matching and follow-up operation was to

produce the correct ratio of cases classified as omitted

from the census to those classified as correctly included in

the census. After the computer matching, P-sample and

E-sample people who did not match were reviewed clerically. The clerical matchers were able to match people the

computer could not, because they had the whole household to aid in matching. The P-sample nonmatches were

searched for in the census. A duplicate search was also

conducted clerically. The matching and duplicate search

was aided by the software in sorting and searching the

census records. The computer assisted clerical matching

software contained all A.C.E. and census information

about P-sample and census people, including names, characteristics, outcome of the interview, and address.

The A.C.E. technicians carried out the quality assurance

for the clerical matchers and resolved the cases flagged by

the clerical matchers as needing further review. The A.C.E.

analysts did the quality assurance for the technicians and

resolved the cases flagged by the technicians as needing

further review. There were 235 clerks, 46 technicians, and

10 analysts to do the clerical matching.

Census Images. Scanned images of census questionnaires were available for matching for the first time in

Census 2000. The clerical matchers used these images as

an aid in matching and when additional information (like

names) was found, the new information was made available for the follow-up interview. An E-sample record could

be updated by the clerks to provide sufficient information

for matching and follow-up or to correct image capture

errors. In addition, some information written outside the

capture boxes was used to update the data.

For Census 2000, all census forms were scanned and the

subsequent information was interpreted using Optical

Mark Recognition and Optical Character Recognition or

was keyed. For person matching, images were only available for housing units on the January, 2000 DMAF. Images

were not available for census housing units added after

January, 2000. An address identified by census identification number (ID) could return more than one form, including the following: original census form, Be Counted form,

a foreign language form, and/or a Simplified Enumerator

Questionnaire. Be Counted forms were not available to use

for viewing images, since they did not have a census ID

associated with the form when data captured.

The clerical matchers reviewed data for census people

with insufficient information for matching and follow-up

and searched for additional information that might allow

them to be matched when the image was available. All

review of census people with insufficient information for

matching and follow-up was done before the clerical

matching began and the census data in the matching software was updated. The software did not permit the

assignment of a code until there were two characteristics

and a complete name. After the software data were

updated, the clerical matching process began and the

matchers could match the P-sample person to the census

people now containing sufficient information for matching. The matchers were also able to review data for nonmatches when they suspected data capture errors and to

correct the records of name, relationship to person number one, sex, age, Hispanic origin, and race.

The corrected data were used on the follow-up form, but

not sent to estimation. The updated data were not

inserted into the HCUF. This updating was for matching in

A.C.E. and for the follow-up form only. The matchers were

NOT looking at people who were not data-defined to see

if there was more information on the census form to make

them data-defined. Therefore, people were NOT created in

the census.

Duplicate Search Within Cluster. The search for duplicates was done clerically. A person was duplicated when

the data collected for the person was repeated within the

block cluster. The printouts used in 1990 for duplicate

search were automated in 2000. Search routines in the

2000 clerical matching software made the searches

quicker and more accurate. Duplicates were linked in the

matching system for later analysis.

Duplicated People Were Identified:

• Within the P sample. A duplicated P-sample person

was removed from the final P sample, because both

people were not needed in that household in the P

sample. When the whole households of P-sample people

were duplicated, one of the housing units was converted to a noninterview because the interview was not

a good one. The duplicated P-sample household was in

a different housing unit and one of them was included

instead of the people who actually lived at the address.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–11

U.S. Census Bureau, Census 2000
For example, the Smith family was collected in apartments A and B. Both apartments were housing units.

The P-sample interview for the duplicated family is not a

good interview and is converted to a noninterview after

the P-sample people were removed.

• Within the E sample. An E-sample person duplicate

was an erroneous enumeration in the census.

• Between E-sample people and people not in the E

sample. The E-sample people were also compared to

the census people in housing units within the same

sample cluster who were not in sample in large block

clusters after the E-sample identification. There was no

duplicate search between E-sample people and people

enumerated in group quarters. Also, there was no duplicate search within group quarters.

When duplication between an E-sample person and a

non-E-sample person was identified, it indicated that

there was not a full erroneous enumeration. Therefore,

the probability of erroneous enumeration caused by

duplication was needed for the duplicated E-sample person. The formula for the probability of erroneous enumeration, was 100 times d divided by c+d+1 percent or

Pr (EE)  100 d / (c + d + 1) percent

where

c = number of times the E-sample person was

duplicated with another E-sample person

d = number of times the E-sample person

was duplicated with a non-E-sample person

In 1990, when there was duplication between a person in

the E sample and a person in a household that was not in

the large-cluster subsample, and therefore not in the E

sample, the E-sample person was assigned a probability of

erroneous enumeration of one half. This methodology was

refined in the 2000 A.C.E. to accommodate triplicates. The

1990 estimate was biased when there was a triplicate enumeration in the census and this triplicate involved two

E-sample duplicates and the triplicate was not in the E

sample. However, there were only a few of these cases in

2000.

This assumes the E-sample person had been coded as correctly enumerated. If the E-sample person was coded unresolved, the final probability of erroneous enumeration

included an imputation for unresolved enumeration status.

If the E-sample person was assigned a match code that

indicated erroneous enumeration, the number of times

that the E-sample person was duplicated with non-Esample people was irrelevant and ignored. A person could

not have a probability of erroneous enumeration that was

larger than 100 percent.

Census Geocoding Errors

The clerical matchers reviewed people in census housing

units identified in the housing unit matching as geocoding

errors. The clerical matchers assigned a code indicating

geocoding error to E-sample persons for whole household

E-sample nonmatches. There was no need for a follow-up

interview, since the housing unit follow-up operation identified these housing units with geocoding errors. These

E-sample people were erroneously enumerated in this

sample cluster because they were enumerated in a housing unit that was incorrectly geocoded to this sample cluster. In 1990, these people were followed up because it

wasn’t clear who was incorrectly geocoded until after the

follow-up interview.

Coding Nonmatches in Large Households

The mail return short form had a continuation roster to

collect names for persons seven through twelve. The mail

return long form had a roster for the names of persons

one through twelve. Data were collected for the first six

people in the household, for both long and short forms. If

the large household follow-up was unsuccessful, there

were only names for persons seven through twelve for the

long and short mail return forms. Census records were not

created for the people in households with only names,

since they were not data-defined.

The names on the rosters were used to reduce the

P-sample follow-up of nonmatches in large households.

P-sample people in large households who were found on

the large household roster were not followed up because

they were residents of the housing unit on Census Day.

They were still counted as not matched to a census enumeration, but a follow-up interview was not needed to

establish their residence on Census Day.

Targeted Extended Search

P-sample whole household nonmatches with no address

match and E-sample whole households of nonmatched

people in housing units coded as geocoding errors had

their search area expanded into the first ring of surrounding blocks. The expanded search is referred to as targeted

extended search (TES). See Chapter 5 for a full discussion.

The targeted extended search for 2000 A.C.E. was a twostage process. First, clusters were identified that would

benefit most from expanding the search area to surrounding blocks. Second, blocks within the surrounding blocks

were targeted for searching.

This extended search was targeted at the clusters most

likely to benefit from expanding the search area. The clusters selected for targeted extended search for the 2000

Accuracy and Coverage Evaluation were:

• Clusters included with certainty

• Relisted clusters in A.C.E.

• The 5 percent of clusters having the most

unweighted census geocoding errors and A.C.E.

address nonmatches

4–12 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
• The 5 percent of clusters having the most weighted

census geocoding errors and A.C.E. address nonmatches

• Clusters selected at random from the clusters with

A.C.E. housing unit nonmatches (i.e., A.C.E. housing

units coded CI or UI) or census housing units identified

as geocoding errors (i.e., coded GE)

The clusters not selected for targeted extended search

were:

• Clusters not selected from the clusters with A.C.E. housing unit nonmatches (i.e., A.C.E. housing units coded CI

or UI) and census housing units identified as geocoding

errors (i.e., coded GE), (i.e. TES eligible for sampling, but

not selected)

• Clusters with no A.C.E. housing unit nonmatches or census geocoding errors identified in the housing unit

matching.

• List/Enumerate clusters

Table 4-9 contains the number of clusters selected for TES

and the number of P-sample and E-sample people in TES.

The number of clusters includes the clusters included with

certainty because they were relisted. P-sample people with

a residence probability of zero have been excluded from

the table.

Table 4-9. The TES Sample

Clusters

P-sample

people

E-sample

people

Included with certainty ........... 1,150 28,533 20,572

Sampled for TES . . ............. 1,089 3,889 2,281

Total . .......................... 2,239 32,422 22,853

Clusters with the most unweighted and weighted census

geocoding errors and A.C.E. address nonmatches were

included because some clusters with large weights contribute disproportionately to the estimates. Approximately

10 percent of the clusters of the remaining clusters with

A.C.E. housing unit nonmatches and census geocoding

errors (49 percent of all clusters) were selected at random.

There were 2,239 clusters selected for targeted extended

search.

In the second stage of targeting, the work was targeted to

blocks within the search area where the geocoding error

was located. In 1990, the effort required to search for

matches and duplicates in large areas that had only a few

possible matches or duplicates appeared to lead to errors.

There was anecdotal evidence of clerks who did not

bother to look in surrounding blocks because they rarely

found anything. Targeting the expanded searching probably reduced clerical errors, as well as the cost of the

operation.

P-Sample Matching Extended Search

The search area was expanded to clerically search the ring

of surrounding blocks for the P-sample whole household

nonmatches, when a housing unit was not a match in

housing unit matching, (i.e., the housing unit match code

was a nonmatch or unresolved). There was no searching in

surrounding blocks for partial household nonmatches or

for whole household nonmatches with matching

addresses.

How the search was done depended on whether the cluster and its surrounding blocks consisted solely of urban

type addresses, or whether they consisted of some or all

rural type addresses.

• In areas that are completely urban, if the clerk located

the basic street address in the surrounding blocks or

the clerk determined the range of addresses was in the

surrounding blocks, person matching was conducted in

that block where the basic street address or range was

located. The matching was also conducted when there

was a possible address match in a surrounding block.

• In rural or mixed urban and rural areas, because of the

difficulties in matching rural type addresses, there was

no attempt to match addresses in the surrounding

blocks. Instead, people were searched for in all of the

surrounding blocks.

E-Sample Extended Search for Geocoding Errors

A census person in a housing unit that was coded as a

geocoding error was an erroneous enumeration unless the

housing unit was located inside the expanded search area.

The census geocoding errors were identified in the housing unit phase of the A.C.E. Another interview identified

the housing units that physically existed in the surrounding blocks, instead of within the cluster where they were

enumerated. This field work was done for whole household E-sample nonmatches in housing units identified during the housing unit phase as geocoding errors. This field

visit was conducted at about the same time as the A.C.E.

person interview.

The people in these housing units were coded as follows:

• If the housing unit was found to exist in the surrounding blocks, the clerks coded the E-sample person as

geocoded to the surrounding blocks during the before

follow-up person matching.

• If the housing unit existed in the sample cluster, the

E-sample person was coded as not a geocoding error,

because that housing unit did exist in the sample

cluster.

• If the housing unit did not exist in the surrounding

blocks or could not be located on the map sent with the

case, the E-sample person was coded as a geocoding

error, indicating the person was erroneously enumerated because the housing unit was incorrectly geocoded

in the block cluster.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–13

U.S. Census Bureau, Census 2000
• If the field work was not done or if it could not be determined if the block number entered on the form was in

the block cluster or in the surrounding blocks, the unresolved code was used. There was no follow-up for the

unresolved cases.

A person follow-up interview for the E-sample nonmatches

coded in the sample cluster or in the surrounding blocks

was needed to identify other reasons for erroneous enumeration, such as fictitious people and other residences

where people should have been counted on Census Day.

E-Sample Targeted Duplicate Search

A search for duplicated people was conducted clerically in

the targeted extended search clusters, when the housing

unit was identified during the field interview as physically

existing in the surrounding blocks. Like the P-sample

search for missed units, the duplicate search was created

to identify people who were duplicated because of geocoding error. There was no searching for duplicates in the

group quarters enumerations.

If an E-sample housing unit was identified as existing in

the surrounding blocks, a housing unit duplicate search

was conducted. How this was done depended on whether

the cluster and its surrounding blocks consisted solely of

urban style addresses or whether they were some or all

rural style addresses.

• In urban areas, this duplicate search was done first on

housing units and then on people. First, the clerks

searched in the block where the housing unit should

have been counted in the ring of surrounding blocks. If

the housing unit was duplicated, a search was conducted to identify duplicated people. The duplicate

search was conducted only in the block where the duplicated housing unit was located. These people were

duplicated because the housing unit was enumerated

correctly in a surrounding block and incorrectly in the

sample cluster. If the housing unit was not duplicated, a

search for person duplication was not conducted. The

search concentrated on people who were duplicated and

were in duplicated housing units caused by housing

unit geocoding error in the surrounding blocks.

• The duplicate search in rural or mixed areas was a

search throughout the entire search area for person

duplicates.

Added and Deleted Census Housing Units

Census coverage operations continued past the creation of

the January, 2000 DMAF. As a result, an added census

housing unit is one that was not in the initial housing unit

matching, because it was added to the inventory of census

housing units after the January, 2000 DMAF was created. A

deleted census housing unit is one that was in the January,

2000 DMAF, but was removed from the cluster before the

final inventory of housing units was created.

The targeted extended search was based on the A.C.E.

housing unit matching to the January, 2000 DMAF and did

not cover census housing units added to the block cluster

since housing unit matching, thus excluding any geocoding errors that were not recognized in time to conduct the

TES field follow-up. If a cluster was not identified for targeted extended search and a large building was added to

the cluster, the first time it could have come to our attention was during person matching and any added housing

units would be identified as geocoding errors during the

person follow-up. If any of these cases should have been

included in the targeted extended search and were incorrectly geocoded, another follow-up operation would have

been needed to identify the ones that actually existed in

the surrounding blocks and those that existed outside the

expanded search area.

There was not sufficient time to conduct another interview

to determine which added census housing units with

geocoding error really existed in the first ring of surrounding blocks. These cases were handled in two ways:

• In TES clusters and clusters eligible for TES sampling,

the people in added housing units where person

follow-up identified geocoding error were treated as

unresolved and the probability of correct enumeration

was imputed. These new unresolved cases were treated

the same as any other person coded with unresolved

geography.

• When the housing unit was not in a TES cluster, the

people remained coded as geocoding errors and were

erroneous enumerations.

A similar limitation existed when a housing unit that was

matched in the housing unit matching was later deleted.

There was a concern that the deleted unit may have been

moved to a surrounding block. Clusters, where matched

housing units in the DMAF that were deleted from the

HCUF, had no chance of being TES clusters, if the cluster

had no A.C.E. housing unit nonmatches or census geocoding errors.

These deleted cases were also treated differently depending on whether they were in TES clusters:

• If in a TES cluster, they were identified as TES people

and a surrounding block search was conducted for the

housing units in the TES P-sample matching.

• If the housing unit was not in a TES cluster, there was

no surrounding block matching. Surrounding block

matching could not be done because there were no surrounding block people in non-TES clusters.

Before Follow-Up Results

Tables 4-10 and 4-11 contain the results of before

follow-up matching for the P sample and the E sample. For

details of these codes, see Childers (2001). These before

4–14 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
follow-up matching results are from unweighted data from

the fifty states and the District of Columbia.

The P-sample codes are grouped into:

• Matched

• Not matched

• Possible match

• Unresolved match status

• Removed from the P sample

Matched. The P-sample person was found in the census.

Not matched. The P-sample person was not found in the

census. A follow-up interview was conducted for:

• Partial household nonmatches

• Whole households of conflicting household members

(i.e., whole households of P-sample and census nonmatches)2

• Other whole household nonmatches where the P-sample

interview was conducted with a nonhousehold member3

Possible match. The P-sample person may have been a

match to the census person. A follow-up interview was

needed to determine if the two names referred to the

same person.

Unresolved match status. The only category of unresolved in the before follow-up matching was insufficient

information for matching and follow-up.

Removed from the P sample. The only category of

removed from the P sample in the before follow-up matching were the P-sample people coded as duplicates.

The E-sample codes are grouped into:

• Correctly enumerated

• Erroneously enumerated

• Nonmatch

• Possible match

• Unresolved

Correctly enumerated. The correctly enumerated

people in before follow-up matching were the ones matching the P sample.

Erroneously enumerated. The categories during before

follow-up were fictitious people, duplicates, insufficient

information for matching and follow-up, and geocoding

errors.

• The fictitious people were those where notes on the

census image identified the person as one who died

before or was born after Census Day, or as not a real

person such as a dog or other pet.

• The E-sample people enumerated more than once were

coded as duplicates.

• The E-sample people with insufficient information for

matching and follow-up were those who were datadefined, but did not contain full name and at least two

characteristics.4

• Census people in housing units identified as geocoding

errors5 during the initial housing unit follow-up were

coded as erroneously enumerated because of geocoding

error.

Nonmatch. All E-sample people who did not match to the

P sample were sent for a follow-up interview.

Possible match. E-sample people who were coded as

possible matches were followed up to determine whether

they were, in fact, matches.

Unresolved. In before follow-up matching, the unresolved category only includes the census housing units

that needed targeted extended search field work and that

field work was not done.

Table 4-10. P Sample Before Follow-Up

Matching

P-sample match status Unweighted

people Percent

Matched .............................. 573,506 85.7

Not matched .......................... 76,804 11.5

Possible match ........................ 5,070 0.8

Unresolved ........................... 7,524 1.1

Removed ............................. 5,923 0.9

Total ................................. 668,827 100.0

2

These cases have been called the Smith/Jones cases in the

past. 3

No follow-up interview was conducted when there were

whole households of P-sample nonmatches from interviews with

household members in a housing unit that did not match in the

housing unit operation or matched to a housing unit containing

no data-defined people.

4

This is the same rule that was used in the 1990 PES. There

must have been enough information about the person to have a

chance at locating the person for a follow-up interview before the

person was allowed into the matching process. See Childers

(2001). 5

A geocoding error is an error in assigning the housing unit to

the correct location.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–15

U.S. Census Bureau, Census 2000
Table 4-11. E-sample Before Follow-Up

Matching

E-sample enumeration status Unweighted

people Percent

Correctly enumerated .................. 544,995 76.4

Erroneously enumerated . .............. 27,934 3.9

Not matched . . . ....................... 134,916 18.9

Possible match . . . ..................... 4,751 0.7

Unresolved . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 0.0

Total ................................. 712,900 100.0

Note: Percentages in table may not add to total due to rounding.

A.C.E. Person Follow-Up

The person follow-up was conducted to gather additional

information to accurately code the residence status of the

nonmatched P-sample people and the enumeration status

of the E-sample people. In addition, the match status of

the possible matches was resolved during the follow-up

interview. The following cases were sent to person followup:

• P-sample partial household nonmatches

• P-sample whole household nonmatches where the census enumerated different E-sample people (i.e., conflicting households or Smith/Jones cases)

• P-sample whole household nonmatches where the

A.C.E. person interview was with a proxy respondent

• E-sample nonmatches

• Possible matches between the P sample and the census

• P-sample matches and nonmatches with unresolved

residence status

• P-sample nonmatches needing additional geographic

work6

The results of the follow-up interview were recorded in the

matching software by the matching clerks. Table 4-12 contains the results of the follow-up coding for the P-sample

people who were followed up. The P-sample people who

were followed up were clerically classified as:

• Matched

• Nonmatched resident of the cluster on Census Day

• Unresolved residence or match status

• Nonresident of the cluster on Census Day

Matched. The P-sample person was found in the census

in the block cluster or in a surrounding block after the

follow-up interview.

Nonmatched resident of the cluster on Census

Day. The P-sample nonmatch was not found in the

census, and the follow-up interview determined he or she

should have been counted in the search area for this

cluster.

Unresolved residence or match status. The person

had unresolved residence status, because the follow-up

interview did not successfully collect the information

required to accurately identify this person as a resident of

the cluster on Census Day. In the case of possible

matches, the follow-up interview was not able to ascertain

the match status of the people.

Nonresident of the cluster on Census Day. The

P-sample person was not a resident of the housing unit on

Census Day and was removed from the P sample. These

people were duplicates, fictitious, living in a P-sample

housing unit that was listed in the cluster in error (i.e.,

P-sample geocoding error), or the P-sample person should

have been counted at another residence on Census Day.

The results of the follow-up interview in Table 4-12 indicate 14.7 percent unresolved and 12.5 percent removed

from the P sample.

Table 4-12. Results of P-sample Follow-Up

Interview

After follow-up match code Unweighted

people Percent

Matched .............................. 9,793 19.4

Nonmatched resident .................. 26,961 53.4

Unresolved ........................... 7,451 14.7

Nonresident .......................... 6,296 12.5

Total ................................. 50,501 100.0

Table 4-13 contains the results of the E-sample follow-up

interviews. The followed-up E-sample people were classified as:

• Matched

• Correctly enumerated

• Erroneously enumerated

• Unresolved

Matched. The P-sample and E-sample enumerations refer

to the same person. The match was made after the

follow-up interview.

Correctly enumerated. The E-sample nonmatch was

identified during the follow-up interview as correctly enumerated in the census.

6

Housing units in relist and list/enumerate clusters did not

have housing unit matching. Therefore, P-sample geocoding

errors in such clusters needed to be identified during person

matching. In addition, when the interviewer changed the address

in the CAPI instrument, the P-sample geography was checked to

make sure the interviewer did not interview outside the sample

cluster.

4–16 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
Erroneously enumerated. The E-sample nonmatch was

identified during the follow-up interview as erroneously

enumerated in the census, because the person should

have been counted at another residence on Census Day,

was fictitious, had insufficient information for matching

and follow-up, was duplicated, or lived in a household that

was a geocoding error.

Unresolved. The follow-up interview for the census nonmatch was not successful.

The results of the E-sample follow-up in Table 4-13 indicate 7.4 percent of the E-sample people followed up were

erroneously enumerated and 14.1 percent were unresolved.

Table 4-13. Results of E-sample Follow-Up for

Nonmatches and Possible Matches

After follow-up match code Unweighted

people Percent

Matched . . . ........................... 9,088 6.3

Correctly enumerated .................. 103,589 72.2

Erroneously enumerated . .............. 10,618 7.4

Unresolved ........................... 20,185 14.1

Total ................................. 143,480 100.0

After Follow-Up Coding

After the follow-up was completed, the results of the interviews were reviewed and codes entered into the system

by the matching clerks. See Attachments 5, 6, and 7 for

definitions of the individual match, enumeration, and residence status codes assigned by the matching clerks.

The final P-sample results are shown in Tables 4-14 and

4-15. The P-sample people have been classified as

matched, not matched, unresolved match status, and

removed in Table 4-14 and also tabulated as resident, nonresident, and unresolved residence status in Table 4-15.

The data are unweighted, but the people sampled out of

the targeted extended search are removed from tabulations for this section.

The P-sample match status is defined as:

• Matched

• Not matched

• Unresolved match status

• Removed from the P sample

Matched. The P-sample person was found in the cluster

or in the surrounding block in either a housing unit or in

group quarters.

Not matched. The P-sample person was not found in the

search area. If the nonmatch was sent to follow-up, the

person was confirmed to be a resident of the cluster on

Census Day. If the nonmatch was not sent for a follow-up

interview, a household member identified the person as a

resident of the housing unit during the original A.C.E.

interview.

Unresolved match status. The match status was unresolved for possible matches with unsuccessful follow-up

interviews and for P-sample people with insufficient information for matching and follow-up.

Removed from the P sample. People were removed

from the P sample when they were fictitious, duplicates,

geocoding errors, or not residents of the housing unit on

Census Day.

Table 4-14. P-sample Match Status After

Follow-Up

P-sample after follow-up

match status

Unweighted

people Percent

Matched .............................. 578,695 88.6

Not matched .......................... 54,424 8.3

Unresolved ........................... 7,826 1.2

Removed ............................. 12,393 1.9

Total ................................. 653,338 100.0

The P-sample residence status was defined as:

• Resident

• Nonresident

• Unresolved residence status

Resident. The P-sample matched or not matched person

was a resident of the housing unit on Census Day.

Nonresident. P-sample people were nonresidents of the

cluster when they were fictitious, duplicates, geocoding

errors, or should not have been included as a resident of

the housing unit on Census Day. Nonresidents were

removed from the P sample.

Unresolved residence status. A matched or not

matched P-sample person had unresolved residence status

when the follow-up interview did not successfully determine the person’s residence on Census Day. The residence

status of the possible match was unresolved when the

follow-up interview was not successful. The residence status was also unresolved when the P-sample person had

insufficient information for matching.

Table 4-15. P-sample Residence Status After

Follow-Up

P-sample after follow-up

residence status

Unweighted

people Percent

Resident . ............................ 625,863 95.8

Nonresident .......................... 12,393 1.9

Unresolved ........................... 15,082 2.3

Total ................................. 653,338 100.0

A.C.E. Field and Processing Activities Section I—Chapter 4 4–17

U.S. Census Bureau, Census 2000
The final E-sample results are in Table 4-16. The E-sample

people were classified as correctly or erroneously enumerated or having an enumeration status of unresolved.

These were the unweighted match results that go to imputation and estimation with the people sampled out of the

targeted extended search removed.

The E-sample enumeration status was defined as:

• Correctly enumerated

• Erroneously enumerated

• Unresolved enumeration status

Correctly enumerated. E-sample people were correctly

enumerated when they were matched to the P sample, or

when they have been followed up and they should have

been enumerated in this cluster.

Erroneously enumerated. E-sample people were erroneously enumerated when they have another residence

where they should have been counted on Census Day,

were fictitious, were duplicated, lived in a housing unit

that was a geocoding error, or had insufficient information

for matching and follow-up.

Unresolved enumeration status. E-sample people had

unresolved enumeration status when the follow-up interview was unsuccessful. The E-sample person may have

been followed up to obtain information about the

E-sample nonmatch, possible match, matched person with

unresolved residence status, or geographic work to obtain

the location of the housing unit.

Table 4-16. E-sample Matching After Follow-Up

E-sample enumeration status Unweighted

people Percent

Correctly enumerated .................. 652,390 92.6

Erroneously enumerated . .............. 31,064 4.4

Unresolved ........................... 21,148 3.0

Total ................................. 704,602 100.0

There were unresolved codes assigned to P-sample and

E-sample people. A probability of being matched was

imputed for a P-sample person with unresolved match status. A probability that the P-sample person was a resident

was imputed when the follow-up did not give enough

information to resolve the person’s residence status. The

probability that a P-sample person was a resident was the

probability that the person should have been included in

the P-sample. The probability that the E-sample person

was correctly enumerated was also imputed for the

E-sample people with unresolved enumeration status. A

P-sample person could be matched, but have unresolved

residence status or have both match and residence status

unresolved. Therefore, tabulations for match status and

residence status are shown separately for the P-sample.

Estimation Outcome Codes

Two sets of outcome codes were prepared, one for the

Census Day household and one for the Interview Day

household. The final P-sample estimation outcome code

identified the status of the interview for estimation on

Census Day and on the day of the interview. For example,

there were cases that were complete interviews for the

current residents, but were reported as noninterview or

vacant for the Census Day residents.

The final Census Day outcome codes are in Table 4-17.

Outcome codes were changed as a result of the follow-up

interview in the following types of situations:

• No Census Day residents noninterview. Whole

households of P-sample people who said they lived elsewhere on Census Day were converted to noninterviews.

• No Census Day residents vacant. Whole households

who lived in group quarters on Census Day or should

have been enumerated at another residence were converted to vacant.

The outcome codes for these two situations were changed

because new information from the follow-up interview

indicated the original interview was incorrect. The housing

unit outcome code for people identified as residents of the

housing unit from the person interview who said in the

follow-up interview that they lived elsewhere was changed

to noninterview. The original person interview listed this

household as residents of the housing unit when they did

not live at this address. The interview is incorrect and is

converted to a noninterview.

The housing unit outcome codes for people identified as

residents of the housing unit, from the person interview

who said in the follow-up interview that they lived in

group quarters or should have been enumerated at

another residence, were changed to vacant. The original

person interview should have classified the housing unit

as vacant, because the people should have been enumerated at another address.

The table also contains numbers of housing units identified as interviews, noninterviews, and vacant and percentages of total housing units and numbers and percentages

of occupied housing units. The noninterview rate for occupied housing units for Census Day was 3.0 percent.

Addresses that were not housing units on Census Day

were removed from the P sample.

4–18 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
Table 4-17. Final Census Day Estimation Outcome Codes for A.C.E. Housing Units (Unweighted)

Census Day outcome code

Total housing units Occupied housing units

Number Percent Number Percent

Census Day interview ................................................ 254,175 87.5 254,175 97.0

Complete Census Day interview with a household member.............. 233,327

Complete Census Day interview with a proxy respondent . . ............. 18,335

Sufficient partial interview ........................................... 2,513

Census Day noninterview . ............................................ 7,794 2.7 7,794 3.0

No Census Day residents ........................................... 2,709

Field Census Day noninterview ...................................... 2,667

All people have insufficient information for matching and follow-up ....... 2,418

Total occupied Census Day housing units .............................. 261,969 100.0

Vacant ............................................................. 28,472 9.8

No Census Day residents ........................................... 4,561

Vacant on Census Day . ............................................ 23,911

Total occupied and vacant housing units on Census Day ................. 290,441 100.0

Not a housing unit on Census Day ..................................... 10,472

Total housing units ................................................... 300,913

The Census Day noninterview rates in Tables 4-18 and

4-19 are for occupied housing units. The percent noninterview was calculated for the unweighted numbers of Census Day noninterviews divided by the occupied Census

Day interviews, which was the interviews plus the noninterviews on Census Day. The Census Day noninterview

rates were recalculated to reflect changes due to coding in

after follow-up matching.

Table 4-18. P-sample Noninterview Rates for

Census Day in Occupied Housing

Units by Interview Mode

Interview mode Percent

noninterview

Telephone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1

Personal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7

Quality assurance . .............................. 37.4

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.0

Table 4-19. P-sample Noninterview Rates for

Census Day in Occupied Housing

Units by Type of Interview

Type of interview Percent

noninterview

Interview with a household member . . . . . . . . . . . . . . . 1.8

Proxy interview ................................. 17.4

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.0

Comparison of Initial and Final P-Sample

Estimation Outcome Codes for Census Day

Table 4-20 compares the preliminary and final Census Day

interview outcome codes. The preliminary Census Day

outcome codes were changed, when the follow-up interviews for the P-sample classified people as nonresidents

because they did not live at the sample address at the

time of the census, or they were considered as living at

the sample address but should have been counted at

another residence such as group quarters or another

home. The housing unit could also be identified as not

being a housing unit on Census Day.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–19

U.S. Census Bureau, Census 2000
Table 4-20. Comparison of the Preliminary and Final Census Day Outcome Codes

Preliminary Census Day

outcome codes

Final Census Day outcome codes

Interview

with

household

member

Interview

with

proxy

Partial

interview

No Census

Day

residentsnoninterviewField

noninterview

Whole

household

insufficient

information

No Census

Day

residentsvacant Vacant

Not

a

housing

unit

Interview with Household member .... 233,327 0 0 2,033 0 0 125 0 147

Interview with proxy . ................ 0 18,335 0 676 0 0 252 0 117

Partial interview . ................... 0 0 2,513 0 0 97 0 0 2

Field noninterview . . ................ 0 0 0 0 2,667 0 0 0 0

Whole household insufficient

information . . . ..................... 0 0 0 0 0 2,321 0 0 0

No Census Day residents-vacant ..... 0 0 0000 4,184 0 0

Vacant ............................ 0 0 00000 23,911 0

Not a housing unit .................. 0 0 0 0 0 0 00 10,206

Table 4-21. Final Interview Day Estimation Outcome Codes for A.C.E. Housing Units (Unweighted)

Interview Day outcome code

Total housing units Occupied housing units

Number Percent Number Percent

Interview Day interview . . ................................................... 264,103 89.0 264,103 98.9

Complete interview on Interview Day with a household member . .............. 249,854

Complete interview on Interview Day with a proxy respondent ................ 12,317

Sufficient partial interview ................................................. 1,932

Interview Day noninterview ................................................. 3,052 1.0 3,052 1.1

No Interview Day residents-household converted to noninterview . . . . . . . . . . . . . . 483

Field noninterview on Interview Day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

All people have insufficient information for matching and follow-up ............. 2,196

Total occupied housing units on Interview Day ................................. 267,155 100.0

Vacant on Interview Day . ................................................... 29,662 10.0

Total occupied and vacant housing units on Interview Day . ..................... 296,817 100.0

Not a housing unit on Interview Day . . ....................................... 4,096

Total housing units ......................................................... 300,913

Final P-Sample Estimation Outcome Codes for

Interview Day

The final Interview Day outcome codes are in Table 4-21.

The interview outcome, as of Interview Day, was for cases

originally classified as nonmovers and inmovers. Changes

as a result of the follow-up interview were from whole

households of nonmovers who said they:

• Never lived at this residence

• Lived in group quarters on Census Day

• Lived at another residence on Census Day

The outcome codes for these cases were converted to

noninterviews.

The Interview Day noninterview rates were recalculated to

reflect changes due to coding in after follow-up matching.

The final noninterview rates for Interview Day by interview mode and type of interview are in Tables 4-22 and

4-23.

Table 4-22. P-sample Noninterview Rates for

Interview Day in Occupied Housing

Units by Interview Mode

Interview mode Percent

noninterview

Telephone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.7

Personal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0

Quality assurance .......................... 15.4

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1

Table 4-23. P-sample Noninterview Rates for

Interview Day in Occupied Housing

Units by Type of Interview

Type of interview Percent

noninterview

Interview with a household member . . . . . . . . . . 0.5

Proxy interview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1

4–20 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
Attachment 1.

A.C.E. Mover and Residence Status Code

• A.C.E. Mover Code

1 = Nonmover

2 = Inmover

3 = Outmover

• A.C.E. Born Since Census Day Code

0 or blank = Default for inmovers

1 = Born on or before Census Day

2 = Born since Census Day

D = Don’t know

R = Refused

• A.C.E. Group Quarters Code

0 or blank = Default for whole household inmovers7

1 = In group quarters on Census Day

2 = Not in group quarters on Census Day

D = Don’t know

R = Refused

• A.C.E. Other Residence Code

0 or blank = Default for whole household inmovers

1 = In other residence on Census Day

2 = Not in other residence on Census Day

D = Don’t know

R = Refused

• A.C.E. Status

N = Nonmover, resident on Census Day

O = Outmover, resident on Census Day

I = Inmover, nonresident on Census Day

R = Removed, nonresident on Census Day

U = Unresolved residence status

B = Born since Census Day, nonresident on Census

Day

7

Partial household inmovers were assigned the codes of 1, 2,

D, or R during the edit for CAPI data review.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–21

U.S. Census Bureau, Census 2000
Attachment 2.

The Treatment of Group Quarters in A.C.E.

The A.C.E. was designed to provide estimates of person

coverage in housing units. There was no sample of, and

no estimates for, persons in group quarters. The P-sample

housing units were selected for the A.C.E. and the people

in the P-sample housing units were matched to the people

enumerated in census housing units.

Classifying a structure as group quarters was difficult at

times. For example, homes for the elderly have made it

more common for a single structure to contain apartments

for retired people, assisted living, and full care. Another

example was college dormitories. A dormitory was group

quarters when it was occupied by unmarried students.

The dormitory contained housing units if it was occupied

by married students. If the dormitory was mixed with married, unmarried, faculty, and staff, it contained housing

units. As a result, housing units or group quarters could

be misclassified, when they were not easily classified as

housing units or group quarters. This misclassification

could be found in both the A.C.E. and the census.

When the P-sample people in A.C.E. housing units did not

match to people enumerated in housing units in the census, they were matched to people enumerated in the census in group quarters. That is, group quarters were

searched for P-sample nonmatches. If the P-sample people

were found in the group quarters enumerations, they were

treated as matched. However, no attempt was made to discover whether the misclassification was in the A.C.E. or

the census.

Likewise, if a census person in the E-sample was enumerated in a housing unit, but the housing unit was misclassified and should have been group quarters, the follow-up

of the census nonmatch obtained information about the

residence of the person. If it found the person should have

been counted in this block in group quarters or a housing

unit, the person was coded as correctly enumerated in

A.C.E. processing. The ideal was not to classify someone

as erroneous when they really should have been counted

in this cluster, but the type of residence was misclassified.

If a structure contained both housing units and group

quarters, the people who were enumerated in the census

in a housing unit were eligible to be in the E sample. The

follow-up interview identified such E-sample people who

were not matched as living in the cluster and having no

other residence. They were coded as correctly enumerated. There was no duplicate search between people enumerated in group quarters and housing units.

In summary, then, the approach was balanced:

• Look for P-sample people in group quarters when they

were not found in census housing units.

• Follow up E-sample people in both housing units and

group quarters in the cluster.

The population in housing units was covered, but there

was no estimate of coverage in group quarters. If the

housing unit was duplicated in the group quarters, the

group quarters people were not counted as duplicates.

Likewise, if a group quarter was missed, there was no

determination of undercounted inhabitants.

4–22 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
Attachment 3.

The A.C.E. Person Interview8

Household Roster

If the person lived at the sample address, the interviewer

began the interview with a series of questions to obtain

the names of everyone currently living at the sample housing unit. The first question was:

‘‘I need to get a list of everyone living here permanently

or staying temporarily at this address. What is your

name?’’

After obtaining the name of the person with whom the

interviewer was speaking, the interviewer asked, ‘‘Anyone

else?’’ If there was a ‘‘yes’’ response, the interviewer asked,

‘‘What is his or her name?’’ and followed that with ‘‘Anyone

else?’’ until the interviewer received a ‘‘no’’ response.

As a check for types of people who were frequently left off

listings of household members, there were two additional

questions. The first question asked about people who may

have lived at the household sometimes, but not all the

time, such as children in joint custody or people who traveled a great deal of the time. The question was:

‘‘Are there any additional people who currently live or

stay here, like someone who’s temporarily away or

someone who stays here off and on?’’

If the response was ‘‘yes’’ the interviewer asked, ‘‘What

was his or her name?’’ and followed with ‘‘Anyone else?’’

until the interviewer received a ‘‘no’’ response.

Other persons who were frequently omitted from household listings were roommates or live-in employees. The

interviewer asked, ‘‘Is there anyone else like a roommate

or a live-in employee who lives here?’’

If the response was ‘‘yes’’ the interviewer asked, ‘‘What is

his or her name?’’ and followed with ‘‘Anyone else?’’ until

the interviewer received a ‘‘no’’ response.

At this point in the interview, the interviewer had collected

a list of household members that the respondent had voluntarily mentioned, and the interviewer had also checked

for two types of persons that research had shown were

frequently left off household listings.

The interviewer then reviewed a screen that contained a

list of the household members the respondent reported.

The interviewer read the list of names and asked if the list

was correct. The interviewer said, ‘‘I have listed [READS

NAMES ON SCREEN]. Is that correct?’’ After the respondent

had reviewed the names, the interviewer could change the

spelling, or add or delete a name.

Movers

When the respondent agreed that the list was correct, the

interviewer handed the respondent a calendar containing

the months of March, April, and May of 2000 that had

Census Day clearly marked. At this point in the interview,

the goal was to begin determining whether the people

listed as current residents were also residents of the

sample housing unit on Census Day and if anyone else

should have been included as a Census Day resident. The

interviewer asked if any of the listed persons (current residents) had moved into the sample housing unit after Census Day. The interviewer said to the respondent:

‘‘Please look at this calendar. Did any of the people I just

listed move into <sample address> after Census Day,

April 1, 2000?’’

If the answer was ‘‘yes,’’ the interviewer asked, ‘‘Who

moved in after April 1?’’ Any person mentioned was considered a nonresident of the sample housing unit on Census Day. If everyone in the household was mentioned,

then the whole household was considered nonresidents on

Census Day.

The interviewer now had a list of current residents who

also lived at the sample housing unit on Census Day. It

was necessary to determine if there was anyone living at

the sample housing unit on Census Day who did not live

there currently. The interviewer asked, ‘‘Was there anyone

else living or staying here on April 1, 2000 who has

moved out?’’ If the response was ‘‘yes,’’ the interviewer

asked, ‘‘What is his or her name?’’ and ‘‘Anyone else?’’ until

a ‘‘no’’ response was received.

The interviewer now had a list of the names of everyone

the respondent had reported living at the sample housing

unit currently and on Census Day. The interviewer then

established a reference person (relationships will be relative to this person) by asking who owns or rents the

house or apartment. The interviewer asked, ‘‘In whose

name is this (house/apartment) owned or rented?’’ The

interviewer also asked whether the housing unit was

owned or rented by saying, ‘‘Do you own this

(house/apartment), rent it, or live here without payment of

rent?’’ 8

See Keeley (2000) for details.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–23

U.S. Census Bureau, Census 2000
Demographics

At this point in the interview, the interviewer began to collect demographic characteristics about all listed persons

to facilitate matching the persons collected in this interview to persons listed on the census questionnaire for the

sample housing unit. Demographic characteristics are also

used to create post-strata in dual system estimation. See

Chapter 7 for more details.

The demographic characteristics collected in the interview

were:

1. Sex. The interviewer may have entered the sex of the

person or asked the question when in doubt. The

question was, ‘‘Is [NAME9] male or female?’’

2. Age. Age was collected in a series of questions. The

interviewer asked for date of birth (‘‘What is [NAME’S]

date of birth?’’). When the date of birth was entered in

the instrument, the age of the person was calculated

and the interviewer verifies the age by saying, ‘‘So

[NAME] was about [AGE] on April 1?’’ If the age was

not correct, the interviewer changed the date of birth

in the previous question and the age was then recalculated.

If the respondent did not know the date of birth, then

the interviewer asked the person’s age. The interviewer asked, ‘‘What was [NAME’S] age on April 1,

2000?’’

3. Relationship. Relationship was to the person in

whose name the house or apartment was owned or

rented (called the Reference Person). The interviewer

handed the respondent a card containing relationship

categories and asked, ‘‘How is [NAME] related to [THE

REFERENCE PERSON]?’’ for each person.

4. Hispanic Origin. Hispanic origin was collected in a

series of questions. The first question was, ‘‘Is anyone

of Spanish, Hispanic, or Latino origin?’’ If the response

was ‘‘yes,’’ the interviewer asked, ‘‘Who is?’’ followed

by ‘‘Is there anyone else of Spanish, Hispanic, or

Latino origin?’’ until the response was ‘‘no.’’

If anyone was mentioned as being of Hispanic origin,

the interviewer asked, ‘‘Is [NAME] of Mexican, Puerto

Rican, Cuban, or some other Spanish origin?’’ for each

person mentioned.

5. Race. Race was also collected in a series of questions.

The interviewer referred the respondent to the part of

the card containing racial categories and said, ‘‘I’m

going to read a list of race categories. Please choose

one or more categories that best describe [NAME’S]

race.’’

If the respondent said, ‘‘American Indian or Alaska

Native,’’ the interviewer asked, ‘‘What is [NAME’S]

enrolled or principal tribe(s)?’’ The interviewer

recorded as many responses as given.

If the respondent said, ‘‘Asian,’’ the interviewer asked,

‘‘To what Asian group did [NAME] belong? Is [NAME]

Asian Indian, Chinese, Filipino, Japanese, Korean, Vietnamese, or, some other Asian group?’’ The interviewer

recorded as many responses as given.

If the respondent said, ‘‘Pacific Islander,’’ the interviewer said, ‘‘To what Pacific Islander group did

[NAME] belong? Is [NAME] Guamanian or Chamorro,

Samoan, or some other Pacific Islander group?’’ The

interviewer recorded as many responses as given.

At this point, the interviewer had a list of all reported current and Census Day residents and their demographic

characteristics for use in matching these residents to

residents reported on the census questionnaire for this

housing unit.

For households that reported moving into the sample

housing unit after Census Day, this information was

verified. The interviewer said to the respondent:

‘‘So, everyone you mentioned today moved into

<sample address> after April 1, 2000. Is that

correct?’’

If the information was correct, the interview was continued by asking the respondent if he or she knew and had

information about the residents of the sample housing

unit who lived there on Census Day. (This part of the interview was discussed in the section on movers.)

Residence Section

For all households in which at least one member lived at

the sample housing unit on Census Day, the interviewer

continued with a few questions that checked for two types

of special living situations that were potential sources of

duplicate enumerations. Respondents tended to forget

that household members may have been living or staying

at a place away from the sample housing unit. This may

have caused some persons to be reported more than once,

at the sample housing unit and again at other places

where they may have lived or stayed.

The first situation that had the potential to cause duplicate

enumerations was when a person may have lived at a

place that was not a private household on Census Day.

Since the Census Bureau did special enumerations at

9

The brackets containing name, age, and the Reference Person’s name were filled by the instrument. When speaking to the

respondent, ‘‘Are you’’ or other appropriate fillers replaced ‘‘Is

[NAME].’’

4–24 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
places such as college dorms, nursing homes, prisons,

and emergency shelters, the interviewer inquired if anyone was staying at any of these types of places by saying:

‘‘Your answers to the next few questions help us

count everyone at the right place. The Census

Bureau did a special count at all places where groups

of people stay. Examples include college dorms,

nursing homes, prisons, and emergency shelters. On

April 1, 2000, were any of the people you mentioned

today staying elsewhere at any of these types of

places?’’10

If the response was ‘‘yes,’’ the interviewer asked,

‘‘Who stayed at one of these types of places?’’

The next situation that could result in a duplicate enumeration was when a person might have had another residence. The interviewer said:

‘‘Some people have more than one place to live.

Examples include a second residence for work, a

friend’s or relative’s home, or a vacation home. On

April 1, 2000, did any of the people you mentioned

today have a residence other than <sample

address>?’’

If the response was ‘‘yes,’’ the interviewer asked,

‘‘Who had another residence?’’

For each person mentioned as having another residence,

the interviewer asked, ‘‘As of April 1, did [NAME] spend

most of the time at <sample address> or at the other residence?’’ If the response was, ‘‘I don’t know,’’ the interviewer asked:

‘‘Which of the following categories, most accurately

describes the amount of time [NAME] stays at the

other residence? A few days of each week; entire

weeks of each month; months at a time; or some

other period of time.’’

If the respondent still was not sure where the person

spent most of the time, there was a series of questions

designed to assign an amount of time spent at some

other residence, such as, ‘‘During a typical week, did

[NAME] spend more days at <sample address> or at the

other residence?’’ or ‘‘During a typical month, did [NAME]

spend more weeks at <sample address> or at the other

residence?’’

If these questions did not help the respondent decide

where the person spent ‘‘most of the time,’’ the person’s

residence was determined by asking:

‘‘Was [NAME] staying at <sample address> or the

other residence on April 1, 2000?’’

At this point, the interviewer had a reported list of current

and Census Day residents of the sample housing unit

developed through an extensive household listing procedure. The interviewer had obtained the demographic characteristics of the listed persons. Through questions on

mobility and other possible residences it had been determined:

• whether everyone listed in the household currently

should be considered a Census Day resident of the

sample housing unit

• whether anyone currently absent from the household

should be considered a Census Day resident.

Conclusion of Interview

The interviewer now was ready to conclude the interview.

Before concluding, there was one last check of the household listing. The first name, middle initial, last name, sex,

and age of each person listed as a current and Census Day

resident was shown on the screen. The interviewer, again,

showed the respondent the computer screen and asked,

‘‘Do I have the spelling, sex, and age correct for everyone?’’ If not, corrections could be made at this screen and

the respondent was asked to verify and/or change the

information until the respondent said that everything was

correct.

The interviewer asked the respondent for his/her telephone number by saying, ‘‘In case we need to contact you

again, may I please have your telephone number?’’ then

thanked the respondent and concluded the interview by

saying, ‘‘This concludes our interview. The Census Bureau

thanks you for your participation.’’

10An interviewer help screen was available with a complete list

of special enumeration places.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–25

U.S. Census Bureau, Census 2000
Attachment 4.

Insufficient Information for Matching and Follow-Up

The census person records were reviewed both by computer and clerically to identify people with insufficient

information for matching and follow-up. Only people with

sufficient information for matching and follow-up were

allowed to be processed in the matching and follow-up

interviewing phases of the person matching. The three

types of insufficient information were:

• The census people were not data-defined.

• The census people were data-defined, but computer

coded as insufficient information for matching and

follow-up.

• The census people were computer coded as sufficient

information, but converted clerically to insufficient

information for matching and follow-up.

The first type of census people who were not data-defined

were not included in the E sample. Only data-defined

people were included in the E sample. These data-defined

people create person records in the census.

Census Data-Defined

The term ‘‘data-defined’’ was a term that has been used in

the past at the Census Bureau to mean that a census person record has been created. The term ‘‘Total Persons’’ was

the total number of people counted in the census at a census housing unit. The term ‘‘Selected Persons’’ referred to

data-defined census people in a census household. The

difference was people who were not data-defined. These

people had no census person record. A whole person

imputation procedure was employed to create characteristic data in the census for these people.

Two characteristics were required to be data-defined,

where name counts as a characteristic. Name must have

had at least three characters in the first and last name

together. Other characteristics that could be used in the

counting were relationship, sex, race, Hispanic origin,

and either age or year of birth11. Census records were created on the HCUF for all data-defined people. Anyone who

was not data-defined was a whole person imputation.

The count of census people who were whole person imputations were identified separately from the other census

people with insufficient information for matching, because

they were treated differently in the Dual System Estimator.

The number of whole person imputations was subtracted

from the census count within post-strata. The E-sample

people who were data-defined but with insufficient information for matching were included in the count of erroneous enumerations, and were, thus, excluded from the

count of whole person imputations in the Dual System

Estimator.

The mail return census forms were designed to collect

characteristics for six people. However, space was provided for the names of the additional residents in households with seven to twelve people. The large household

follow-up operation attempted to obtain characteristics for

these people by telephone.

The exception was the enumerator questionnaire used in

nonresponse follow-up. There was space for five people,

but a continuation form was used to record data for persons six and above in large households.

There was some consideration given to using the names in

the long form roster for persons seven through twelve to

create person records and having them data-defined. However, it seemed preferable not to do this, and the A.C.E.

did not attempt to create additional census data-defined

11Person one did not automatically have a relationship of head

of household like it did in 1990, and the telephone number in

item 2, on the mail return questionnaire, did not count as a characteristic. The age and date of birth were examined together. If

age was present, age/year of birth counted as a characteristic. If

age was blank, but year of birth was present, then the age/year

of birth counted as a characteristic. If age and year of birth were

both blank, the age/date of birth did not count as a characteristic.

The month and day of birth were used in Dress Rehearsal in the

determination of counting the age/date of birth as a characteristic, but not in Census 2000.

4–26 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
people for these people with only names in large households. These people were whole person imputations.

The number of whole person imputations used in the Dual

System Estimator will correspond to the counts used in

the census.

Computer Coding of Insufficient Information for

Matching and Follow-Up for the E Sample

The A.C.E. requires a minimum amount of information for

matching and follow-up. The data-defined census people

were reviewed to identify the ones with sufficient information for matching and follow-up for A.C.E. The minimum

amount of data required for data-defined census people to

have sufficient information for matching and follow-up

was complete name and two characteristics.

Complete name was defined as:

• First name12, middle initial, and last name

• First name and last name

• First initial, middle initial, and last name

The A.C.E. used the same criteria for classifying age as

data-defined as the census, which is only age and year of

birth were used to determine if age was present in counting characteristics to determine if the person had enough

data to be data-defined in the census. In other words,

when the age and year of birth were both blank, month

and day of birth were not considered.

Clerical Coding of Insufficient Information for

Matching and Follow-Up for the E Sample

There were cases where the name was not blank, but was

too incomplete or unlikely to be real to permit matching

and follow-up. Census names like Mr. Doe, Donald Duck,

and White Female were coded insufficient information by

the clerical matchers. The computer could not recognize

names that were not real or were really incomplete names.

The retrieval system contained an image of the census

questionnaire. The image of the census questionnaire was

reviewed for census people coded as insufficient information for matching and follow-up to see if there was additional data that could be used to convert them to sufficient information for matching and follow-up. The data

capture system may have had problems reading the hand

written entries, or there may be information outside the

boxes on the census questionnaire. Names were obtained

from the roster on the image of the questionnaire for the

long forms. Children with first names and no last names

were converted to sufficient information for matching and

follow-up when the last name could be assumed from an

adult with first and last name in the household. These

updates to the names were captured into the matching

software, which was programmed to decide if the person

had sufficient information for matching and follow-up.

P-Sample Insufficient Information for Matching

and Follow-Up

The P-sample people were reviewed by computer to identify people with insufficient information for matching and

follow-up. The P-sample rules for sufficient information for

matching and follow-up were the same as the E-sample

rules, which was complete name and two characteristics.

Cases identified by the computer as missing sufficient

information were suppressed from viewing by the clerical

matchers to prevent errors in matching people with insufficient information for matching. There were fewer than

4,000 P-sample people computer coded with insufficient

information for matching and follow-up.

This computer review was established to avoid certain

types of clerical errors in matching. For example, names

like D K or Don’t Know (D or Don’t is the first name and K

or Know is the last name), R R (refused for the first name

and refused for the last name), or M Smith, which could

not be matched with certainty or, if treated as a nonmatch,

followed up with a high rate of success. The census might

have recorded a person with a complete name, which

might be matched by a clerk. If matching were allowed, it

would have been biased by what was enumerated in the

census. A match would have resulted if the names were

present at the address, and a nonmatch if the names were

not in the census. Since names like DK could not be followed up, they would have been coded as insufficient

information for matching and follow-up. Therefore, a

match would have been assigned when the census

obtained complete names, and unresolved when no match

was found. The best way to avoid a bias was to suppress

the P-sample cases computer coded as insufficient information for matching and treat them as unresolved.

The probability of a match was imputed for the P-sample

people coded as insufficient information for matching and

follow-up. They were treated in the same way as other

P-sample people with unresolved match status. If the

whole household had insufficient information for matching and follow-up, the people were removed and converted to noninterview status.

12The minimum number of characters to be a name was two.

Two characters were required in the first name and two characters in the last name.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–27

U.S. Census Bureau, Census 2000
Attachment 5.

Final P Sample Person Match Codes

Matched

M = The P-sample and census people were matched. The P-sample person was a resident of the housing unit on Census Day.

MR = The follow-up interview determined that the matched person with unresolved residence status was a resident.

MU = The A.C.E. person was matched, but the follow-up interview obtained no useful

information to resolve the residence status for the matched person who had a

residence status of unresolved before follow-up. The P-sample person’s residence

status was unresolved.

Not Matched

NP = The P-sample person was not matched to a census person. There was no follow-up

for the whole household nonmatches from person interviews with household

members and the whole household nonmatches were not conflicting household

nonmatches.

NC = The P-sample nonmatch was found on the census roster. This person in a partial

nonmatch household was not matched to the census because only name was collected in the census for this person in a large household and the census person

was not data-defined. No follow-up interview was necessary.

NR = The P-sample person was not matched and was identified as a resident in the

block cluster on Census Day during the A.C.E. person follow-up interview.

NU = The P-sample person was not matched. Not enough information was collected

during the A.C.E. person follow-up interview to identify the P-sample person as a

resident or nonresident in the block cluster. The residence status for the P-sample

person was unresolved. This code was also used when the P-sample person was

followed up to collect geographic information and that information was not collected. The NU code was also used when the person did not live at the sample

address on Census Day and the Census Day address was not complete enough to

determine if the Census Day address was in the sample cluster.

Unresolved

P = There was not enough information collected during the follow-up interview to

determine if the possible match was a match or not. The match status of the

P-sample person was unresolved.

KI = Match not attempted for the P-sample person, because the person had insufficient

information for matching and follow-up. The name was blank or incomplete or the

name was complete, but the person had only one characteristic. This was a computer assigned code and these people were suppressed from view by the matchers.

KP = Match not attempted for the P-sample person, because (1) the name was incomplete, such as ‘‘Mr. Jones,’’ or (2) the name was not a valid name, such as ‘‘White

Female’’ or ‘‘Donald Duck.’’ This was a clerically assigned code.

4–28 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
Removed from

the P Sample

FP = The P-sample person was fictitious in this block cluster. The person was interviewed in error during the person interview. This person was not included in the

final P sample.

NL = The P-sample person did not live at the sample address or in the block cluster on

Census Day and was listed as a nonmover or outmover in error. This person was

removed from the list of P-sample people, since he or she was collected during the

person interview in error.

NN = The P-sample person was identified as a nonresident in the block cluster on Census Day during the A.C.E. person follow-up interview, because the person lived in

group quarters on Census Day, or had another residence where the person should

have been counted on Census Day according to census residence rules. This person was removed from the list of P-sample people, since he or she was collected

during the person interview in error.

DP = The P-sample person was a duplicate of another P-sample person.

MN = The A.C.E. person follow-up interview determined that the matched person with

unresolved residence status was not a resident in this housing unit or in this block

cluster. The person was no longer in the list of P-sample people.

GP = The P-sample person was removed, because the person interview was conducted

at a housing unit that exists outside the sample cluster. The person follow-up identified this housing unit as a P-sample geocoding error.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–29

U.S. Census Bureau, Census 2000
Attachment 6.

E-Sample Person Enumeration Codes

Correctly

Enumerated

M = The P-sample and E-sample people were matched. The E-sample person was correctly enumerated.

CE = The E-sample nonmatch was identified as correctly enumerated during the A.C.E.

person follow-up interview.

MR = The A.C.E. person follow-up interview determined that the matched person with

unresolved residence status was a resident.

Erroneously

Enumerated13

GE = The E-sample person was erroneously enumerated in this block cluster, because

the census housing unit was a geocoding error (i.e., counted in the wrong block

cluster). The E-sample person should have been enumerated elsewhere in the

census.

EE = The E-sample nonmatch was identified during the person follow-up interview as

erroneously enumerated.

FE = The E-sample nonmatch was determined to be fictitious in this block cluster during

the follow-up interview. The person may have existed, but should not have been

enumerated in the census within this block cluster. The E-sample person was erroneously enumerated in the census in this block cluster.

DE = The E-sample person was a duplicate of another E-sample person. The code was

also used when the E-sample person was a duplicate of a census person in a surrounding block. The people in the E-sample housing unit were erroneously enumerated, because they were counted accurately in the surrounding block and

duplicated in the sample cluster.

MN = The A.C.E. person follow-up interview determined that the matched person with

unresolved residence status was not a resident in this housing unit or in this block

cluster. The E-sample person was an erroneous enumeration.

KE = Match not attempted for the E-sample person. The name was blank or incomplete

or the name was complete, but the person had only one characteristic. The name

was incomplete or not a valid name, such as ‘‘Child Jones,’’ or ‘‘Mickey Mouse.’’

13The E-sample people who were duplicated with non-E-sample people were not full erroneous enumerations. See the section on

Duplicate Search Within Cluster in this chapter for a discussion of the probability of erroneous enumeration when there was duplication

between a census person in the E sample and a non-E-sample person.

4–30 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
Unresolved

UE = Not enough information was collected during the A.C.E. person follow-up interview to identify the E-sample person as correctly or erroneously enumerated in the

block cluster. The enumeration status for the E-sample person was unresolved. The

UE code was also used when the person did not live at the sample address on Census Day and the Census Day address was not complete enough to determine if the

Census Day address was in the sample cluster. This code was also used when the

E-sample person was followed up to collect geographic information and that information was not collected.

MU = The E-sample person was matched, but the follow-up interview obtained no useful

information to resolve the residence status for the matched person who had a residence status of unresolved before follow-up. The E-sample person’s enumeration

status was unresolved.

P = There was not enough information collected during the follow-up interview to

determine if the possible match was a match or not. The match status of the

P-sample person was unresolved.

GU = The geographic work for the targeted extended search was unresolved. The code

had the same definition in both the before and after follow-up matching. The difference was in after follow-up, the code was only used in the list/enumerate clusters. The field work for the targeted extended search was not done or the block

number on the form was not in the surrounding blocks, in the block cluster, or on

the map. It was not clear where the housing unit was located.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–31

U.S. Census Bureau, Census 2000
Attachment 7.

Final P-Sample Person Residence Status Codes

Resident

M = The P-sample and census people were matched.

MR = The follow-up interview determined that the matched person with unresolved

residence status was a resident.

NR = The P-sample person was not matched and was identified as a resident in the

block cluster on Census Day during the A.C.E. person follow-up interview. The

P-sample person was missed in the census.

NP = The P-sample person was not matched to a census person. There was no follow-up

for the whole household nonmatches from person interviews with household

members and the whole household nonmatches were not conflicting household

nonmatches. These people were considered residents of the housing unit on

Census Day.

NC = The P-sample nonmatch was found on the census roster. This person in a partial

nonmatch household was not matched to the census because only name was

collected in the census for this person in a large household and the census person

was not data-defined. No follow-up interview was necessary.

Nonresident

FP = The P-sample person was fictitious in this block cluster. The person was interviewed in error during the person interview. This person was not included in the

final P sample.

NL = The P-sample person did not live at the sample address or in the block cluster on

Census Day and was listed as a nonmover or outmover in error. This person was

removed from the list of P-sample people, since he or she was collected during the

person interview in error.

NN = The P-sample person was identified as a nonresident in the block cluster on

Census Day during the A.C.E. person follow-up interview, because the person lived

in group quarters on Census Day or had another residence where the person

should have been counted on Census Day according to census residence rules.

This person was removed from the list of P-sample people, since he or she was

collected during the person interview in error.

DP = The P-sample person was a duplicate of another P-sample person.

MN = The A.C.E. person follow-up interview determined that the matched person with

unresolved residence status was not a resident in this housing unit or in this block

cluster. The person was no longer in the list of P-sample people.

GP = The P-sample person was removed because the person interview was conducted

at a housing unit that exists outside the sample cluster. The person follow-up

identified this housing unit as a P-sample geocoding error.

4–32 Section I—Chapter 4 A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000
Unresolved

MU = The A.C.E. person was matched, but the follow-up interview obtained no useful

information to resolve the residence status for the matched person who had a

residence status of unresolved before follow-up. The P-sample person’s residence

status was unresolved.

NU = The P-sample person was not matched. Not enough information was collected

during the A.C.E. person follow-up interview to identify the P-sample person as a

resident or nonresident in the block cluster. The residence status for the P-sample

person was unresolved. This code was also used when the P-sample person was

followed up to collect geographic information and that information was not collected. The NU code was also used when the person did not live at the sample

address on Census Day and the Census Day address was not complete enough to

determine if the Census Day address was in the sample cluster.

P = There was not enough information collected during the follow-up interview to

determine if the possible match was a match or not. The residence status of the

P-sample person was unresolved.

KI = Match not attempted for the P-sample person, because the person had insufficient

information for matching and follow-up. The name was blank or incomplete or

the name was complete, but the person had only one characteristic. This was a

computer assigned code and these people were suppressed from view by the

matchers.

KP = Match not attempted for the P-sample person, because (1) the name was incomplete, such as ‘‘Mr. Jones,’’ or (2) the name was not a valid name, such as ‘‘White

Female’’ or ‘‘Donald Duck.’’ This was a clerically assigned code.

A.C.E. Field and Processing Activities Section I—Chapter 4 4–33

U.S. Census Bureau, Census 2000
FORM D-1302 (6-23-99)

Section 4 – LISTING PAGE

Hello, I’m (Your name) from the U.S. Bureau of the Census. Here’s my identification. We are listing addresses as part of the Census 2000, and I have a few questions to ask you.

Fill items 9 and 10 in areas without city style addresses (see cover, Section 1, item 5).

(9) Householder name

MI

Last

MULTI-UNIT ADDRESS '

(15a)

Basement

Canvass the multi-unit basic address and enter the number of units on each floor.

(15d)

respondent total, resolve the difference. If there is a difference between your canvass and

Enter the

correct total in 16.

(16)

this basic address.units, occupied or vacant, atTotal number of housing

Proxy*HH member*

(1) Line No. (2) Block No.(6) Map Spot No. – Do not fill for Mobile Home Park.

(3) House No. (4a) Road/street name (5a) Rural

(7) PO Box No. (8) ZIP Code

(11a) How would you describe this type of address? (12) REMARKS (Do

description.)space for locationNOT use this

1st floor 2nd floor 3rd floor 4th floor (17) Information obtained from: 6th floor

ObservationManager*

(10) Physical location description or E-911 address (Maximum 50 characters)

buildings – Detached or attached to one or moreOne family house (occupied or vacant) –

1

Go to 11b.

(example: apartment house) – Basic address with two or more housing units

Go to 15a.

Mobile home/trailer, construction, skip 15 and go to 16.However, if under construction or future

NOT in a park – Go to 17.

vacant) in special place – One family house (occupied or

In 12, enter

person. Then go to 13.name of special place and contact

Go to 17.goods – household Storage of

SINGLE UNIT ADDRESS

(14)

converted into apartments where other people might live?Besides the unit(s) you have just mentioned, has this address been

Yes – How many ADDITIONAL apartments? ...

'

If sum of 13 plus 14 is: 1 – Go to 16 and 17.

No

10th floor

(15b) Total units from your canvass .(15c) How many apartments, occupied 

or vacant, are there at (basic address) ?

8th floor 9th floor Attic

If more floors, enter additional floor information 

(example: "5 APTS 14th FLR")

7th floor

Mobile home/trailer park – Go to Mobile HomePark Page, Section 6. 2 or more – more housing units" and go to 15a. Change item 11a to "Basic address with two or

1

(11b) Unit status

Other, for example: Occupied camper,tent, van, boat, etc. – Go to 17.

(started) .Under construction

then 17.Go to 12, Other – 

5421 6

432

75

If multi-unit, go to the Multi-Unit Page.

OFFICE USE ONLY

5th floor

11th floor 12th floor

1 2

21

43

17.then 12,Go to 

⎭⎬⎫

(13)

there at How many (housing units/living quarters/apartments), occupied or vacant, are

(basic address)? Example: basement apartment, garage apartment . . occupancy – 

and intended forOccupied, or vacant

Go to 13.

0001

8

Box No.(5b) 

Number Letter

housing units in special place – Basic address with two or more

In 12,

contact person. Then go to 15a.enter name of special place and

6

Boarded up.Unfit for habitation(not started)Future construction 3

*Respondent name Telephone No.

Rte. No.

First

Fill items 9 and 10 in areas without city style addresses (see cover, Section 1, item 5).

(9) Householder name

MI

Last

MULTI-UNIT ADDRESS '

(15a)

Basement

Canvass the multi-unit basic address and enter the number of units on each floor.

(15d)

respondent total, resolve the difference. If there is a difference between your canvass and

Enter the

correct total in 16.

(16)

this basic address.units, occupied or vacant, atTotal number of housing

Proxy*HH member*

(1) Line No. (2) Block No.(6) Map Spot No. – Do not fill for Mobile Home Park.

(3) House No. (4a) Road/street name (5a) Rural

(7) PO Box No. (8) ZIP Code

(11a) How would you describe this type of address? (12) REMARKS (Do

description.)space for locationNOT use this

1st floor 2nd floor 3rd floor 4th floor (17) Information obtained from: 6th floor

ObservationManager*

(10) Physical location description or E-911 address (Maximum 50 characters)

buildings – Detached or attached to one or moreOne family house (occupied or vacant) –

2

Go to 11b.

(example: apartment house) – Basic address with two or more housing units

Go to 15a.

Mobile home/trailer, construction, skip 15 and go to 16.However, if under construction or future

NOT in a park – Go to 17.

vacant) in special place – One family house (occupied or

In 12, enter

person. Then go to 13.name of special place and contact

Go to 17.goods – household Storage of

SINGLE UNIT ADDRESS

(14)

converted into apartments where other people might live?Besides the unit(s) you have just mentioned, has this address been

Yes – How many ADDITIONAL apartments? ...

'

If sum of 13 plus 14 is: 1 – Go to 16 and 17.

No

10th floor

(15b) Total units from your canvass .(15c) How many apartments, occupied 

or vacant, are there at (basic address) ?

8th floor 9th floor Attic

If more floors, enter additional floor information 

(example: "5 APTS 14th FLR")

7th floor

Mobile home/trailer park – Go to Mobile HomePark Page, Section 6. 2 or more – more housing units" and go to 15a. Change item 11a to "Basic address with two or

1

(11b) Unit status

Other, for example: Occupied camper,tent, van, boat, etc. – Go to 17.

(started) .Under construction

then 17.Go to 12, Other – 

5421 6

432

75

If multi-unit, go to the Multi-Unit Page.

OFFICE USE ONLY

5th floor

11th floor 12th floor

1 2

21

43

17.then 12,Go to 

⎭⎬⎫

(13)

there at How many (housing units/living quarters/apartments), occupied or vacant, are

(basic address)? Example: basement apartment, garage apartment . . occupancy – 

and intended forOccupied, or vacant

Go to 13.

8

Box No.(5b) 

Number Letter

housing units in special place – Basic address with two or more

In 12,

contact person. Then go to 15a.enter name of special place and

6

Boarded up.Unfit for habitation(not started)Future construction 3

*Respondent name Telephone No.

Rte. No.

First

A.C.E. Field and Processing Activities

U.S. Census Bureau, Census 2000

4–34 Section I — Chapter 4

Figure 4-1.

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Chapter 5.

Targeted Extended Search

INTRODUCTION

The concept behind the dual system estimate is to estimate the census omission rate using the P sample and the

erroneous enumeration rate using the E sample. The complete definition of being omitted from or erroneously enumerated in the census includes the concept of ‘‘location,’’

that is, a successful enumeration must have located the

person in the right place. ‘‘Right location’’ in the census

means anywhere in the block where the reported housing

unit address was located, or in the ‘‘search area,’’ defined

as one ring of adjacent blocks. The operation concerned

with locating and matching the persons in the surrounding

areas is ‘‘Targeted Extended Search,’’ or TES. The name

was chosen because, unlike the similar procedure in the

1990 Post-Enumeration Survey (PES) where the surrounding area of every cluster was searched, the A.C.E. search

was ‘‘targeted’’ in two ways:

1. Results from the initial housing unit matching operation were used to select the housing units that are

candidates for TES.

2. In most cases, only clusters that include TES-eligible

housing units were included in TES.

This chapter focuses on the statistical methods used in

TES. A.C.E. field and processing activities, including TES,

are described in Chapter 4.

Overview

The 1990 PES included a search in all blocks surrounding

each sample cluster. Every person in every house in every

block adjoining every sample block cluster was included

in the search. This was determined to be burdensome in

terms of time, cost, and perhaps mental fatigue on the

part of matchers performing low-payoff searches (Hogan,

1993). To improve efficiency, the Census 2000 A.C.E. took

a more focused (i.e. ‘‘targeted’’) approach in selecting clusters, defining search areas, and determining which housing units and residents would be part of surrounding

block operations.

The Census 2000 A.C.E. search operation differed from

the 1990 PES in four primary ways:

1. Search area definition.

2. Amount of searching.

3. Persons eligible for search.

4. TES weighting.

Search Area Definition

The search area for the 2000 A.C.E. was limited to either

just the sample block cluster or one ring of adjacent

blocks. An adjacent block is one that touches the cluster

of sample blocks at one or more points. This definition

includes the blocks that touch the corner of the block cluster. Results from empirical research, using Census 1998

Dress Rehearsal data, show that the additional benefits

of using two rings of surrounding blocks are negligible

(Wolfgang, 1999).

Amount of Searching

There were two important differences between the extent

of searching in the 1990 PES and the 2000 A.C.E.:

1. Only about 20 percent of A.C.E. block clusters had

their surrounding areas searched, whereas in 1990 the

surrounding area of every block cluster was searched.

2. The search was targeted (in most cases) to only

housing units identified as being likely to exhibit

geocoding error; in 1990, all persons in surrounding

areas were eligible for search.

The clusters with a high number of potential geocoding

errors were identified from the results of the initial housing unit matching operation and subsequent field

follow-up (see Chapter 4). These were A.C.E. block clusters with a large number of Independent Listing housing

units not found in the January 2000 Census Address List.

These types of nonmatches are possibly census geocoding

errors of exclusion (i.e. not included in the census within

the sample area although they should have been). On the

census side, A.C.E. block clusters with a large number of

census geocoding errors are likely to be errors of inclusion

(i.e. reported by the census in the block cluster, although

the unit is physically outside the A.C.E. block cluster).

These two types of housing units were eligible to be in the

extended search as part of TES operations, and are thus

TES-eligible housing units.

Any cluster that included at least one potential census

geocoding error, of either inclusion or exclusion, was eligible to have TES operations performed in it and is termed

a TES-eligible cluster. Clusters with no such potential

geocoding errors became non-TES-eligible. The clusters

in which TES was actually done are TES clusters, and

were selected from among the TES-eligible clusters either

with certainty or by probability sampling.

Targeted Extended Search Section I—Chapter 5 5–1

U.S. Census Bureau, Census 2000
Results from the 1990 PES show that geocoding errors are

highly clustered. Slightly over 77 percent of the whole

household nonmatches were concentrated in less than

one-fourth of the PES sample block clusters. On the other

hand, about 72 percent of the census geocoding errors

were found in less than 3 percent of the PES sample block

clusters. TES is a good example of Deming’s ‘‘80-20’’

guideline—80 percent of the benefits are realized by solving 20 percent of the problems.

Persons Eligible for Search

In order to be included in TES operations, a person must

live in:

• a TES cluster; and

• a TES-eligible housing unit

A person in a housing unit that was not a TES-eligible

housing unit, was a non-TES person, and thus, was not

directly affected by TES operations. Any person in a

TES-eligible housing unit was a TES person, unless

someone in the housing unit matched (i.e. someone is

confirmed to be not a TES person). TES persons in clusters

that were not selected for TES operations were identified,

but did not have TES operations applied. Instead, these

cases were effectively removed from the sample by having

an assigned weight of zero. They were represented by

persons in other TES clusters selected by sampling.

TES Weighting

Every selected TES cluster was assigned a sampling weight

equal to the reciprocal of its selection probability. This TES

cluster weight was assigned to all TES persons in that

cluster and was multiplied by their A.C.E. sampling

weights to produce their TES-adjusted weights. The TESadjusted weight for TES persons in clusters not selected

for TES is zero. In this way, the TES persons in the TES

clusters represent the TES persons in non-TES clusters. All

elements of the dual system estimate (DSE) calculation,

except those involving inmovers, can be affected by the

TES weighting because TES persons can be nonmovers

or outmovers, matches or nonmatches, and correct or

erroneous enumerations.

CLUSTER SAMPLING

The decision to select 20 percent of the A.C.E. block clusters for TES was based on the assumption that most of the

TES-eligible housing units and persons would be concentrated in a small fraction of the block clusters. Hence,

most of the benefits of a complete surrounding area

search could be realized at a substantial reduction in cost,

if a disproportionate share of the effort was concentrated

in the clusters with the greatest likely payoff—the ones

with the most TES-eligible housing units and persons.

Targeting these clusters would achieve one of the principal goals of the surrounding areas search—variance

reduction. However, it is of at least equal importance that

the surrounding area search be ‘‘balanced.’’ There are two

ways TES could have been out of balance: 1) the geographical area included in the search could have differed

between the P and E samples; 2) the TES block cluster

sampling could have selected clusters containing errors of

inclusion with greater or less likelihood than clusters with

errors of exclusion. To achieve the balancing in sample

selection, it was necessary for each cluster with

TES-eligible housing units and persons to have some

probability of being selected for TES and be weighted by

the inverse of the selection probability.

The information available for TES selection included the

results of the initial housing unit matching, which

included the results from the housing unit follow-up.

Housing unit follow-up indicated, among other things, the

count of potential geocoding errors of inclusion and exclusion. The geocoding errors of inclusion were census units

found outside the cluster. Potential geocoding errors of

exclusion were coded as address nonmatches in the

independent listing. The combined number of census

geocoding errors and independent listing address nonmatches were considered to be the number of potential

geocoding errors in each cluster. The probability that any

cluster would be selected for TES depended on the count

of its potential geocoding errors for most clusters.

Exceptions are relisted clusters and clusters that were

enumerated in the census using the List/Enumerate methodology. Those clusters did not go through housing unit

matching and follow-up.

A housing unit that represented a potential geocoding

error could have been discovered by TES operations to be

a geocoding error or an actual coverage error. Putting a

particular housing unit in the category of ‘‘potential’’ made

it, and the persons living in it, eligible for TES. This search

was intended to determine whether the housing unit and

persons were geocoded incorrectly into a neighboring

block, in which case they would be counted as correctly

enumerated, or were truly enumeration errors.

Hence, the following TES selection strategy was implemented:

• Clusters that did not have counts of potential geocoding

errors available at the time of the TES sampling operation were assigned to a separate TES procedure. Clusters that were relisted (which were later included in TES

with certainty) or enumerated using the List/Enumerate

methodology (which were ultimately excluded from TES)

fall into this group.

• The 5 percent of clusters that included the largest number of housing units that were potential geocoding

errors were included in TES with certainty.

• The 5 percent of clusters that had the most housing

units that were potential geocoding errors, when

weighted by their A.C.E. cluster weight, were also

5–2 Section I—Chapter 5 Targeted Extended Search

U.S. Census Bureau, Census 2000
included in TES with certainty. The 5 percent of clusters

included in the above bullet for having the most

unweighted cases were excluded before this step was

performed, so that a total of 10 percent of the A.C.E.

clusters were selected based on the two certainty

criteria.

• All clusters with at least one potential geocoding error

housing unit were assigned to a noncertainty stratum to

be sampled at a uniform national rate to be included in

TES. The sampling rate was set so that the overall size

of the TES sample, including those selected by certainty

and by sampling, totaled 20 percent of A.C.E. clusters

(excluding the first group).

Clusters with no potential geocoding errors were excluded

from TES selection since there were no housing units or

persons that were candidates for TES operations. This

creates a potential for a small bias in TES, because housing units added to or deleted from the address lists after

the selection of TES clusters were not eligible for TES

operations.

Sampling Methodology

For the United States as a whole, there were 11,303 A.C.E.

clusters. Of these, 420 were excluded from TES selection

because they used the List/Enumerate census method. Of

the remaining 10,883 clusters, 20 percent, or 2,177 were

selected for TES. Of the eligible clusters, 62 were relist

clusters and were not part of the normal TES selection.

(These clusters did not count as part of the 2,177 TES

target sample size.) Five percent of the sampling universe,

or 544 clusters, with the most potential geocoding errors

were selected for TES with certainty and assigned a TES

weight of 1. Of the remaining clusters, an additional 544

with the most potential geocoding errors, when weighted

by the A.C.E. cluster weight, were also selected with

certainty and assigned a TES weight of 1.

Of the remaining clusters that included at least one potential geocoding error, 1,089 were selected using systematic

random sampling with equal probability. There were 5,326

clusters in the noncertainty stratum (i.e. all those that

were not already selected by one of the other means and

that contained at least one potential geocoding errors),

so the selected clusters were assigned a TES weight of

5,326 divided by 1,089 or 4.8907. The remaining 4,407

clusters were out of scope for TES because they had no

identified potential geocoding errors.

For purposes of drawing the systematic sample, clusters

were sorted in the order:

• State

• First-phase Sampling Stratum

• Second-phase Sampling Stratum

• Small Block Cluster Sampling Stratum

• Cluster Number

The first four characteristics are the same ones used to

select the A.C.E. sample. Sorting clusters in this order for

TES improved the representativeness of TES with respect

to the national A.C.E. sample. After sorting in this order,

the clusters were systematically sampled with equal probability using a take-every of 4.8907 and were assigned a

TES weight equal to that figure.

Results of Cluster Sampling

The TES sample included 2,239 block clusters out of

11,303, or 19.8 percent. (Originally it had been intended

to include a small number of List/Enumerate clusters in

TES, and some sample was set aside for them but never

used.) The clusters included 45,000 E-sample and 77,000

P-sample housing units, representing 80 and 73 percent of

TES-eligible units in their respective samples before subsampling within large block clusters was performed.

Because of differences in procedures, more E-sample units

got into TES by certainty (76 percent versus 66 percent),

while more P-sample units were selected by sampling, 7

percent to 5 percent. TES units represent about 7 percent

of the housing units resulting from initial housing unit

matching. (See Table 5-1.) This was not the final number

of housing units included in TES field operations because:

• Subsampling within large block clusters reduced the

number of A.C.E. housing units in clusters with 80 or

more housing units; and

• Housing unit counts for Relist clusters were not

available at the time the sample was selected

Subsampling within large block clusters reduced the final

TES workload to 12,000 E-sample and 18,000 P-sample

housing units.

Targeted Extended Search Section I—Chapter 5 5–3

U.S. Census Bureau, Census 2000
Table 5-1. TES Sampling Frame and Selection Results

Clusters

Potential geocoding errors

Total potential errors Errors of inclusion Errors of exclusion

Number Percent Number Percent Number Percent

Total ................. 11,303 122,440 100 45,053 100 77,387 100

Out-of-scope .............. 4,827 0 ... 0 ... 0 ...

List/Enumerate . . . . . . . 420 0 ... 0 ... 0 ...

No TES HUs . . . . . . . . . 4,407 0 ... 0 ... 0 ...

Eligible for TES . ........... 6,476 122,440 100 45,053 100 77,387 100

Certainty .................. 1,150 85,309 70 34,089 76 51,220 66

Top weighted . . . . . . . . . 544 11,858 10 4,037 9 7,821 10

Top unweighted . . . . . . 544 73,451 60 30,052 67 43,399 56

Relist . . . . . . . . . . . . . . . 62 0* ... 0* ... 0* ...

Noncertainty .............. 5,326 37,131 30 10,964 24 26,167 34

Selected into sample . . 1,089 7,642 6 2,106 5 5,536 7

Not selected ......... 4,237 29,489 24 8,858 20 20,631 27

TES clusters . ............. 2,239 92,951 76 36,195 80 56,756 73

*TES units in Relist clusters had not been determined at the time the sample was selected.

Note: Percentages in table may not add to total due to rounding.

TES FIELD AND PROCESSING ACTIVITIES

Details on the operations involved in TES are described in

Chapter 4. In summary, the main activities are:

• Cluster selection (Spring 2000). This operation

selects the clusters for TES. Because of the need to

select the cluster sample at a particular time, the final

E and P samples had not been selected at the time of

this operation.

• Search for census units in surrounding blocks

(Summer 2000). Determines if census units erroneously included in the sample block cluster are located

within the surrounding ring of blocks. This field operation is described more fully in Chapter 4.

• Identify TES Persons (Fall 2000). An automated

activity performed at the National Processing Center

in Jeffersonville, Indiana. See Chapter 4 for more

information.

• Extend the search area to surrounding blocks for

TES persons (Fall 2000). The P-sample TES persons

were allowed to match to census records in the surrounding block. The E-sample TES persons were treated

as correct enumerations if the census unit was located

in a surrounding block. This was a clerical operation.

• Assign TES weights (Winter 2000/2001). TES persons identified in TES-eligible clusters were assigned the

TES weight associated with that cluster, either 1.0 for a

cluster selected with certainty or 4.8907 for a cluster

selected by sampling. TES persons in TES clusters not

selected into the sample were assigned a zero weight.

Adds and Deletes

The preliminary census address list of housing units as of

January 2000 was the source for the initial housing unit

matching on which TES is based. Since some housing units

on the January 2000 list were later deleted and others

added, the final list of census housing units did not

exactly match the initial housing unit matching counts

of potential geocode errors. Therefore, procedures were

necessary to update the TES identifications for adds and

deletes.

In the vast majority of cases, where adds and deletes were

not involved, P-sample housing units are TES-eligible if

they did not match to a census address. However, if a

P-sample unit was matched to an address during initial

housing unit matching, but that address was deleted, then

the unit was considered nonmatched. To adjust for deletions, P-sample persons in housing units that were

matched to deleted census housing units were flagged

as TES persons, as long as the unit did not contain any

persons matched within the sample block (i.e. non-TES

persons). This adjustment was performed only on persons

in TES clusters.

E-sample housing units that were added to the final census list after January 2000 could represent geocoding

errors, but they were not part of TES field operations.

Without field operations, persons in such units would

never be identified as surrounding block correct enumerations. Therefore, a correct enumeration probability was

imputed for such persons in TES clusters. The imputed

probability is the overall correct enumeration probability

of all resolved persons in geocoding error housing units in

the TES sample. See Chapter 6 for a description of the procedure.

5–4 Section I—Chapter 5 Targeted Extended Search

U.S. Census Bureau, Census 2000
Table 5-2. Effect of Census Address List Changes after January 2000

Count Weighted

Matches/ correct

enumerations

P sample - persons in housing units matched to deletes . . 2,319 2,036,564 675,892

E sample - geocode error adds . . . . . . . . . . . . . . . . . . . . . . . . . 53 15,307 14,915

TES IN DUAL SYSTEM ESTIMATION

Accounting for TES in the DSE calculation is primarily a

matter of applying weights properly. Every person in the

A.C.E. is either a TES person or a non-TES person, and

every A.C.E. cluster is either a TES cluster or a non-TES

cluster. Every TES person is assigned the TES weight of his

A.C.E. cluster. The calculation of the DSE requires the use

of seven distinct components, all but one of which represents the sum of the A.C.E. weights for some group of

persons in the A.C.E., including both TES and non-TES persons. Hence, six of the seven components represents a

weighted sum of TES and non-TES persons, the former

with their TES cluster weights applied.

Applying TES Weights

Every A.C.E. cluster including TES persons has a TES

weight, although that weight is zero if the cluster is not

selected for TES. A TES person must be weighted by the

associated TES weight. The A.C.E. weight is multiplied by

the TES weight to produce a person weight. TES weighting

does not affect the weight of non-TES persons. Their individual weights are the same as the A.C.E. weights.

Table 5-3. TES Weights by TES Status of the

Person and Cluster

TES cluster Non-TES cluster

TES persons . . . . . . . . . . . 1, if cluster in TES

with certainty

0

4.8907, if cluster

selected for TES by

sampling 0

Non-TES persons ....... 1 1

The issues related to inmovers, outmovers and noninterviews are the same for TES persons as for all other persons. From a calculation standpoint, the only effect that

TES status has on the dual system estimates is in applying

the cluster’s TES weight.

DSE Calculation

The DSE for Census 2000 is:

DSˆE  (DD) (

CE

Ne

) ( Nn Ni

Mn (

Mo

No

) Ni

)

where

DD  census data-defined persons

CE  estimated number of A.C.E. E-Sample

correct enumerations

Ne  number of A.C.E. E-Sample persons

Nn  estimated number of A.C.E. P-Sample

nonmovers

Ni  estimated number of A.C.E. P-Sample inmovers

No  estimated number of A.C.E. P-Sample

outmovers

Mn  estimated number of A.C.E. P-Sample

nonmover matches

Mo  estimated number of A.C.E. P-Sample

outmover matches

The estimator has seven A.C.E. distinct components (plus

DD from the census enumeration). Six of the seven components represent a weighted sum of persons, including

both TES- and non-TES persons.

Other than inmovers, who cannot be TES persons, each of

the DSE components is expressed as:

n



i1

np



j1

wij

* mij xij 

n



i1

np



j 1

wij

* mij yij 

n



i1

np



j1

w ij

* tij mijz ij

where

i  cluster index

j  person index

n  number of block clusters in the A.C.E. sample

np  number of persons in block cluster i

xij  1 if the person is not a TES person, 0

otherwise

yij  1 if the person is a TES person and is in the TES

sample with certainty, 0 otherwise

zij  1 if the person is a TES person and is in the

TES systematic sample, 0 otherwise

mij  characteristic of interest, match, correct enumeration,

E-sample person, or P-sample person

wij

*  weight used for estimation (includes inverse of

the probability of selection for A.C.E.,

adjustment for household noninterview

and weight trimming)

tij  TES sampling weight, the TES systematic sample

take-every

EFFECTS OF TES ON DUAL SYSTEM ESTIMATION

The principal effect of TES in Census 2000 is approximately what was expected–the overall correct enumeration rate was 2.9 percent higher with TES, than it would

Targeted Extended Search Section I—Chapter 5 5–5

U.S. Census Bureau, Census 2000
Table 5-4. Effect of TES at the National Level

With TES Without TES Difference* Effect of TES

(1) (2) (1)-(2) (1)/(2)

E sample

Persons (Ne) ......................................... 264,578,862 264,634,794 (55,932)** 1.000

Correct Enumerations (CE) ............................ 252,096,238 244,387,951 7,708,288 1.032

CE Rate (%) . ........................................ 95.3 92.3 2.9 1.032

P sample

Persons (Np) ......................................... 263,037,259 262,906,916 130,343** 1.000

Matches ............................................. 240,878,622 230,681,205 10,197,418 1.044

Match Rate (%) . ..................................... 91.6 87.7 3.8 1.044

Ratio of CE to Match Rate ................................. 1.040 1.053 (0.012) 0.989

Coefficient of Variation for Ratio . . . ......................... 0.129 0.314 (0.197) 0.405

*Percentages were calculated on unrounded values.

**The weighted E- and P-sample sizes differed slightly because of variance in TES sampling.

Note: Table above reflects national totals without regard to post-stratification and differs from other totals in which post-stratum totals were

aggregated.

have been without, and the overall match rate was 3.8

percent higher (see Table 5-4). The larger increase in the

match rate, as compared to the correct enumeration rate,

occurred because there were more identified potential

geocoding errors in the P sample than in the E sample.

The difference in the number of matches versus correct

enumerations (10.2 million and 7.7 million, respectively)

from TES had been a source of concern, since it suggested

the possibility of ‘‘balancing error.’’ Balancing error would

have occurred if the geographic boundaries included in

the P and E samples had not been consistent. For instance,

suppose the P sample was allowed to match to census persons in housing units beyond the first ring, while a census

unit could only be classified correct if it was within the

first ring. Adams and Liu (2001) performed an evaluation

study of the P-sample housing units in A.C.E. and concluded that the main source of the measured imbalance

was geocoding error in the P sample.

Table 5-4 shows that TES increased the number of correct

enumerations from 244.4 million to 252.1 million and

matches from 230.7 million to 240.9 million. Before TES,

there had been 20.2 million erroneous enumerations, of

which 7.7 million were geocoding errors that were classified as correct enumerations by TES. TES also allowed

10.2 million additional P-sample matches to occur out of

32.2 million original nonmatches. Improving both the

match and correct enumeration rate this much significantly improves the variance of the DSE, since over 90 percent of people match or are correctly enumerated.

Table 5-5 shows the significant contribution that TES

makes to variance reduction. For the A.C.E. considered as

a whole (i.e. a direct DSE of the entire population without

post-stratification), the coefficient of variation is 0.129

percent with TES and 0.314 percent without TES.

Table 5-5. Effect of TES on Coefficient of

Variation (CV)

Standard

error

CV

(percent)

With TES ............................. 355,451 0.129

Without TES .......................... 877,664 0.314

Note: Table above reflects national totals without regard to poststratification and differs from other totals in which post-stratum totals

were aggregated.

At the post-stratum level, the average improvement in the

DSE standard error is about 33 percent. The gains in precision as measured by variance show that TES makes dual

system estimates more precise, and that TES improves the

quality of the A.C.E., so long as it does not make the DSEs

less accurate by introducing bias. The coefficient of variation was reduced for a majority of the collapsed poststrata (448 original post-strata were collapsed into 416

post-strata for DSE calculation purposes).

Table 5-6. Effect of TES on Post-Stratum CVs

[Percent]

With TES Without TES

Average CV .......................... 2.07 2.66

Median CV ........................... 1.81 2.32

Average CV weighted by census count . . 1.30 1.93

5–6 Section I—Chapter 5 Targeted Extended Search

U.S. Census Bureau, Census 2000
Chapter 6.

Missing Data Procedures

INTRODUCTION

This chapter gives an overview of missing data procedures

for the Census 2000 Accuracy and Coverage Evaluation

(A.C.E.). General background information is presented

first, while the following sections describe three types of

procedures used to account for data missing in the A.C.E.

The noninterview adjustment accounts for wholehousehold nonresponse. The next section describes the

characteristic imputation used to assign values for specific

missing demographic variables. Finally, for persons with

unresolved match, residence, or enumeration status, a

probability of matching, residence, or correct enumeration

was assigned according to procedures.

As missing data in the A.C.E. were addressed after the

completion of the field operations that produced the

A.C.E. data files, a knowledge of the field activities and the

circumstances that led to specific outcomes is necessary

to understand the motivation for these procedures. For

this information, the reader is referred to Chapter 4 for

details on the field operations.

The missing data procedures used in the Census 2000

A.C.E. were similar to those used on the Integrated Coverage Measurement (ICM) sample in the Census 2000 Dress

Rehearsal. An outline of the ICM procedures and a summary of related research are given in Ikeda, Kearney, and

Petroni (1998). Kearney and Ikeda (1999) provide an overview of the results from the Dress Rehearsal. For detailed

missing data procedures for the 2000 A.C.E., see Cantwell

(2000) and Ikeda and McGrath (2001). A few basic results

on missing data from 2000 are found in this chapter;

many more results can be found in Cantwell et al. (2001).

BACKGROUND

Before dual system estimates were calculated, it was necessary to account for missing information from the interviews of P-sample people and from the matching operations. It should be noted that the term ‘‘missing data’’

applies after all follow-up attempts have been made.

Chapter 4 describes some of the extensive field procedures conducted to minimize the resulting level of such

missing data. These activities – all specified in

advance – included multiple attempts at interviews, the

use of highly trained clerks and technicians to resolve

cases, and the follow up of cases where a second interview could provide additional required information.

There were two main types of missing data in the A.C.E.

and three processes used to correct for them. The first

type was unit missing data. These were households that

were not interviewed in the A.C.E. either because they

could not be contacted or because the interview was

refused. The noninterview adjustment process spread the

weights of these households among households that were

interviewed in the same noninterview cell.

The other type of missing data was item missing data.

This situation occurred when some information for a

household or person was available but portions of the

data were missing. Two groups of missing data items had

to be addressed: demographic items and items relating to

a specific operational status. Missing age, sex, tenure,

race, and Hispanic origin were imputed to allow the production of estimates of the census undercount by these

characteristics, and because they were necessary to assign

people to post-strata.

For a small number of people in the P sample, there was

not enough information available to determine the match

status (whether or not the person matched to someone in

the census in the appropriate search area) or the residence

status (whether or not the person was living in the block

cluster on Census Day). Determining residence status was

important for the P sample because Census Day residents

of the block clusters in the sample were used to estimate

the proportion of the population who were not counted in

the census. Similarly, some people in the E sample lacked

information to determine whether the person was correctly enumerated. Such cases where status could not be

determined were said to be ‘‘unresolved.’’ Generally for

cases with missing status a probability of residence,

match, or correct enumeration was assigned based on

information available about the specific case and about

cases with similar characteristics.

In the 1990 Post-Enumeration Survey, a hierarchical logistic regression program was used to calculate probabilities

of match and correct enumeration for cases with missing

information. (Due to the procedure used to treat movers in

1990, residence status played a different role then.) The

model and some results are discussed in Belin et al.

(1993). During census tests in 1995 and 1996, certain

components of missing data were addressed using logistic

regression, while for other components a simpler procedure called imputation cell estimation was used. The latter

procedure was used exclusively in the Census 2000 Dress

Rehearsal in 1998. Data from these tests indicate that the

exact method of calculating probabilities for unresolved

status (match, residence, or correct enumeration) has a

Missing Data Procedures Section I—Chapter 6 6–1

U.S. Census Bureau, Census 2000
minor effect on the dual system estimates. More details of

this research can be found in Ikeda (1997, 1998, 1998b,

and 1998c) and Cantwell (1999). Based on these findings

and concerns about implementing logistic regression in a

production environment, the simpler procedure (that is,

imputation cell estimation) was used to estimate missing

data items in the A.C.E.

Noninterview Adjustment (Household Level)

At the time of the Computer Assisted Personal Interview

(CAPI), questions were asked to determine who lived in

the household on Interview Day and who lived there on

Census Day, and a mover status was assigned based on

the replies. Thus two rosters were created for each household–the Census Day roster and the Interview Day roster.

The A.C.E. used inmovers to estimate the number of

P-sample movers in the post-stratum, while using outmovers to estimate the match rate of the movers. This method

is referred to as Mover Procedure C or PES-C in the

research studies. See Chapter 4 for descriptions of the

terms nonmover, inmover, and outmover.

All inmovers and all nonmovers were generally assumed

to be A.C.E. Interview Day residents, with the exception of

infants born after Census Day. People living in group quarters, such as college students in dormitories, were not eligible for the P sample. Therefore, for the purpose of estimating the number of inmovers, person inmovers aged 18

to 22 who were living in group quarters on Census Day

were not considered to be Interview Day residents.

Noninterview adjustment was performed only on the P

sample. The procedure was similar to that used in the

Census Dress Rehearsal. Due to the mover procedure

described above, there were two noninterview adjustments – one based on housing unit status as of Census

Day (i.e., the Census Day roster), and the other based on

housing unit status as of the day of the A.C.E. interview

(i.e., the Interview Day roster). An occupied housing unit

was defined as an interview (for the given reference day –

Census Day or Interview Day) if there was at least one person (with a name and at least two demographic characteristics) who possibly or definitely was a resident of the

housing unit on the given reference day. An occupied

housing unit (as of the given reference day) that was not

an interview was a noninterview. Thus a unit that was

vacant, removed from the list of eligible housing units

(because, for example, it was demolished or used only as

a business), or in certain special places was not considered an interview or a noninterview. In the latter two situations, the unit was ‘‘deleted’’ from the list of A.C.E. sample

housing units.

If a housing unit was found to be vacant on Census Day or

deleted from the sample, then that household did not factor into the Census Day noninterview adjustment. The

same concept applies to Interview Day. Thus, vacant and

deleted units did not contribute toward dual system estimation. An example of an illustrative block cluster, provided in Figure 6-1, page 6-10, shows how the status of a

housing unit on Census Day and Interview Day would be

determined. Results of the A.C.E. interviewing operation

are shown in Table 6-1.

Table 6-1. Status of Household Interviews in

the A.C.E. [Unweighted]

Census Day A.C.E.

Interview Day

Number Percent Number Percent

Total housing units ......... 300,913 100.0 300,913 100.0

Interviews . . ............. 254,175 84.5 264,103 87.8

Noninterviews ............ 7,794 2.6 3,052 1.0

Vacant units ............. 28,472 9.5 29,662 9.9

Deleted units ............ 10,472 3.5 4,096 1.4

Noninterview rate ........... 3.0% 1.1%

Note: Percentages in table may not add to total due to rounding.

Of the 261,969 housing units occupied on Census Day,

7,794 (3.0 percent) were noninterviews. The corresponding numbers for Interview Day were 267,155 and 3,052

(1.1 percent). The noninterview rate was higher for Census Day than Interview Day, because interview status was

determined by results obtained on Interview Day. On that

date, information was sought for both Census Day and

Interview Day. Any time a household member or knowledgeable proxy could be reached, an interview for Interview Day was generally obtained. Census Day data was

not always obtainable from the same respondent, usually

in cases when the housing unit’s occupants had moved in

after Census Day. Each of the two noninterview adjustments generally spread the weights of noninterviewed

units over interviewed units in the same noninterview cell,

defined as the sample block cluster crossed with the type

of basic address. For purposes of this adjustment, the

types of basic address were single-family, multiunit (such

as apartments), and all others. The Census Day noninterview adjustment, determined according to the status of

housing units as of Census Day, was used to adjust the

person weights of nonmovers and outmovers. Similarly,

the Interview Day noninterview adjustment, determined

according to the status of housing units as of Interview

Day, was used to adjust the person weights of inmovers.

The formulae are described as follows:

For a given block cluster and type of basic address, the

Census Day noninterview adjustment factor was computed as

f *c

wi 

Census Day

interviews

wi

Census Day

noninterviews

wi

Census Day

interviews

6–2 Section I—Chapter 6 Missing Data Procedures

U.S. Census Bureau, Census 2000
where wi represents the weight of housing unit i, that is,

the inverse of its probability of selection into the A.C.E.

sample. When computing the noninterview adjustment

factor, the weight wi incorporated the trimming that

occurred in some block clusters. (See Appendix C.) However, the weights did not reflect the sampling for targeted

extended search (TES, Chapter 5) for two reasons. First,

the noninterview adjustment was done at the housing unit

level, but a housing unit could contain some people with

TES status and others without it. Second, TES status was

not determined until after the matching operation, but

information was usually not collected about people in noninterviewed units, and these people were generally not

sent to be matched. Therefore, there was not a reasonable

way of systematically classifying noninterviews into those

with and without TES status.

Similarly, for a given cluster and type of basic address, the

Interview Day noninterview adjustment factor was computed as

f *i



wi 

Interview Day

interviews

wi

Interview Day

noninterviews

wi

Interview Day

interviews

The example in Figure 6-1 on page 6-10, demonstrates the

calculation of the noninterview adjustment. When the

unweighted number of noninterviewed units in a given

noninterview cell (sample block cluster by type of basic

address category) was more than twice the unweighted

number of interviewed units, then the weights of the noninterviewed units were spread over the interviewed units

in a broader cell. This cell was formed by combining the

sample block clusters in the same A.C.E. sampling stratum

within the same type of basic address. Because the noninterview rates were so small, the noninterview adjustment

factors were close to 1 for most housing units in the

sample. For Census Day, the factors were smaller than

1.10 for more than 92 percent of the units; for Interview

Day, the factors were less than 1.10 for over 98 percent of

the units.

Characteristic (Item) Imputation (Person Level)

Production of A.C.E. undercount estimates required data

on age, sex, tenure (owner versus nonowner), race, and

Hispanic origin to classify respondents by these important

demographic characteristics, so they had to be imputed

whenever the data were not collected. Characteristic imputation was not carried out for other missing variables

(with the exception of the items with unresolved status).

Several variables also used to assign post-strata, such as

the location or return rate of the census tract, were the

same for everyone in the block. The extent of the missing

characteristics is portrayed in Table 6-2.

The imputation rates in the E sample for the five characteristics listed above ranged from 0.3 percent for sex up to

3.8 percent for tenure (using unweighted frequencies).

Since the A.C.E. record for each person in the E sample

was matched to the Census 2000 edited file and the five

characteristics were extracted and copied, the following

imputation procedures apply only to the P sample.

P-sample characteristic imputation for the A.C.E. was similar to that for the 1990 PES and the various Census 2000

tests, including the Dress Rehearsal. Age and sex were

imputed based on the available demographic distributions

determined from the P sample. Tenure was imputed using

a form of nearest-neighbor hot-deck procedure. To impute

for race and Hispanic origin, the two approaches were

combined.

For missing tenure, race, and Hispanic origin, a hot-deck

procedure was used to take advantage of the correlations

often found in these characteristics among people living in

the same block cluster (or, generally, in geographic proximity). The characteristics age and sex are geographically

less clustered than tenure, race, and Hispanic origin. Further, the value of age or sex is often considerably affected

by specific conditions, such as the person’s relationship to

the reference person, or whether information is available

on the person’s spouse. Thus, national distributions conditioned on relevant covariates were used to impute for age

and sex. These distributions were constructed before the

imputation began, without regard to the imputation for

other missing characteristics.

Table 6-2. Percent of Characteristic Imputation in the P and E

Samples [Unweighted]

Total

people

Percent of people with imputed

characteristic Percent of people

with one or more

imputed

characteristics

Age Sex Tenure Race

Hispanic

origin

P sample .............. 706,245 2.5 1.7 1.9 1.4 2.4 5.5

E sample .............. 704,602 3.1 0.3 3.8 3.5 3.6 11.2

Missing Data Procedures Section I—Chapter 6 6–3

U.S. Census Bureau, Census 2000
Age. The value of age was missing for 2.5 percent

(unweighted) of the P sample. When age was missing, one

of four age categories (0-17, 18-29, 30-49 and 50 or

older) – rather than a number – was imputed, because

only the category was used to assign people to a poststratum for estimation. In one-person households, missing

age was imputed from the distribution of ages reported in

such households. In multiperson households, if the relationship to the reference person was missing, the distribution of ages (excluding those of reference persons) in all

multiperson households was used. Otherwise, if the person was the spouse, child, sibling, or parent of the reference person, missing age was generally imputed from a

distribution of reported ages using the relationship to the

reference person and the age of the reference person. For

reference persons, other relatives, and nonrelatives, age

was imputed from the distribution of ages reported by

persons with the same ‘‘relationship.’’ See Figure 6-2, on

page 6-11, for details.

Sex. The imputation rate for sex was 1.7 percent in the P

sample. For one-person households, sex was imputed

from the distribution of sex in all one-person households.

To impute the sex of a reference person, if the household

had more than one person but no spouse was present, the

distribution of sex for reference persons of multiperson

households with no spouse present was used. If a spouse

was present, the missing sex of the reference person or

the reference person’s spouse was imputed as the sex

opposite to that of the spouse. If sex was missing for the

reference person and the spouse, then the sex of the reference person was imputed from the distribution of sex for

reference persons with a spouse present. The spouse was

then assigned the sex opposite to that of the reference

person.

For other persons in multiperson households (that is,

other than reference persons and spouses): 1) if the relationship to the reference person was missing, and if no

one else in the household was recorded as a spouse of the

reference person, sex was imputed from the distribution

of sex for persons (excluding reference persons) from all

multiperson households; 2) otherwise, sex was imputed

from the distribution of sex for persons (excluding reference persons, spouses, and persons with missing relationship) from all multiperson households. Figure 6-3, on page

6-12, illustrates the procedure.

Tenure. Household tenure (owner versus nonowner) was

missing for 1.9 percent of the people in the P sample. Tenure was imputed from the previous household that had

the same type of basic address and had tenure recorded.

As with the adjustment for noninterviews, three types of

basic address were used: single-family, multiunit, and all

other types of units. See Figure 6-4, on page 6-13, for further information.

Race. When race was missing – 1.4 percent of the P

sample – the imputed race could be any of the 63 possible

combinations of the six basic race categories: White,

Black, American Indian or Alaskan Native, Asian, Native

Hawaiian or Other Pacific Islander, and Some Other Race.

All 63 categories were treated the same in the imputation.

That is, there were no special procedures for any categories or groups of categories.

Whenever possible, missing race was imputed from the

same household. Independently for each household member with missing race, one person was selected at random

from those household members with reported race and

the selected person’s race was imputed to the given

household member. If race was missing for all household

members but someone had reported origin (Hispanic or

non-Hispanic), then the race distribution of the nearest

previous household with any reported race and the same

origin was used. Note that the Hispanic origin of the

household was that of the first person on the household

roster with origin reported. When race and Hispanic origin

were missing for the whole household, the race distribution of the nearest previous household with reported race

was used—regardless of Hispanic origin. See Figure 6-5,

on page 6-14, for details.

Hispanic Origin. A value of origin – Hispanic or nonHispanic – was imputed for 2.4 percent (unweighted) of

the P sample. The procedure was analogous to that for

imputing missing race. That is, whenever possible, origin

was imputed from within the same household. If everyone

in the household was missing origin, then the nearest previous household with reported origin and the same race

category was used. When both Hispanic origin and race

were missing for the whole household, the Hispanic origin

distribution of the nearest previous household with

reported Hispanic origin was used – regardless of race. For

the imputation procedure and the race categories used in

it, see Figure 6-6, on page 6-15.

For each of the five characteristics discussed, the distribution of imputed values did not necessarily mirror the distribution of reported values – nor was this expected. However, because the imputation rates were low in the P and E

samples, the distributions before and after imputation

were very similar. See the distribution of characteristics on

the following page.

6–4 Section I—Chapter 6 Missing Data Procedures

U.S. Census Bureau, Census 2000
Distribution of Characteristics Before and After Imputation [Weighted]

P sample E sample

Before

imputes Imputed

After

imputes

Before

imputes Imputed

After

imputes

Race 1.4% Imputed 3.2% Imputed

White Only 73.5% 67.5% 73.4% 76.9% 57.2% 76.2%

Black Only 11.0% 10.2% 11.0% 11.8% 6.6% 11.6%

AIAN Only 0.6% 0.7% 0.6% 0.8% 0.8% 0.8%

Asian Only 3.5% 3.4% 3.5% 3.7% 2.9% 3.7%

NHPI only 0.1% 0.3% 0.1% 0.1% 0.3% 0.1%

Some other race only 8.3% 14.4% 8.4% 4.5% 28.5% 5.3%

Multiple races 3.0% 3.5% 3.0% 2.3% 3.7% 2.3%

Hispanic origin 2.3% Imputed 3.4% Imputed

Hispanic 12.4% 11.5% 12.4% 12.5% 9.0% 12.4%

Age 2.4% Imputed 2.9% Imputed

0-17 26.1% 21.7% 26.0% 25.9% 19.7% 25.7%

18-29 16.7% 18.9% 16.7% 15.5% 19.0% 15.6%

30-49 30.7% 33.0% 30.8% 31.0% 30.9% 31.0%

50+ 26.5% 26.4% 26.5% 27.6% 30.5% 27.6%

Sex 1.7% Imputed 0.2% Imputed

Male 48.4% 47.2% 48.3% 48.8% 53.9% 48.8%

Female 51.6% 52.8% 51.7% 51.2% 46.1% 51.2%

Tenure 1.9% Imputed 3.6% Imputed

Owner 68.4% 70.3% 68.4% 69.9% 65.1% 69.7%

Nonowner 31.6% 29.7% 31.6% 30.1% 34.9% 30.3%

Assigning Probabilities for Unresolved Cases

(Person Level)

After all follow-up activities were completed, there

remained a small fraction of the A.C.E. sample without

enough information to compute the components of the

dual system estimator given in Chapter 7. Their status

was said to be ‘‘unresolved.’’ A procedure called imputation cell estimation was used to assign probabilities for

P-sample people with unresolved match or Census Day

residence status, and for E-sample people with unresolved

enumeration status.

All P- and E-sample persons – resolved and unresolved –

were placed into groups called imputation cells based on

operational and demographic characteristics. Different

variables were used to define cells for P-sample match

and residence status and in the E-sample for enumeration

status. Within each imputation cell the weighted average

of 1’s and 0’s (representing, e.g., match and nonmatch,

respectively) among the resolved cases was calculated,

and that average was imputed for all unresolved persons

in the cell.

One should note that the noninterview adjustment factor

was not incorporated into the person weights when these

averages were calculated. This is because the noninterview adjustment was designed to spread the weight of

noninterviewed housing units over interviewed housing

units. However, all persons with resolved residence status

in noninterviewed units were nonresidents (since, by definition, if one person in the household was a resident then

the household was considered an interview). Therefore,

using the noninterview factor to calculate the averages for

unresolved cases would have produced a biased estimate

of residence probability. The issue of which weights to use

was moot when resolving E-sample cases with missing

enumeration status, as a noninterview adjustment was not

applied to E-sample persons.

Thus, the weights, wi

, used here incorporated all stages of

sampling, including the selection of people for targeted

extended search, but were not adjusted for household

noninterviews. Any trimming of the weights was also performed before these weighted averages were calculated.

Unresolved Residence Status in the P Sample

After follow-up was completed, all persons in the P sample

who were eligible to be matched to the Census (see Chapter 4) were classified into three types, according to their

status as a resident in their sampled block at the time of

the census: Census Day residents, Census Day nonresidents, and unresolved persons – those for whom there

was not enough information to determine the residence

status. The results are displayed in Table 6-3.

Missing Data Procedures Section I—Chapter 6 6–5

U.S. Census Bureau, Census 2000
Table 6-3. Final Residence Status for the P Sample by Mover Status

[Unweighted]

Total

people

Final residence status Residence

rate for

resolved

cases

Confirmed

resident

Confirmed

nonresident

Unresolved

resident

U.S. total .......................... 653,337 95.8% 1.9% 2.3% 98.1%

Mover status

Nonmover ....................... 627,992 96.6% 1.7% 1.7% 98.3%

Outmover ........................ 25,345 75.2% 7.5% 17.4% 91.0%

Because of the uncertainty of the actual status of the

15,082 people (2.3 percent of 653,337) with unresolved

residence status, a probability of being a Census Day

resident was assigned (see equation (6.2)). Then, when

computing the dual system estimate, all person

nonmovers and outmovers were included with their estimation weight (see Chapter 7) and the following residence

probability:

(6.1)

Prres,j { 1, if person j is a resident on Census Day

0, if person j is NOT a resident on Census Day

Pr*res, j

, if person j is unresolved

To assign Pr*res, j for unresolved cases, the Census Day

residence probability for inmovers was irrelevant for estimation and was not used. Only nonmovers and outmovers

in the P sample who had a resolved final residence status

and went through the person matching operation (formally, those with a final match-code status) were used.

They were placed into a number of imputation cells as

defined in Table 6-4. Within each cell, among the resolved

cases (those with Prres, j = 1 or 0) the weighted proportion

of Census Day residents, that is, the weighted average of

1’s and 0’s, was computed:

Pr*res, j 

wi Prres, j

resolved

persons

wi

resolved

persons

(6.2)

where wi was defined at the beginning of this section.

This proportion was then assigned as Pr*res,j to each unresolved case in the cell. (The exception is for follow-up

match code group 7; this is explained below.) The cells

used to resolve residence status, along with the probabilities assigned to the unresolved cases, are given in

Table 6-4.

Match code groups 1 through 7, which partition the population into mutually exclusive and exhaustive groups,

were determined from the match codes and other variables derived before the follow-up operation as explained

in Chapter 4. Group 8 was formed differently. Some information from the follow-up operation was coded in time for

Table 6-4. Imputation Cells and Probabilities Assigned for Resolving Residence Status in the

P Sample

Match code group

Owner Nonowner

Non-Hispanic White Others Non-Hispanic White Others

1 = Matches needing follow-up ................... 0.982 0.986 0.993 0.991

2 = Possible matches ............................ 0.973 0.968 0.966 0.972

3 = Partial household nonmatches needing

follow-up ...................................

V3a*

0.755

V3b*

0.956

V3a*

0.901

V3b*

0.971

V3a*

0.883

V3b*

0.959

V3a*

0.928

V3b*

0.969

4 = Whole household nonmatches needing

follow-up, not conflicting households .......... 0.920 0.943 0.911 0.914

5 = Nonmatches from conflicting household . ....... 0.910 0.927 0.945 0.954

6 = Resolved before follow-up . ................... 0.993 0.990 0.990 0.988

7 = Insufficient information for matching (Weighted

column average of groups 1-5 and 8) . . ........ 0.813 0.867 0.844 0.872

8 = Potentially fictitious or said to be living elsewhere on Census Day ....................... 0.119 0.123 0.177 0.157

* V3a = Group 3 Persons age 18-29 listed as child of reference person; V3b= All other group 3 persons.

6–6 Section I—Chapter 6 Missing Data Procedures

U.S. Census Bureau, Census 2000
the A.C.E. missing data procedures. (Under the original

schedule, this information would have become available

too late to be of use.) After the follow-up operation, a

small number of people in the P sample were coded as

being potentially fictitious or said to be living elsewhere

on Census Day. Such people were placed in Group 8, even

though they also qualified for one of the Groups l1

through 7.

The two tenure categories were owners and nonowners.

Persons were placed into one of two race categories: nonHispanic White and all others. People of multiple races (for

example, a person responding as White and Asian) were

placed in the latter group. V3 was a variable defined only

for match code group 3, partial household nonmatches.

V3a comprised persons in group 3 who were 18 to 29

years of age and were listed on the A.C.E. household roster as a child of the reference person. V3b included all

other persons in group 3.

The residence probability for unresolved P-sample persons

was computed as described above, except for those in

match code group 7 – people with insufficient information

for matching. Within this set of four cells (see Table 6-4),

there were almost no resolved cases from which to extract

a probability of being a Census Day resident. Because of

the lack of information – most of these cases did not even

have a valid name – these people did not go through the

matching operation and were not sent to follow-up. To

adjust for these cases, a weighted proportion of Census

Day residents (1’s and 0’s) was computed among the

resolved cases in each of the four columns of Table 6-4

using match code groups 1 through 5 and 8. Separately

for each of the four tenure race/ethnicity classes, the overall weighted probability of being a resident among those

sent to follow-up (groups 1 through 5 and 8) was assigned

to those with insufficient information for matching (group

7). Left out of this computation were those people who

were resolved before follow-up (group 6). Observations

from the Census 2000 Dress Rehearsal indicated that, in

terms of their demographic and operational characteristics, people in group 7 tend to be more like those in

groups 1 through 5 and 8, than like those in group 6.

In the Dress Rehearsal, only three weighted ratios were

calculated for residence probability: a ratio for persons

sent to follow-up, a ratio for persons not needing followup, and an overall ratio used for persons with insufficient

information for matching. Based on Dress Rehearsal

results, Kearney and Ikeda (1999) suggest calculating

separate ratios by match code group and splitting persons

from conflicting households into a separate match code

group. The larger Accuracy and Coverage Evaluation

sample size in Census 2000 than in the Dress Rehearsal

made it possible to separate matches needing follow-up

from possible matches. Additional research and discussion

suggested adding additional variables within match code

group.

Unresolved Match Status

Computing the dual system estimator required measuring

the total number of P-sample people who were matched to

persons included in the census. (Separate estimates were

obtained for nonmovers and outmovers, but that does not

affect what follows.) After follow-up activities were completed, each confirmed or possible (unresolved) Census

Day resident in the P sample was determined to be a

match, a nonmatch, or unresolved (that is, persons for

whom match status could not be determined). Match status of confirmed Census Day nonresidents was not used in

the estimation. As is seen in Table 6-5, unresolved

matches were infrequent in the P sample.

The treatment of unresolved matches was similar to that

for unresolved residence status. For each confirmed or

possible Census Day resident j in the P sample, the value

Prm, j was assigned as 1, 0, or Pr*m, j, in a manner analogous to equation (6.1), according to whether the person

was a match, a nonmatch, or had unresolved match status, respectively. Unresolved matches accounted for 7,826

of 640,945 people in the P sample, or 1.2 percent. Pr*m, j

was assigned using imputation cell estimation based on

those with a resolved match status. The formula is the

same as in equation (6.2), but pertains to match status,

that is, uses the values of Prm, j.

Table 6-5. Final Match Status for the P Sample by Mover Status [Unweighted]

P sample (confirmed or possible residents) Number of

persons

Final match status Match rate

for

resolved

Match Nonmatch cases

Unresolved

match

U.S. total ......................................... 640,945 90.3% 8.5% 1.2% 91.4%

Mover status ......................................

Nonmover ...................................... 617,490 91.1% 8.0% 0.9% 91.9%

Outmover ...................................... 23,455 67.8% 21.7% 10.5% 75.8%

Missing Data Procedures Section I—Chapter 6 6–7

U.S. Census Bureau, Census 2000
As with residence status, the cases were first classified

according to several characteristics. Within cells, the

weighted proportion of matches among the resolved cases

– excluding all confirmed Census Day nonresidents – was

computed and assigned to each of the unresolved cases in

the same cell. Again, the weights, wi

, are defined earlier.

The characteristics used to define the imputation cells for

match status – different from those used for residence status – are shown in Table 6-6. They were based on observations from the Census 2000 Dress Rehearsal and an analysis of the A.C.E. operations. Kearney and Ikeda (1999)

showed that mover status (nonmover versus outmover)

discriminated well between matches and nonmatches

among the resolved cases. The housing unit address

match code refers to the initial match between housing

units on the independent (A.C.E.) listing and the census

address list; conflicting housing units were determined

during A.C.E. person matching activities.

People with at least one imputed demographic variable

(i.e., age, sex, race, Hispanic origin, or tenure) were

grouped together for imputation of match status. Unpublished studies indicate that, at least in the Dress Rehearsal,

the presence of these imputed characteristics among

resolved cases is negatively associated with the propensity to be a match. For outmovers from a unit that was a

nonmatch or a conflicting household, people were not

separated according to their imputed characteristics. The

reason was to maintain a reasonable number of resolved

cases in each cell from which to estimate the weighted

proportion of matches. The probabilities assigned to

people with unresolved match status are provided in

Table 6-6. It is useful to note that most persons with

unresolved match status (7,693 of the 7,826) had insufficient information for matching; most of them did not have

a valid name, and their rate of missing characteristics was

much higher than the average. Further, almost all of these

people (7,506) were in match code group 7. As such, they

did not go through the matching process, nor were they

sent for follow-up. This information was considered when

cells were selected for imputation of match status. Variables such as age and ethnicity – that had a high chance

of being imputed and might be of questionable quality –

were avoided.

In the Dress Rehearsal, within each of the four geographic

sites, one overall weighted ratio for match probability was

calculated and used. Kearney and Ikeda (1999) suggest

that separate ratios for outmovers and nonmovers should

be calculated.

Unresolved Enumeration Status (E Sample)

The dual system estimator also required the total number

of correct enumerations in the E sample. As with operations previously discussed, follow-up activities left each

person in the E sample with one of three types of enumeration status: correct, erroneous, or unresolved. The

person was assigned a number, Prce, j, equal to 1, 0, or

Pr*ce, j, respectively, according to that status, similar to

equation (6.1). Table 6-7 shows the distribution of persons

according to enumeration status. The values of Pr*ce,j for

the 21,148 unresolved E-sample people (3.0 percent of

704,602) were determined through imputation cell

estimation.

Table 6-6. Imputation Cells and Probabilities Assigned for Resolving Match

Status in the P Sample

Mover status

Housing Unit Address Match Code

Housing unit was a match (code 1)

Housing unit was a nonmatch or

the household is conflicting (code 2 or 4)

No imputes 1 or more imputes No imputes 1 or more imputes

Nonmover 0.945 0.901 0.690 0.567

Outmover 0.798 0.791 0.516

Table 6-7. Final Enumeration Status for the E Sample [Unweighted]

E sample

Number of

persons

Final enumeration status Correct

enumeration

rate for

resolved

cases

Correct

enumeration

Erroneous

enumeration

Unresolved

enumeration

U.S. total .......................... 704,602 92.6% 4.4% 3.0% 95.5%

6–8 Section I—Chapter 6 Missing Data Procedures

U.S. Census Bureau, Census 2000
The resolved and unresolved cases were placed in the

cells defined shown in Table 6-8. Within each cell, the

weighted proportion of correct enumerations among

resolved cases was computed before accounting for

duplication with non-E-sample people, analogous to equation (6.2), and then assigned to each unresolved case in

the cell.

As with residence status for P-sample people, a key factor

in determining enumeration status was the E-sample person’s match code. These codes can be found in Chapter 4.

People were placed in match code groups accordingly in

the following sequence: 1) People coded as potentially

fictitious or said to be living elsewhere on Census Day

(based on information collected during the follow-up

operation) were placed in groups 11 and 12, respectively.

2) All other people included in the operation for targeted

extended search were placed in group 10. See Chapter 5

for details. 3) People in the remainder of the E sample

were then placed in the appropriate match code group, as

defined in Table 6-8. Other characteristics used to define

cells were the presence or absence of imputed characteristics (as was used to define cells for match status); whether

the person was non-Hispanic White or any other raceethnicity combination; and V3, as defined in the section

on residence status.

There was an additional adjustment made to the enumeration probability of E-sample people as a result of duplication with persons subsampled out of the E-sample in large

clusters. If the same identity was assigned to u E-sample

persons and v persons who were subsampled out of the

E sample, 1) one of the u E-sample persons was selected

during the person matching operation, and 2) the initial

correct enumeration probability was multiplied by

u/(u + v) during the missing data activities, as it was not

known which person was the ‘‘actual’’ E-sample person.

The other u-1 E-sample persons were assigned a correct

enumeration probability of 0.

Table 6-8. Probabilities Assigned for Resolving Enumeration Status in the E Sample

Match code group No imputed characteristics 1 or more imputed characteristics

1 = Matches needing follow-up 0.977 0.977

2 = Possible matches 0.968 0.968

3 = Partial household nonmatches V3a* 0.871 V3b* 0.974 V3a* 0.908 V3b* 0.960

4 = Whole household nonmatches where the housing unit

matched; not conflicting households

Non-Hispanic

White

0.965

Others

0.974 0.958

5 = Nonmatches from conflicting households; for housing units

not in regular nonresponse follow-up 0.975 0.965

6 = Nonmatches from conflicting households; housing units in

regular nonresponse follow-up 0.914 0.926

7 = Whole household nonmatches, where the housing unit did

not match in housing unit matching

Non-Hispanic

White

0.959

Others

0.947 0.950

8 = Resolved before follow-up

Non-Hispanic

White

0.995

Others

0.990 0.979

9 = Insufficient information for matching 0.000

10 = Targeted extended search people 0.928 0.858

11 = Potentially fictitious people 0.058 0.088

12 = People said to be living elsewhere on Census Day 0.229 0.210

* V3a = Group 3 Persons age 18-29 listed as child of reference person; V3b= All other group 3 persons

Missing Data Procedures Section I—Chapter 6 6–9

U.S. Census Bureau, Census 2000
Figure 6-1.

Adjustment for Noninterviews: An Example

Consider a block cluster with nine housing units, all having the same type of basic address, for example, all single-family

homes, as depicted below.

Housing

unit Weight Actualsituation

Status of

(and information from)

A.C.E. Interview

Census Day

interview

status

A.C.E.

Interview Day

interview status

1 100

Resident on 4/1/00 and at

time of A.C.E. interview

Interviewed in A.C.E. Interview Interview

2 100

Resident on 4/1/00 and at

time of A.C.E. interview

Neighbor(proxy)interviewed

in A.C.E. Interview Interview

3 100

Resident on 4/1/00 and at

time of A.C.E. interview

No one interviewed inA.C.E. Noninterview Noninterview

4 100

Vacant on 4/1/00, resident

at time of A.C.E. interview

Interviewed inA.C.E., knows

of 4/1/00 status Vacant Interview

5 100

Vacant on 4/1/00, resident

at time of A.C.E. interview

Interviewed in A.C.E., no

knowledge of 4/1/00

status

Noninterview Interview

6 100

Vacant on 4/1/00, resident

at time of A.C.E. interview

No one interviewed inA.C.E. Noninterview Noninterview

7 100

Resident on 4/1/00, vacant

at time of A.C.E. interview

Information obtained from

proxy

Interview Vacant

8 100

Resident on 4/1/00, vacant

at time of A.C.E. interview

No information on 4/1/00

status; Census staff determines vacant at time of

A.C.E.

Noninterview Vacant

9 100

Resident on 4/1/00, different resident at time ofA.C.E.

interview

Interviewed inA.C.E., knows

of 4/1/00 status Interview Interview

Note: In this noninterview cell (sample block cluster × type of basic address), people in interviewed housing units would have received the following noninterview adjustments:

a) To the person weights of nonmovers and outmovers, Census Day Noninterview adjustment = 800 / 400 = 2.

b) To the person weights of inmovers, A.C.E. Interview Day Noninterview adjustment = 700 / 500 = 1.4.

6–10 Section I—Chapter 6 Missing Data Procedures

U.S. Census Bureau, Census 2000
	


	



	




	
		
	

	 

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Chapter 7.

Dual System Estimation

INTRODUCTION

Dual System Estimation (DSE) was used to estimate coverage of Census 2000 using data from the Accuracy and

Coverage Evaluation (A.C.E.) Survey. DSE was also used by

the U.S. Census Bureau to estimate census coverage for

the 1980 and 1990 censuses, and to evaluate coverage

prior to 1980. The use of DSE for measurement of coverage in 1980 is described in Fay et al. (1988), while Hogan

(1992,1993) describes the use of DSE in 1990. As

described in Killion (1998), several alternatives to DSE

were considered for Census 2000. These alternatives were

either shown to produce results grossly inferior to DSE or

research was not conclusive.

This chapter provides the details of DSE for the Census

2000 A.C.E. The DSE was calculated separately for a set of

population groups referred to as post-strata. The poststratification variables and the final post-stratification plan

are discussed in detail. In addition, the variance estimation

methodology used in each post-stratum is summarized

and some basic results are given.

DUAL SYSTEM ESTIMATION

This section contains the details of the DSE calculated

within each final post-stratum. It describes the basic DSE

model, including a discussion of the advantage of poststratification. The details of the DSE computed within each

final post-stratum for Census 2000 are presented. All components of the DSE are defined. The DSE accounted for

special handling of missing data, search areas for matching, and movers. Missing data and search areas for matching are covered in detail in Chapters 6 and 5, respectively.

The method used to handle special problems caused by

movers in Census 2000 DSE is also discussed. The attachment provides detailed background on options for dealing

with movers in census coverage measurement surveys.

The section concludes with a short discussion of how the

DSE results serve as input to synthetic estimation down to

the block level. A detailed discussion of synthetic estimation is provided in Chapter 8 and Haines (2001).

DSE Model

The DSE model is discussed in detail in Wolter (1986) and

more generally in Hogan (1992). This chapter gives a general presentation. The DSE model (applied within each

post-stratum) conceptualizes each person as having a

probability of being either in or not in the census enumeration, as well as either in or not in the A.C.E.

Table 7-1. DSE Model

In census Out of census Total

In A.C.E. N11 N12 N1+

Out of A.C.E. N21 N22 N2+

Total N+1 N+2 N++

All cells are conceptually observable except N22 and any

of the marginal cells that include N22 (i.e., N2+, N+2, and

N++). The model assumes independence between the census and the A.C.E. This means that the probability of being

in the ijth cell, pij, is the product of the marginal probabilities, pi+p+j. The estimate of total population in a poststratum with the independence assumption is

DSE  N N1 N1

N11

.

The independence assumption can be in error, either due

to causal dependence between the census enumeration

and the A.C.E. enumeration, or due to heterogeneity in

capture probabilities within a post-stratum. Causal dependence occurs when the event of an individual’s inclusion

or exclusion from one system affects his or her probability

of inclusion in the other system. For example, some

people who did answer the census may not have cooperated with the A.C.E., thinking they had helped enough.

As another example, a person contacted during A.C.E. listing may not have responded to the census thinking that

the A.C.E. lister already recorded them. However, even if

causal independence is true for all individuals

(pij = pi+p+j ), the independence assumption can be violated by heterogeneity. Either the census inclusion probabilities p+1 or the A.C.E. inclusion probabilities p1+ must

be the same for all individuals. This means that homogeneity in both systems is not required. For example, some

people may try their best to avoid being counted in both

the census and A.C.E., resulting in these people having

much smaller inclusion probabilities than other people.

Error in the independence assumption for either reason

results in correlation bias.

Post-stratification, or grouping of individuals likely to have

similar inclusion probabilities, and calculating DSEs within

post-strata was done to decrease correlation bias.

Research was carried out to determine effective variables

Dual System Estimation Section I—Chapter 7 7–1

U.S. Census Bureau, Census 2000
for the A.C.E. post-stratification design. All variables

included in the 1990 PES post-stratification were considered as were several new ones. The specific variables considered were race/Hispanic origin, age/sex, tenure, household composition, relationship, urbanicity, percent owner,

return rate, percent minority, type of enumeration area,

household size, hard-to-count scores, census division,

census region, and regional census center. From these

variables, fifteen post-stratification options were developed for empirical research. For each post-stratification

option, mean square errors of total population estimates

and synthetic estimates were computed at the national,

state, and congressional district levels, as well as for

selected cities. The major conclusions were as follows:

• The demographic variables used in the 1990 PES were

effective, but did not fully capture the geographic differences, especially those affected by the quality of the

Master Address File. An urbanicity/type of enumeration

variable appeared to capture much of the geographic

differences.

• The tract-level return rate variable captured some of the

socioeconomic differences for synthetic estimates at

lower levels of aggregation.

Details of the Census 2000 post-stratification research

methodology are given in Kostanich et al. (1999) and Griffin (1999). Results of this research are given in Griffin and

Haines (2000) and Schindler (2000). The post-stratification

design chosen for Census 2000 is provided in this chapter.

The DSE can be written as follows:

DSE  N 1 (

N1

N11

)

That is, the total population is estimated by the number

captured in the census times the ratio of those captured in

the A.C.E. survey to those captured in both systems. In

practice, the components of the DSE are estimated from a

sample survey. N+1 is not the census count; the census

count (C) must be corrected for erroneous enumerations,

as well as for persons enumerated in the census with

insufficient information to match to the A.C.E. enumeration. To actually estimate the number of people correctly

enumerated in the census, a sample of all data-defined

persons is selected. This sample of data-defined census

persons is called the enumeration or E sample. To estimate

the ratio of those captured in both systems to those captured in A.C.E., the population or P sample is used. The P

sample consists of persons interviewed during A.C.E. enumeration.

The form of the DSE used in census coverage measurement surveys such as A.C.E. is as follows:

DSE  DD 

CE

Ne



Np

M

where

DD = the number of census data-defined persons

eligible and available for A.C.E. matching,

CE  the estimated number of correct enumerations from

the E sample,

Ne  the estimated number of people from the E sample,

Np  the estimated total population from the P sample,

M  the estimated number of persons from the P-sample

population who match to the census.

Note: Persons in Group Quarters are excluded from all the

above counts for A.C.E., as were persons in housing units

who were added to the census after E sample Identification (late adds).

Definitions

Block Cluster. A grouping of one or more census blocks.

Block clusters are the primary sampling units for A.C.E.

and average about 30 housing units each.

Correct Enumeration (CE). A correct enumeration is a

person who is enumerated in a sample block cluster during the census who is also determined by A.C.E. operations to have lived in that block cluster (or if appropriate a

surrounding block) on Census Day. Correct enumerations

have a correct enumeration probability, Prce,j, equal to 1

for each person j.

Correct Enumeration Probability (Prce,j). This is

defined as the probability that person j in the E sample

was correctly enumerated in the A.C.E. (or surrounding

block) block cluster. The probability of correct enumeration is typically 0 or 1, but it can take on values within

this range due to missing data imputation.

Coverage Correction Factor (CCF). The coverage correction factor for a post-stratum is calculated by dividing

the DSE for that post-stratum by its census count. A.C.E.

synthetic estimates for any data item for any geographic

area are obtained by multiplying the coverage correction

factor by the census count within each post-stratum, then

summing over all post-strata (see Chapter 8 for details on

synthetic estimation).

Data-Defined Person. This concept is defined for all

census persons. A data-defined person is a person who

has two or more of the 100-percent data items answered

on the census form. Any items can be selected from the

100-percent data items, which include name, age, sex,

race, and Hispanic origin. Relationship to person one is

also a 100-percent data item for all persons besides person one. Persons not satisfying this criteria are referred to

as non-data-defined.

E Sample. The E sample is the Enumeration sample. It

consists of all data-defined persons in the A.C.E. block

clusters who were enumerated in the census.

7–2 Section I—Chapter 7 Dual System Estimation

U.S. Census Bureau, Census 2000
Group Quarters (GQ) Persons. Persons living in GQs,

such as college dormitories, prisons, or military barracks.

GQ persons were not covered in the A.C.E. and are

excluded from the A.C.E. universe.

Inmover. A person who moved into a P-sample housing

unit after Census Day.

Insufficient Information in Census (II). Those persons

in the census for whom there is insufficient information

for inclusion in the E sample. Very little data is available

for these persons. This category includes non-data-defined

persons and persons in whole household imputations.

Note that insufficient information in census is different

than insufficient information for matching. The former are

excluded from the E sample and the latter are included in

the E sample.

Late Adds. Late Adds are persons in housing units who

were added to the census after E-sample Identification.

These housing units had an unknown final status at the

time of A.C.E. matching but were subsequently included in

the census. Persons who are Late Adds were ineligible for

matching and, therefore, not included in the census DSE

component.

Match Probability (Prm,j). This is defined as the probability that person j in the P sample was matched to a

census person in the search area (or in a TES block) . The

match probability is typically 0 or 1, but it can take on values within this range due to missing data imputation.

Mover Status. Each person in the P sample was classified

as a nonmover, outmover, or inmover.

Nonmover. An A.C.E. sample person whose housing unit

on Census Day and A.C.E. Interview Day are identical.

Outmover. A person who moved out of an A.C.E. housing

unit between Census Day and the date of the A.C.E. interview.

P Sample. Also known as the Population sample. The P

sample consists of those persons confirmed to be residents of the housing units in the A.C.E. block clusters as

of Census Day by the independent portion of the A.C.E.

reinterview and subsequent operations.

Residence Probability (Prres,j). The probability that person j on the P-sample file is a resident of the sample

household on Census Day. All inmovers are assumed to be

A.C.E. Interview Day residents. Nonmovers and outmovers

can be Census Day nonresidents, if information indicates

they were not a resident of the sample household based

on census residency rules. The residence probability is

typically 0 or 1 but it can take on values within this range

due to missing data imputation.

Targeted Extended Search (TES). A.C.E. operation in

which block clusters are identified and selected for a

search of the immediate surrounding area to find persons

geographically mis-located in a block neighboring the

A.C.E. block cluster. More generally, it is the methodology

for targeting, sampling, and implementing the search

operations in the field.

DSE Formula

The DSE for any given post-stratum was calculated by:

DSˆE  DD (

CE

Ne

) [ Nn Ni

(Mn (

Mo

No

)Ni)

]

All counts and estimates are for a specific post-stratum

and the subscripts n, i, and o stand for nonmovers, inmovers, and outmovers, respectively. Adjustments to this DSE

were occasionally made to avoid the unlikely event that

the formula results in division by zero. For post-strata

with less than ten (unweighted) outmover persons, the

ratio inside the square brackets was changed to the following:

Nn No

Mn Mo

.

Coverage Correction Factor Formula

The coverage correction factor (CCF) is a measure of the

net overcount or net undercount of the household population within the census. The CCF for a post-stratum is the

ratio of the DSE to the census count:

CCF  DSE

C

where

C = the final census household population

count where C  DD + II + LA,

II  the number of census people with insufficient

information,

LA  the number of people added (late) to the census

and not available for A.C.E. matching. Late Adds

include both data-defined and non-data-defined records.

Note: The numerator of the CCF is based on data-defined

persons. The denominator includes data-defined and nondata-defined persons as well as late adds. Thus, we are

implicitly assuming the coverage of late adds and nondata-defined persons is the same as that for data-defined

persons. For example, a coverage correction factor of 1.05

would imply that for every 100 people within the given

post-stratum, the net undercount is five persons.

DSE Components

Each component of the DSE is described next.

Dual System Estimation Section I—Chapter 7 7–3

U.S. Census Bureau, Census 2000
DD is the census count (unweighted) of data-defined persons in the post-stratum.

The estimated number of E-sample persons is written as:

Ne   Wj

*

j  E sample

where Wj* = inverse of the probability of selection,

including a factor for Targeted Extended Search

sampling.

The estimated number of correct enumerations is calculated as:

CE   Prce, j W j

*

j  E sample

where Prce,j is:

1 if person j correctly enumerated,

0 if person j NOT correctly enumerated, or

Pr*ce, j if person j is unresolved, where Pr*ce, j is

estimated through missing data imputation.

Note: Probabilities for persons with unresolved final correct enumeration status in the E sample or unresolved

final residence or match status in the P sample are

assigned using imputation cell estimation within groups.

See Chapter 6 for details. Within each group, a probability

equal to a simple proportion is imputed for unresolved

persons. For example, E-sample (or P-sample) persons in a

group with unresolved enumeration (match) status were

assigned a correct enumeration (match) probability that is

the proportion of correct enumerations (matches) among

persons with resolved enumeration (match) status in the

group. The probabilities are estimated in the DSE formulas

as:

Pr*m, j is the estimated match probability for

unresolved match status

Pr*res, j is the estimated residence probability for

unresolved residence status

Pr*ce, j is the estimated enumeration probability for

unresolved enumeration status

Some persons moved between Census Day and A.C.E.

Interview Day. A mover is a person whose location on the

day of the A.C.E. interview differs from his or her location

on Census Day. The treatment of movers has important

ramifications for estimation. The attachment to this chapter titled ‘‘The Effect of Movers on Dual System Estimation’’

provides a discussion on alternative methodologies for

handling movers. For Census 2000, movers were treated

by a procedure known as Procedure C, unless a poststratum had less than ten (unweighted) outmover persons.

In this case, Procedure A was implemented. Procedure C

identifies all current residents living or staying at the

sample address at the time of the A.C.E. interview (nonmovers and inmovers), plus all other persons who lived at

the sample address on Census Day who have since moved

(outmovers). The P sample includes nonmovers and outmovers. For outmovers, the interviewers attempted a

proxy interview to obtain data such as name, sex, and age

that was used for matching. The match rate for inmovers

was estimated by the match rate of outmovers. In contrast, the number of movers in the P sample for A.C.E.

sample areas was estimated by the inmovers. Note that no

matching was done for inmovers.

Nn is the weighted total population for nonmovers for the

post-stratum from the P sample. The weight for each person j is the product of three values:

1. the inverse of the P-sample selection probability

including a factor for the Targeted Extended Search

sampling (Wj

*),

2. a noninterview adjustment based on Census Day interview status (f *c,j ), and

3. a Census Day residence probability (Prres,j).

The estimated number of P-sample nonmovers is calculated as:

Nn   f * c, j Prres, j

Wj

*

j  Nonmovers

where, Prres, j is:

1 if person j is a resident on Census Day,

0 if person j is NOT a resident on Census Day, or

Pr*res, j if person j is unresolved, where Pr*res, j is

estimated through missing data imputation.

Note: Persons who were not residents on Census Day are

not included in Nn since Prres, j = 0 is a multiplicative factor in each person’s contribution to Nn.

The estimated number of P-sample nonmover matches is

written as:

Mn   Prm, j f * c, j Prres, j

Wj

*

j  Nonmovers

where, Prm,j is:

1 if person j is a match on Census Day,

0 if person j is NOT a match on Census Day, or

Pr*m, j if person j is unresolved, where Pr*m, j is

estimated through missing data imputation

Ni is the weighted total population for inmovers for the

post-stratum from the P sample. The weight for each person j is the product of two values:

1. the inverse of the P-sample probability of selection

(Wj

* as defined above), and

2. a noninterview adjustment factor based on A.C.E.

Interview Day status (f*a,j).

The estimated number of P-sample inmovers is denoted:

Ni   f* a, j

Wj

*

j  Inmovers

7–4 Section I—Chapter 7 Dual System Estimation

U.S. Census Bureau, Census 2000
Note that all inmovers are assumed to be A.C.E. Interview

Day residents.

The estimated number of P-sample outmovers is written:

No   f* c, j Prres, j

Wj

*

j  Outmovers

The estimated number of P-sample outmover matches is

calculated as:

Mo   Prm, j f* c, j Prres, j

Wj

*

j  Outmovers

Synthetic Estimation

The estimated coverage correction factors for each poststratum were used to form synthetic estimates. Synthetic

estimation combines coverage error results with census

counts at the block level to produce adjusted block-level

population estimates. The synthetic methodology assumes

coverage correction factors do not vary within a poststratum. As a result, one coverage correction factor is

assumed to be appropriate for all geographic areas within

each post-stratum. To obtain block-level synthetic estimates, block-level census counts for post-strata are multiplied by post-stratum coverage correction factors and

aggregated. There is one coverage correction factor for

each post-stratum, and each person in a block is in one

post-stratum. For example, suppose all persons in a block

fall into one of six post-strata. A synthetic estimate for

this block is formed by summing the product of census

counts for that block and post-stratum with its corresponding coverage correction factor. A controlled rounding technique was implemented, resulting in the creation

of person records at the block level. Subsequent tabulations, based on the original and replicated records, are

corrected for coverage error. A detailed discussion of synthetic estimation is provided in Chapter 8 and Haines

(2001).

POST-STRATIFICATION

Background

The goal of post-stratification for dual system estimation

is to establish groups of persons who are expected to

have similar coverage. A common assumption is that

people who are subject to similar housing, language, education, and cultural attitudes would also share similar census coverage. Hogan (1993) indicated that tenure, race

and ethnic origin, age/sex, and degree of urban development were reasonable markers for these similarities in the

1990 census. An earlier section noted, however, that the

independence assumption of the DSE model can be in

error due to heterogeneous capture probabilities within a

post-stratum. Post-strata are formed to support DSE by

grouping persons with similar census coverage, so as to

reduce heterogeneity in capture probabilities for DSEs. In

many surveys, post-stratification is done to reduce variances and partially correct for problems in sampling or

undercoverage. For DSE, the primary reason for poststratification is to reduce heterogeneity bias. Any variance

reduction or sampling bias correction associated with

post-stratification is a bonus. In fact, the usual trade-off is

that forming many post-strata reduces heterogeneity at

the expense of adding variance. As the number of poststrata increases, fewer people in the coverage measurement survey fall into each individual post-strata.

The post-stratification plan for Census 2000 A.C.E. is summarized in this section. Also, the detailed definitions of

the post-stratification variables and the race/Hispanic origin domains are given. See Haines (2001b) for further

details. The 2000 A.C.E. differs from the 1990 PostEnumeration Survey (PES) in that it has approximately

twice the sample size of the PES. This larger sample size

permitted the formation of more post-strata that has the

advantage of reducing correlation bias, as well as sampling variance. Additionally in 2000, multiple responses to

the race question were permitted; in 1990 only one race

could be selected.

The 1990 PES post-strata started with a cross-classification

of seven variables: age, sex, race, Hispanic origin, tenure,

urbanicity, and region. There were 840 cells in the crossclassification. Collapsing was necessary in order to produce post-strata with sufficient sample for reliable Dual

System Estimation (DSE). The collapsing reduced the number of post-strata to 357.

Race and Hispanic origin were considered the most important variables to retain in 1990. After collapsing, five

race/Hispanic origin post-strata were maintained: NonHispanic White or Other, Black, Hispanic White or Other,

Asian and Pacific Islander, and Reservation Indians. Offreservation American Indians were placed in either the

Non-Hispanic White or Other group or the Hispanic White

or Other group, depending on whether they were of Hispanic origin. Within each of these race/Hispanic origin

post-strata, seven age/sex categories were maintained.

The other variables were collapsed in the following order:

region, urbanicity, then tenure, if necessary. For American

Indians residing on reservations, all these variables were

collapsed. For Asian and Pacific Islanders, region and urbanicity were collapsed and tenure maintained. For the Black

and Hispanic White or Other groups, region was collapsed

for two levels of urbanicity. For Non-Hispanic White or

Other, the full cross-classification of region, urbanicity and

tenure were maintained. Griffin and Haines (2000b) provides a detailed table on the 1990 PES post-stratification.

Post-Stratification Plan

The Census 2000 A.C.E. retained most of the 1990 PES

post-stratification variables and included several additional ones. Nine variables were used in 2000: age, sex,

Dual System Estimation Section I—Chapter 7 7–5

U.S. Census Bureau, Census 2000
race, Hispanic origin, tenure, region, Metropolitan Statistical Area size/Type of Enumeration Area, and tract-level

return rate. The Metropolitan Statistical Area size variable

replaced the urbanicity variable that was not available

until the summer of 2001. Type of Enumeration Area (TEA)

and the tract return rate were two new features of the

2000 A.C.E. post-stratification. The mailout/mailback

areas were differentiated from other types of enumeration

areas. In addition, tracts were classified by high or low

return rates. Multiple responses to the race question were

reflected in the race and Hispanic origin groupings.

Table 7-2 shows the 64 post-stratum groups for the Census 2000 A.C.E. Within each post-stratum group, there are

seven age/sex groups (shown in Table 7-3). Thus, there

was a maximum of 64 × 7 = 448 post-strata. The P-sample

size was too small or the sampling variance too high for

eight of the 64 post-stratum groups. For each of these

eight groups, the 7 age/sex post-strata were collapsed

into 3 post-strata (under 18; males 18+ and females 18+).

As a result, direct DSEs were calculated within each of 416

post-strata, which were expanded to 448 DSEs using synthetic estimation for the collapsed groups. The poststratification plan was chosen to reduce correlation bias

without having an adverse effect on the variance of the

dual system estimator. Following is a detailed description

of the post-stratification variables including an explanation of the race/Hispanic origin domain assignment

7–6 Section I—Chapter 7 Dual System Estimation

U.S. Census Bureau, Census 2000
Table 7-2. Census 2000 A.C.E. 64 Post-Stratum Groups (U.S.)

Race/Hispanic origin

domain number* Tenure MSA/TEA

High return rate Low return rate

NE MW S W NE MW S W

Domain 7

(non-Hispanic White or

‘‘Some other race’’)

Owner Large MSA MO/MB 01 02 03 04 05 06 07 08

Medium MSA MO/MB 09 10 11 12 13 14 15 16

Small MSA & Non-MSA MO/MB 17 18 19 20 21 22 23 24

All other TEAs 25 26 27 28 29 30 31 32

Nonowner Large MSA MO/MB 33 34

Medium MSA MO/MB 35 36

Small MSA & Non-MSA MO/MB 37 38

All other TEAs 39 40

Domain 4

(Non-Hispanic Black)

Owner Large MSA MO/MB

41 42

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

43 44

All other TEAs

Nonowner Large MSA MO/MB

45 46

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

47 48

All other TEAs

Domain 3

(Hispanic)

Owner Large MSA MO/MB

49 50

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

51 52

All other TEAs

Nonowner Large MSA MO/MB

53 54

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

55 56

All other TEAs

Domain 5

(Native Hawaiian or

Pacific Islander)

Owner 57

Nonowner 58

Domain 6

(Non-Hispanic Asian)

Owner 59

Nonowner 60

American

Indian or

Alaska

Native

Domain 1

(On

Reservation)

Owner 61

Nonowner 62

Domain 2

(Off

Reservation)

Owner 63

Nonowner 64

*For Census 2000, persons can self-identify with more than one race group. For post-stratification purposes, persons are included in a single

Race/Hispanic Origin Domain. This classification does not change a person’s actual response. Further, all official tabulations are based on actual

responses to the census.

Dual System Estimation Section I—Chapter 7 7–7

U.S. Census Bureau, Census 2000
Table 7-3. Census 2000 A.C.E.

Age/Sex Groups

Male Female

Under 18 1

18 to 29 2 3

30 to 49 4 5

50+ 6 7

Post-stratification Variables

This section gives a detailed description of the poststratification variables including the handling of multiple

responses to the race question. A.C.E. post-stratification

used the following variables:

• race/Hispanic origin - seven categories

• age/sex - seven categories

• tenure - two categories

• Metropolitan Statistical Area (MSA) by Type of Enumeration (TEA) - four categories

• return rate - two categories

• region - four categories

The seven race/Hispanic origin domains were:

• American Indian or Alaska Native on Reservations

• Off-Reservation American Indian or Alaska Native

• Hispanic

• Non-Hispanic Black

• Native Hawaiian or Pacific Islander

• Non-Hispanic Asian

• Non-Hispanic White or ‘‘Some other race’’

Inclusion in a race/Hispanic origin domain is complicated,

as it depends on several variables and whether there are

multiple race responses. In addition, inclusion in a

race/Hispanic origin domain does not change a person’s

race/Hispanic origin response. All Census 2000 tabulations are based on the actual responses. For example, a

person who responded as American Indian on a reservation and Black was placed in the first race/Hispanic origin

category (Domain 1) for post-stratification purposes, but

was tabulated in the census as American Indian/Black.

The seven age/sex categories were:

1. Under 18

2. 18 - 29 male

3. 18 - 29 female

4. 30 - 49 male

5. 30 - 49 female

6. 50+ male

7. 50+ female

The two tenure categories were:

1. Owner

2. Nonowner

The four MSA/TEA categories were:

1. Large MSA Mailout/ Mailback (MO/MB)

2. Medium MSA MO/MB

3. Small MSA or Non-MSA MO/MB

4. All other TEAs

MSA/CMSA FIPS codes, as defined by the Office of Management and Budget, were used for post-stratification. For

simplification, MSA/CMSA will herein be referred to as

MSA. Large MSA consists of the ten largest MSAs based on

unadjusted, Census 2000 total population counts including the population in Group Quarters. Medium MSAs are

those (besides the largest 10) that have at least 500,000

total population. Small MSAs are those with a total population size less than 500,000. For post-stratification purposes, MO/MB areas were contrasted with the non-MO/MB

areas.

The two return rate categories were:

1. High

2. Low

Return rate is a tract-level variable measuring the proportion of occupied housing units in the mailback universe

that returned a census questionnaire. Low (high) return

rate tracts are those tracts whose return rate is less than

or equal to (greater than) the 25th percentile return rate.

Separate 25th percentile cut-off values were formed for

the six applicable race/Hispanic origin by tenure groups.

Persons in List/Enumerate, Rural Update/Enumerate, and

Urban Update/Enumerate TEAs were automatically placed

in the High category.

The four region categories were:

1. Northeast

2. Midwest

3. South

4. West

Pre-Collapsing

Pre-collapsing was done prior to data collection and

knowledge of the exact sample size in each post-stratum.

All race/Hispanic origin, age/sex, and tenure categories

for the U.S. were initially maintained. The research for the

determination of the important post-stratification variables

7–8 Section I—Chapter 7 Dual System Estimation

U.S. Census Bureau, Census 2000
provided information on the expected sample size in each

category which was then used to define a collapsing hierarchy. The pre-collapsing plan for the region, MSA/TEA

and return rate variables was as follows:

• Non-Hispanic White or ‘‘Some other race’’ Owners: No

collapsing.

• Non-Hispanic White or ‘‘Some other race’’ Non-owners:

Region was eliminated.

• Non-Hispanic Black: Region was eliminated. In addition

there was partial collapsing of the MSA/TEA variable

within return rate and tenure categories.

• Hispanic: Region was eliminated. In addition there was

partial collapsing of the MSA/TEA variable within return

rate and tenure categories.

• Native Hawaiian or Pacific Islander: The region, return

rate and MSA/TEA variables were eliminated. Only tenure and age/sex were retained.

• Non-Hispanic Asian: The region, return rate and

MSA/TEA variables were eliminated. Only tenure and

age/sex were retained.

• American Indian or Alaska Native on Reservations: The

region, return rate and MSA/TEA variables were eliminated. Only tenure and age/sex were retained.

• Off-Reservation American Indian or Alaska Native: The

region, return rate and MSA/TEA variables were eliminated. Only tenure and age/sex were retained.

Post-Collapsing

A.C.E. post-stratification included a plan to collapse poststrata that contained less than 100 (unweighted) P-sample

persons, called post-collapsing, considering such a poststratum too small to produce reliable estimates. If a collapsed post-strata was still too small, it could have been

further collapsed. The collapsing procedure was hierarchical and required a pre-defined collapsing order. Given the

pre-collapsing plan that yielded 448 post-strata, not much

post-collapsing was anticipated, but an extensive postcollapsing strategy was designed for completeness and to

satisfy the requirement of pre-specification.

Note that collapsing does not necessarily imply elimination of a variable. Collapsing can refer to a reduction in

the number of categories for a variable. The following

general outline describes the post-collapsing hierarchy

that was planned:

• If any of the 448 post-strata are too small, collapse

age/sex first. This means that within any of the 64 U.S.

post-stratum groups, if at least one of the seven

age/sex categories defined in Table 7-3 has less than

100 P-sample persons, reduce age/sex to the following

three categories: Under 18, 18+ male, and 18+ female.

• If some post-strata are still too small and require collapsing, collapse region next, if applicable. This collapsing applies only to the Non-Hispanic White or ‘‘Some

other race’’ domain since the variable region is only

included in their post-stratification definition. In this

case, all levels of region (Northeast, Midwest, South,

West) are combined to eliminate the variable.

• Next, collapse the four-level MSA/TEA variable, into the

following two groups:

• Large and medium MSA MO/MB

• Small MSA and non-MSA MO/MB and all other TEAs

• If further collapsing is necessary, return rate is the next

variable to collapse. High and Low return rate categories are combined to eliminate the variable.

• Next collapse the variable MSA/TEA. If necessary, the

two groups defined above would be combined together

to eliminate the variable MSA/TEA completely.

• The next variable to collapse is tenure. Owner and nonowner categories are combined to eliminate the variable

entirely, if necessary.

• If collapsing is still needed, the three remaining age/sex

post-strata are combined to eliminate the age/sex variable completely.

• In the event that there are less than 100 P-sample

persons in a race/Hispanic origin domain, combine all

persons in that domain with Domain 7, which includes

non-Hispanic White and ‘‘Some other race.’’

In practice, only the first step of collapsing was necessary.

Eight of the 64 post-stratum groups had their 7 age/sex

post-strata collapsed to 3 age/sex groups, resulting in 32

fewer post-strata. Thus, there were 448 - 32 = 416 poststrata.

Race and Hispanic Origin Classifications

The Census 2000 questionnaire has 15 possible race

responses. The 15 responses are collapsed into six major

race groups as shown below. Races that are included in

the major groups are shown in parentheses. Persons selfidentifying with a single race essentially place themselves

into one of these six categories.

• White

• Black (Black, African American, Negro)

• American Indian or Alaska Native

• Asian (Asian Indian, Chinese, Filipino, Japanese, Korean,

Vietnamese, Other Asian)

• Native Hawaiian or Pacific Islander (Native Hawaiian,

Guamanian or Chamorro, Samoan, Other Pacific

Islander)

Dual System Estimation Section I—Chapter 7 7–9

U.S. Census Bureau, Census 2000
• ‘‘Some other race’’ (There was a box on the questionnaire labeled ‘‘Some other race - Print race’’ with a line to

enter any race the respondent desired.)

For the first time in census history, persons were able to

respond to more than one race category. Allowing persons

to self-identify with multiple races results in many more

than six race groups. In fact, after collapsing race to the

six major groups, there are 26 -1 = 63 possible race combinations. It is necessary to subtract the 1 in this equation

since each individual is assumed to have a race.

The race variable defined above is often cross-classified

with the Hispanic origin variable to define post-strata. The

Hispanic origin variable consists of two responses, No and

Yes. Categories that are included in the Yes response are

shown in parentheses.

1. No, not Spanish/Hispanic/Latino

2. Yes (Mexican, Mexican American, Chicano, Puerto

Rican, Cuban, Other Spanish/Hispanic/Latino)

Combining the race and Hispanic origin variables yields

63 × 2 =126 possible race/Hispanic origin groups. It is

important to note that in a survey the size of A.C.E., no

post-stratification plan of interest can support 126

race/Hispanic origin groups. Consequently, each of the

126 race/Hispanic origin response possibilities was

assigned to one of seven race/Hispanic origin domains.

The seven race/Hispanic origin domains are defined as

follows:

1. American Indian or Alaska Native on Reservations

2. Off-Reservation American Indian or Alaska Native

3. Hispanic

4. Non-Hispanic Black

5. Native Hawaiian or Pacific Islander

6. Non-Hispanic Asian

7. Non-Hispanic White or ‘‘Some other race’’

Note that missing race and Hispanic origin data are

imputed. The rules used to classify the 126 race and Hispanic origin combinations into one of the seven

race/Hispanic origin domains are now presented. Many of

the decisions on how multiple race persons were classified

are based on cultural, linguistic, and sociological factors,

which are known to affect coverage and are not necessarily data-driven.

A hierarchy was used to assign persons to a race/Hispanic

origin domain. The race/Hispanic origin designation

occurs in the following order: American Indian or Alaska

Native on Reservations, Off-Reservation American Indian

or Alaska Native, Hispanic, Non-Hispanic Black, Native

Hawaiian or Pacific Islander, Non-Hispanic Asian, and NonHispanic White or ‘‘Some other race.’’ This collapsing was

only used for the post-stratification, all census data were

tabulated in accordance with the race and Hispanic origin

categories selected by census respondents.

For the following tables, Indian Country (IC) is a blocklevel variable that indicates whether a block is (wholly or

partly) inside an American Indian reservation/trust land,

Oklahoma Tribal Statistical Area (OTSA), Tribal Designated

Statistical Area (TDSA), or Alaska Native Village Statistical

Area (ANVSA).

Tables 7-4 and 7-5 display the assignment of race/

Hispanic origin domains. Table 7-4 applies to Hispanic

persons, while Table 7-5 applies to non-Hispanic persons.

The first six rows of Tables 7-4 and 7-5 correspond to a

single race response. The remaining portion of the tables

address the assignment of multiple race responses to a

single race/Hispanic origin domain. Although a person

may be associated with multiple race responses, each

person is included in only one of the seven race/Hispanic

origin domains. All persons with a common number are

assigned to the same race/Hispanic origin domain. The

number for each race/Hispanic origin domain was

assigned as follows:

Domain 1 (Includes American Indian or Alaska

Native on Reservations). This domain includes any person living on a reservation marking American Indian or

Alaska Native either as their single race or as one of many

races, regardless of their Hispanic origin.

Domain 2 (Includes Off-Reservation American Indian

or Alaska Native). This domain includes any person living in Indian Country, but not on a reservation who marks

American Indian or Alaska Native either as a single race or

as one of many races, regardless of their Hispanic origin.

This domain also includes any Non-Hispanic person not

living in Indian Country who marks American Indian or

Alaska Native as a single race.

Domain 3 (Includes Hispanic). This domain includes all

Hispanic persons who are not included in Domains 1 or 2.

All Hispanic persons (excluding American Indian or Alaska

Native in Indian Country) are included in Domain 3. The

only exception to this rule occurs when a Hispanic person

lives in the state of Hawaii and classifies himself or herself

as Native Hawaiian or Pacific Islander, regardless of

whether he or she identifies with a single or multiple race.

All Hispanic persons satisfying this condition are

re-classified into Domain 5.

Domain 4 (Includes Non-Hispanic Black). This domain

includes any non-Hispanic person who marks Black as

their only race. It also includes the combination of Black

and American Indian or Alaska Native not in Indian Country. In addition, people who mark Black and another single

race group (Native Hawaiian or Pacific Islander, Asian,

White, or ‘‘Some other race’’) are included in Domain 4.

7–10 Section I—Chapter 7 Dual System Estimation

U.S. Census Bureau, Census 2000
The only exception to this rule occurs when a NonHispanic

Black person lives in the state of Hawaii and classifies himself or herself as Native Hawaiian or Pacific Islander. All

Non-Hispanic Black persons satisfying this condition are

reclassified into Domain 5.

Domain 5 (Includes Native Hawaiian or Pacific

Islander). This domain includes any Non-Hispanic person

marking the single race Native Hawaiian or Pacific

Islander. For NonHispanic persons, it also includes the race

combination of Native Hawaiian or Pacific Islander and

American Indian or Alaska Native not in Indian Country.

Also included is the race combination of Native Hawaiian

or Pacific Islander with Asian for Non-Hispanic persons. All

persons living in the state of Hawaii who classify themselves as Native Hawaiian or Pacific Islander, regardless of

their Hispanic origin and whether they identify with a

single or multiple race, are also included in Domain 5.

Domain 6 (Includes Non-Hispanic Asian). This domain

includes any non-Hispanic person marking Asian as their

single race. If a person self-identifies with Asian and

American Indian or Alaska Native not in Indian Country,

they are included in Domain 6.

Domain 7 (Includes Non-Hispanic White or ‘‘Some

other race’’). Non-Hispanic White or Non-Hispanic ‘‘Some

other race’’ persons are included in Domain 7. NonHispanic persons who self-identify with American Indian

or Alaska Native not in Indian Country and are White or

‘‘Some other race’’ are classified into Domain 7. If a Native

Hawaiian or Pacific Islander response is combined with a

White or ‘‘Some other race’’ response, they also are

included in Domain 7. A person who self-identifies with

Asian and White or Asian and ‘‘Some other race’’ is also

included in this domain. Finally, all Non-Hispanic persons

who self-identify with three or more races (excluding

American Indian or Alaska Native in Indian Country) are

included in Domain 7. The only exception to this rule

occurs when a Non-Hispanic White or Non-Hispanic ‘‘Some

other race’’ person lives in Hawaii and classifies themselves as Native Hawaiian or Pacific Islander, regardless of

whether they identify with other races. Persons who satisfy this criteria are re-classified into Domain 5.

Dual System Estimation Section I—Chapter 7 7–11

U.S. Census Bureau, Census 2000
Table 7-4. Census 2000 A.C.E. Race/Origin Post-stratification

Domains for Hispanic Indian country (IC)

Not in IC

Indian country (IC)

Not on

reservation

On

reservation

Single race:

American Indian or Alaska Native . . . ......... 3 2 1

Black . .................................... 3 3 3

Native Hawaiian or Pacific Islander . . . . . . . . . . *3 3 3

Asian ..................................... 3 3 3

White . . . ................................. 3 3 3

‘‘Some other race’’ ......................... 3 3 3

American Indian or Alaska Native and:

Black ................................. 3 2 1

Native Hawaiian or Pacific Islander . . . . . . *3 2 1

Asian . . ............................... 3 2 1

White . ............................... 3 2 1

‘‘Some other race’’ . .................... 3 2 1

Black and:

Native Hawaiian or Pacific Islander . . . . . . *3 3 3

Asian . . ............................... 3 3 3

White . ............................... 3 3 3

‘‘Some other race’’ . .................... 3 3 3

Native Hawaiian or Pacific Islander and:

Asian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *3 3 3

White . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *3 3 3

‘‘Some other race’’ . .. . . . . . . . . . . . . . . . . . . *3 3 3

Asian and:

White . ............................... 3 3 3

‘‘Some other race’’ . .................... 3 3 3

American Indian or Alaska Native and:

Two or More Races . . . . . . . . . . . . . . . . . . . . *3 2 1

All Else** . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *3 3 3

*All persons living in the state of Hawaii who classify themselves as Native Hawaiian or Pacific

Islander, regardless of their Hispanic origin and whether they identify with a single or multiple race, are

included in Domain 5, which includes Native Hawaiian or Pacific Islander.

**All Else encompasses all remaining combinations that exclude American Indian or Alaska Native.

7–12 Section I—Chapter 7 Dual System Estimation

U.S. Census Bureau, Census 2000
Table 7-5. Census 2000 A.C.E. Race/Origin Post-stratification

Domains for Non-Hispanic

Not in IC

Indian country (IC)

Not on

reservation

On

reservation

Single race:

American Indian or Alaska Native . . . ......... 2 2 1

Black . .................................... 4 4 4

Native Hawaiian or Pacific Islander . ......... 5 5 5

Asian ..................................... 6 6 6

White . . . ................................. 7 7 7

‘‘Some other race’’ ......................... 7 7 7

American Indian or Alaska Native and:

Black ................................. 4 2 1

Native Hawaiian or Pacific Islander ...... 5 2 1

Asian . . ............................... 6 2 1

White . ............................... 7 2 1

‘‘Some other race’’ . .................... 7 2 1

Black and:

Native Hawaiian or Pacific Islander . . . . . . *4 4 4

Asian . . ............................... 4 4 4

White . ............................... 4 4 4

‘‘Some other race’’ . .................... 4 4 4

Native Hawaiian or Pacific Islander and:

Asian . . ............................... 5 5 5

White . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *7 7 7

‘‘Some other race’’ . .. . . . . . . . . . . . . . . . . . . *7 7 7

Asian and:

White . ............................... 7 7 7

‘‘Some other race’’ . .................... 7 7 7

American Indian or Alaska Native and:

Two or More Races . . . . . . . . . . . . . . . . . . . . *7 2 1

All Else** . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *7 7 7

*All persons living in the state of Hawaii who classify themselves as Native Hawaiian or Pacific

Islander, regardless of their Hispanic origin and whether they identify with a single or multiple race, are

included in Domain 5, which includes Native Hawaiian or Pacific Islander.

**All Else encompasses all remaining combinations which exclude American Indian or Alaska Native.

Dual System Estimation Section I—Chapter 7 7–13

U.S. Census Bureau, Census 2000
VARIANCE ESTIMATION

The A.C.E. sample was considered a three-phase

sample—the initial listing sample was the first phase;

A.C.E. reduction and small block cluster subsampling was

the second phase; and Targeted Extended Search (TES)

was the third phase. Multiphase sampling differs from

multistage in the following way. In a multistage design,

the information needed to draw all stages of the sample is

known before the sampling begins; in a multiphase

design, the information needed to draw any phase of the

sample is not available until the previous phase is completed. Because of the multiphase nature of the design

(housing counts not available until after the first-phase

listing), a new variance estimator needed to be developed.

Full details are given in Starsinic and Kim (2001).

Our goal is to obtain a variance estimator for the Dual System Estimator (DSE), of the form:

DSˆE  DD (

CE

Ne

) ( Nn Ni

Mn (

Mo

No

) Ni

) (1)

where:

DD  number of census data-defined persons

CE  estimated number of A.C.E. E-sample

correct enumerations

Ne  estimated number of A.C.E. E-sample

persons

Nn  estimated number of A.C.E. P-sample

nonmovers

Ni  estimated number of A.C.E. P-sample

inmovers

No  estimated number of A.C.E. P-sample

outmovers

Mn  estimated number of A.C.E. P-sample

nonmover matches

Mo  estimated number of A.C.E.

P-sample outmover matches

The DSE is computed separately for each post-stratum

denoted by h. The national corrected population estimate

is computed as:

T

ˆ

US  h

DSˆEh (2)

There is no closed-form solution for the variance estimator, and the Taylor linearization variance estimator is very

complex. That leaves replication methodology as the only

practical variance estimator. Specifically, a stratified jackknife estimator was the type of replication method chosen

for the implementation.

A jackknife estimator is calculated from a set of replicates

where the number of replicates is equal to the number of

observations (clusters in this case) in the sample. Each

replicate represents what the DSE would have been had

each particular cluster not been part of the sample. The

overall variance is calculated by summing the squares of

the differences between the replicate DSE and the wholesample DSE.

The most important challenge for the Census 2000 A.C.E.

variance estimation was the precise form for calculating

the contribution of replicate DSEs to the variance estimator; in particular, new weights had to be calculated for replicates to represent the effect of removing the cluster

whose replicate was being calculated. No previous results

were directly applicable to the DSE, but a methodology

was developed based on the work of Rao and Shao (1992).

The remaining part of this section describes the precise

formulas in detail. They require somewhat complex notation and mathematical steps.

Detailed Methodology

A general estimator of a total is:

Ty i

wi y i (3)

The estimator for the j

th replicate is

T y

i i

w i

j yi (4)

where yi is the characteristic of interest, and wi

(j) is the

replicate weight for the ith unit, which differs from the

original weight in a prespecified subset of the observations. With these replicate estimators, a variance estimator

can be constructed:

Va

ˆr Ty  

j

cj T y

i  Ty

2 (5)

Before continuing, we must set down some specific notation. Let wi be the first phase sampling weight, and let yi

be the cluster-level total of any of the seven estimated

components of the DSE (CE, Nn, etc.). Let A and A2 indicate

the first and second phase samples, respectively. Let xig=1

if unit i is in ‘‘group’’ (second phase stratum) g and zero

otherwise. Let nh be the number of units selected in firstphase stratum h. Let ng be the number of units in stratum

h that are also in group g, and let rg be the number of the

ng units selected in the second phase. In all of the following equations, ‘‘j’’ will represent one cluster that is being

dropped to calculate its associate replicate estimate T(j);

‘‘k’’ is one cluster other than the one being dropped.

For two-phase stratified sampling, there are two different

point estimators, the Double Expansion Estimator (DEE)

DEE  g i  A2

ng

rg

wi xig yi (6)

and the Reweighted Expansion Estimator (REE)

REE  g i  	2

( i  	

wi xig

i  A2

wixig

) wi xig yi (7)

7–14 Section I—Chapter 7 Dual System Estimation

U.S. Census Bureau, Census 2000
There is an established result by Rao and Shao (1992)

which gives a replicate variance estimator for the REE

under two-phase stratified sampling. Unfortunately, all the

individual components of the DSE, such as Ne, the number

of E-sample people, are DEE’s. Taking a closer look at the

DEE, however, suggested a procedure that could be

applied.

ng  iA xig, rg  

iA2

xig

DEE  g iA2

ng

rg

wi xig yi g i	2

( k	

xkg

k	2

xkg

) wi xig yi

 g i	2

( 


	

wk xkg wk

1

k	2

wk xkg wk

1

) wi xig yi (8)

The DEE has just been rewritten in a form that is quite

similar to the REE. This suggests the following generalization:

Ty2  i	2i yi, where

i  g ( k	

wk xkg qk

k	2

wk xkg qk

) wi xig (9)

and where qj = 1 for the REE and wi

-1 for the DEE.

Replicates are then naturally written as:

Ty2

j  iA2

i

j yi

, where

i

j  g ( k	

wk

j xkg qk

k	2

wk

j xkg qk

) wi

j xig (10)

When qj

=1 (i.e. the REE case), the replicate variance estimator of this generalized estimator, based on equation (5),

is the same as the REE replicate variance estimator of Rao

and Shao (1992).

Application To a Three-Phase Dual System

Estimator

Within any of the seven components of the DSE that are

subject to sampling error (CE, Ne, Nn, No, Ni

, Mn, and Mo),

the cluster sums (yi

) can be broken down into two components: the total prior to any adjustments made by TES (ui

),

and the additional total from the TES sample (vi

). This second piece can be further subdivided into TES totals from

clusters sampled with certainty, and TES totals from clusters sampled systematically. The estimator (a DEE) of one

of the components is

T

ˆ

y3  iA2

i ui k1

2

i	2

i tk sik ai vi (11)

where sik is the third phase stratum indicator (sik=1 if the

cluster is selected with certainty, 0 otherwise; si2=1-si1, an

indicator that the cluster is eligible to be selected systematically), ai is the third phase sample indicator (ai

=1 if the

cluster is in A3, 0 otherwise), and tk, the TES conditional

weight, is equal to

tk 

iA2

sik

i	2

sik ai



iA2

sik

i	3

sik

 number of clusers selected in phase 2

number of clusters selected in phase 3

(12)

For si1, the certainty stratum, all clusters within it have

ai

=1, so tk=1 for all clusters in the stratum.

To create the replicate estimator, simply apply what was

learned above in equations (8) and (10).

T

ˆ y3

j  iA2

i

j ui + k1

2

iA2

i

j t

k

j sik ai vi (13)

 iA2

i

j ui iA2

i

j tlj sil ai vi iA2

i

j t2j si2 ai vi

where,

t 1

j  1

t2

j 

iA2

i

j

si2 i

1

iA2

i

j

si2 ai i

1

Implementation of Variance Estimation for the

A.C.E.

The first step in implementing this variance estimation

methodology is calculating the replicate weights. To this

point, the method of replication used to arrive at the variance is immaterial, but we will now state that the jackknife will be used. Let the replicate weights after the first

stage of sampling be the standard jackknife replicate

weights

wi

j  { 0

nh

nh  1

if i j

whi if i and j are in the same first phase stratum

whi otherwise

(14)

Then, the final weights are obtained by applying equation

(10).

Note that this is an unusual form of the jackknife. Normally, the jackknife has as many replicates as observations. Here, there are 11,303 clusters remaining after the

second phase of the sample, but the number of replicates

is equal to the first phase’s sample size of 29,136 clusters.

The clusters sampled out in the second phase obviously

do not contribute to the variance due to the second and

third phases, but they must be included to accurately

Dual System Estimation Section I—Chapter 7 7–15

U.S. Census Bureau, Census 2000
account for the first phase of sampling. ‘‘Deleting’’ a cluster that was sampled out changes the weights of the other

clusters that were in the same first phase sampling stratum.

The second step of the implementation is to adjust the

imputation of certain probabilities to account for the replication. This is a component of the variance that can be

accounted for by including the effect of the replicate

weights in the imputation. For some persons, their match,

residence, or correct enumeration status remains unresolved even after follow-up operations. In these cases, a

probability for each unresolved status is imputed using an

imputation cell technique, with each unresolved case in an

imputation cell getting the same imputed probability. The

general form for the ‘‘replicated’’ imputation of the probability for an unresolved person in imputation cell k is:

Prk

* j 



resolved pk

wp

* j tp* j

Prp



resolved pk

wp

* j

tp

* j (15)

where the summation is over all resolved persons in imputation cell k, and:

wp

* = person-level weight for replicate j, incorporating all

sampling operations except TES, and not including

the noninterview adjustment

tp

* j  { conditional TES weight for replicate j, the inverse of the

probability of selection in the TES sample, if the person

is a TES person

1 if the person is NOT a TES person

Prp 

{ 1 if a person is a 
matchresidentcorrect enumeration

0 if a person is NOT a 
matchresidentcorrect

enumeration}

To complete the estimation of the variances, the 29,136

replicate dual system estimates were computed for each

of the 448 post-strata:

DSˆE h

j  C  II (CE j

N e

j ) ( N n

j N ij

M n

j (M o

j

N o

j

)N i

j

) (16)

Equation (13) was used for the separate computation of

each of the seven replicated terms of the DSE: CE(j), Ne

(j),

Nn

(j), Ni(j), No(j), Mn(j), and Mo(j).

The variance estimates for post-stratum h used formula

(5):

Var DSˆEh  

j

n1, i 1

n1,i

DSˆE h

j  DSˆE h

2 (17)

finally, the variance of the national adjusted population

estimate is:

Var T

ˆ

US  

poststratum h poststratum h ́

Cov DSˆEh, DSˆE h ́,

where Cov DSˆE h, DSˆE h Var DSˆE h, and

(18)

Cov DSˆE h, DSˆEh ́ 

j

n1,i  1

n1,i

DSˆE h

j  DSˆEh DSˆEh  ́j  DSˆEh ́)

Covariances exist between post-strata mostly because of

correlations between members of the same household

being in different post-strata but having the same probability of being included in the sample. For instance,

within a given race/Hispanic origin/tenure/region group

there exists some covariance among males 30-49, females

30-49 and children 0-17, because such persons are likely

to live in the same household, and hence, show very similar census and A.C.E. inclusion probabilities.

RESULTS

The percent net undercount (UC) is the estimated net

undercount (or net overcount) divided by the dual system

estimate for a post-stratum expressed as a percentage. A

positive number implies undercoverage, while a negative

number implies overcoverage. The percent net undercount

for Census 2000 shown in this document is strictly for the

household population and excludes group quarters persons.

UC  (

DSE C

DSE )  100

Table 7-6 presents the estimated percent net undercount

for each of the 64 post-stratum groups. Table 7-7 presents

the standard error of each of these estimates. Many more

results are available in Davis (2001).

7–16 Section I—Chapter 7 Dual System Estimation

U.S. Census Bureau, Census 2000
Table 7-6. Census 2000 A.C.E. 64 Post-Stratum Groups - Percent Net Undercount

Race/Hispanic origin

domain number* Tenure MSA/TEA

High return rate Low return rate

NE MW S W NE MW S W

Domain 7

(non-Hispanic White or

‘‘Some other race’’)

Owner Large MSA MO/MB 0.81 0.01 0.36 -0.38 -3.62 -2.61 2.19 1.14

Medium MSA MO/MB 0.30 -0.12 0.46 -0.28 -4.39 -0.33 0.66 1.81

Small MSA & Non-MSA MO/MB -0.25 0.14 0.44 0.30 2.29 2.61 2.09 2.71

All other TEAs 1.84 -1.11 1.34 0.85 0.56 -0.16 0.15 1.59

Nonowner Large MSA MO/MB 1.82 1.02

Medium MSA MO/MB 0.61 2.83

Small MSA & Non-MSA MO/MB 2.45 3.61

All other TEAs 1.64 4.08

Domain 4

(Non-Hispanic Black)

Owner Large MSA MO/MB

1.63 -1.31

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

0.07 0.46

All other TEAs

Nonowner Large MSA MO/MB

4.18 3.42

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

2.64 0.12

All other TEAs

Domain 3

(Hispanic)

Owner Large MSA MO/MB

1.46 0.04

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

1.66 1.08

All other TEAs

Nonowner Large MSA MO/MB

3.52 4.98

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

4.88 10.74

All other TEAs

Domain 5

(Native Hawaiian or

Pacific Islander)

Owner 2.71

Nonowner 6.58

Domain 6

(Non-Hispanic Asian)

Owner 0.55

Nonowner 1.58

American

Indian or

Alaska

Native

Domain 1

(On

Reservation)

Owner 5.04

Nonowner 4.10

Domain 2

(Off

Reservation)

Owner 1.60

Nonowner 5.57

*For Census 2000, persons can self-identify with more than one race group. For post-stratification purposes, persons are included in a single

Race/Hispanic Origin Domain. This classification does not change a person’s actual response. Further, all official tabulations are based on actual

responses to the census.

A negative net undercount denotes a net overcount.

Dual System Estimation Section I—Chapter 7 7–17

U.S. Census Bureau, Census 2000
Table 7-7. Census 2000 A.C.E. 64 Post-Stratum Groups - Standard Error of the Net Undercount in

Percent

Race/Hispanic origin

domain number* Tenure MSA/TEA

High return rate Low return rate

NE MW S W NE MW S W

Domain 7

(non-Hispanic White or

‘‘Some other race’’)

Owner Large MSA MO/MB 0.43 0.36 0.87 -0.45 1.05 1.43 1.54 2.09

Medium MSA MO/MB 0.85 -0.28 0.42 0.38 1.52 0.84 1.10 2.79

Small MSA & Non-MSA MO/MB 1.33 0.40 0.43 0.57 3.60 2.12 1.08 1.49

All other TEAs 1.06 0.39 0.97 1.66 2.17 1.21 0.65 1.89

Nonowner Large MSA MO/MB 0.63 1.01

Medium MSA MO/MB 0.71 1.24

Small MSA & Non-MSA MO/MB 0.51 1.24

All other TEAs 0.94 1.67

Domain 4

(Non-Hispanic Black)

Owner Large MSA MO/MB

0.56 1.24

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

1.07 1.86

All other TEAs

Nonowner Large MSA MO/MB

0.66 1.05

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

0.96 2.08

All other TEAs

Domain 3

(Hispanic)

Owner Large MSA MO/MB

0.52 1.26

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

1.01 2.09

All other TEAs

Nonowner Large MSA MO/MB

0.67 1.12

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

1.55 4.12

All other TEAs

Domain 5

(Native Hawaiian or

Pacific Islander)

Owner 3.83

Nonowner 4.07

Domain 6

(Non-Hispanic Asian)

Owner 0.87

Nonowner 0.98

American

Indian or

Alaska

Native

Domain 1

(On

Reservation)

Owner 1.45

Nonowner 1.42

Domain 2

(Off

Reservation)

Owner 1.95

Nonowner 2.02

*For Census 2000, persons can self-identify with more than one race group. For post-stratification purposes, persons are included in a single

Race/Hispanic Origin Domain. This classification does not change a person’s actual response. Further, all official tabulations are based on actual

responses to the census.

A negative net undercount denotes a net overcount.

7–18 Section I—Chapter 7 Dual System Estimation

U.S. Census Bureau, Census 2000
Attachment.

The Effect of Movers on Dual System Estimation

This attachment discusses the effect of movers on Dual

System Estimation (DSE). Three alternative methodologies

for handling movers in DSE have been considered by the

U.S. Census Bureau. Historically, they are referred to as

PES-A, PES-B, and PES-C. However, the current terminology

is to refer to them as Procedures A, B, and C. Following are

the definitions of these methodologies as described in U.S.

Bureau of the Census (1985).

Procedure A. This procedure reconstructs the households as they existed at the time of the census. A respondent is asked to identify all persons who were living or

staying in the sample household on Census Day. These

persons are then matched against names on the census

questionnaire for the sample address (and surrounding

area). From this information, estimates of the number and

percent matched for nonmovers and outmovers can be

made.

Procedure B. This procedure identifies all current residents living or staying in the sample household at the

time of the interview. The respondent is asked to provide

the address(es) where these persons were living or staying

on Census Day. These persons are then matched against

names on corresponding census questionnaire(s) at the

nonmover’s or inmover’s census address. Estimates of the

number and percent matched for nonmovers and inmovers can be made.

Procedure C. This procedure identifies all current residents living or staying at the sample address at the time

of the interview plus all other persons who lived at the

sample address on Census Day and have moved since

Census Day. However, only the Census Day residents (nonmovers and outmovers) are matched with the census

questionnaire(s) at the sample address. Estimates of the

number of nonmovers, outmovers, inmovers, and the percent matched for nonmovers and outmovers, can then be

made. Estimates of nonmovers and movers come from

Procedure B and match rate estimates for the movers from

Procedure A (using outmover matching). Thus, Procedure

C is a combination of Procedures A and B.

In 1990, Procedure B was used. The unresolved match rate

for inmovers in 1990 was high, around 13 percent. In

addition, with sampling for nonresponse initially planned

for Census 2000, inmover matching would have had an

even higher level of difficulty. A decision was made that

Procedure B would NOT be used for Census 2000. When

the Supreme Court decided against sampling for apportionment (no sampling for nonresponse), it was too late to

change the decision on Procedure B.

In the 1995 and 1996 Census tests, Procedure A was

used. The U.S. Census Bureau reasoned that an outmover

match rate would be more accurate than an inmover

match rate, particularly with sampling for nonresponse.

For outmovers, interviewers attempted to obtain the

names, new addresses and other data that could be used

for matching from the new occupants or neighbors. Then

an attempt could be made to trace the people to obtain an

interview with a household member. The best available

data for outmovers was matched to their Census Day

addresses in the same manner as for the nonmovers.

Outmover tracing had problems in 1995 and was tested in

1996 and in the Census 2000 Dress Rehearsal. The outmover tracing evaluation by Raglin and Bean (1999)

showed that there is little gain in an outmover tracing

operation. A decision was made to use the outmover

proxy interview data for outmover matching for Census

2000.

Procedure C was tested in the Census 2000 Dress

Rehearsal and it was used in Census 2000 (Schindler,

1999). The advantage of Procedure C is that the estimate

of the number of movers uses inmover data, which is

more reliable since it is collected from the inmovers themselves. The match rate of the movers is estimated using

the outmover match rate so that the difficulties of inmover

matching are avoided. Outmover tracing is a problem,

however, and in many cases it is necessary to use proxy

data for matching. There was no outmover tracing for

Census 2000. Procedure C attempts to obtain a Procedure

B estimate with no inmover matching. Procedure C and

Procedure B estimates are different since outmovers do

not have the same match rate as inmovers. However, the

disadvantage of the Procedure B inmover match rate estimate is that it may yield a high percentage of unresolved

cases.

Dual System Estimation Section I—Chapter 7 7–19

U.S. Census Bureau, Census 2000
Chapter 8.

Model-Based Estimation for Small Areas

INTRODUCTION

This chapter documents the Accuracy and Coverage Evaluation (A.C.E.) methodology of synthetic estimation for

small areas including the estimation of sampling variances

of synthetic estimates and the generalization of the variances. Synthetic estimation is the particular model used

for coverage adjustment for small areas for A.C.E. First,

the synthetic estimation methodology and the implied

model are described. Then, the methodology for estimating sampling variances of these synthetic estimates and

for generalizing these variances are discussed.

SYNTHETIC ESTIMATION METHODOLOGY FOR

SMALL AREAS

Background

As discussed in Chapter 7, dual system estimates (DSE)

and coverage correction factors were calculated at the

post-stratum level. These are direct A.C.E. Survey estimates, based only on data from sample units in the poststratum. However, census counts adjusted for coverage

error are desirable for small geographic areas much

smaller than any post-stratum such as blocks, tracts,

counties and congressional districts. The adjusted counts

were expected to improve data used for congressional

redistricting as well as states, most metropolitan areas,

and larger counties and cities and to provide consistent

totals when census data are aggregated over many small

areas. Many of these areas do not include any A.C.E.

sample units, making a direct estimate impossible (see

Chapter 3 for details of A.C.E. sampling). The geographic

areas that include A.C.E. sample units only have a small

number of sample units. A direct estimate would result in

unacceptably large standard errors. Synthetic estimation is

discussed in Ghosh and Rao (1994), Gonzalez (1973), and

Gonzalez and Waksberg (1973). Gonzalez (1973) describes

synthetic estimation as follows: ‘‘ An unbiased estimate is

obtained from a sample survey for a large area; when this

estimate is used to derive estimates for subareas under

the assumption that the small areas have the same characteristics as the large area, we identify these estimates as

synthetic estimates.’’ Synthetic estimation was first used

by the National Center for Health Statistics (1968) to calculate state estimates of long and short term physical disabilities from the National Health Interview Survey data

(Ghosh and Rao, 1994). Synthetic estimation is a useful

procedure for small area estimation, mainly due to its simplicity and potential to increase accuracy in estimation by

borrowing information from similar small areas.

Synthetic estimation was used for Census 2000 to provide

adjusted population estimates for small geographic areas

such as blocks, tracts, counties, and congressional districts. These block-level estimates can then be aggregated

to any geographic level. The synthetic estimates provide

revised population counts for both all persons and persons 18 and over. Counts are also provided for Hispanic or

Latino persons by race (63 categories) and Not Hispanic or

Latino persons by race (63 categories) for both the total

population and the population 18 years and over. For

example, counts of single-race Asian persons who are Not

Hispanic or Latino are given for both the total population

and the population 18 years and over. Counts of singlerace Asians who are Not Hispanic or Latino who are less

than 18 years of age can be obtained by subtraction.

Synthetic estimates are formed by combining coverage

measurement results with census counts to produce population estimates for any geographic area of interest.

For example, a block-level synthetic estimate is formed by

distributing a post-stratum’s coverage correction factor to

blocks proportional to the size of the post-stratum’s population within the block. Rounded, adjusted synthetic estimates at the tabulation block level constitute the adjusted

redistricting1 data file.

The synthetic estimation model assumes that coverage

correction factors are uniform within a given post-stratum,

meaning that the coverage error rate for a given poststratum is the same within all blocks. To the extent that

the synthetic assumption is incorrect, the estimates of

coverage for individual areas are biased and, hence, so

are the population size estimates based on the coverage

correction factors. Synthetic estimation bias decreases as

the size of the geographic area increases.

Synthetic Estimation

This section describes the calculation of synthetic estimates. Synthetic estimation includes a controlled rounding

procedure used to produce estimates that are integervalued. The visual representation of the twelve steps in

the controlled rounding process given in Haines (2001) is

provided here.

1

Since it was originally intended that the A.C.E. might be used

to adjust census counts for redistricting, such data is called

‘‘redistricting data,’’ although it was not ultimately used for that

purpose.

Model-Based Estimation for Small Areas Section I—Chapter 8 8–1

U.S. Census Bureau, Census 2000
Calculation

Consider forming synthetic estimates for geographic level

g for a given post-stratum. Let Ci,g denote the census

count for post-stratum i in geographic level g and define

CCFi to be the coverage correction factor for post-stratum

i. The general form for a synthetic estimate for poststratum i at geographic level g is calculated as

N

ˆ

i,g

S  Ci,g CCFi .

Aggregating synthetic estimates over all the post-strata in

geographic level g yields a synthetic estimate for the total

population of geographic level g. This is denoted as

N

ˆ

g

s  i

Ci,g CCFi .

One purpose of synthetic estimation and the controlled

rounding procedure is to produce integer-valued adjusted

synthetic estimates at the tabulation block level. Then,

summing over different geographies within a larger area

yields the same estimate as that for the larger geographic

area. These estimates comprise the adjusted redistricting

data file.

Geography

Components of synthetic estimates use two slightly different organizations of geography. Both collection and tabulation blocks are used in the synthetic estimation process.

A collection block is a geographic area used during census

data-collection activities. The Hundred-Percent Census

Edited File (HCEF) is based on collection block geography.

Tabulation blocks, on the other hand, are geographic areas

used for tabulating census data. The Hundred-Percent

Detail File (HDF) is based on tabulation block geography.

Synthetic estimation census counts are based on tabulation block geography while the coverage correction factors associated with post-strata are based on collection

block geography. This could have ramifications on variables with a geographic component, although any such

effects are probably small.

For example, consider the post-stratification variable

‘‘return rate.’’ Return rate was calculated at the tract level

and based on collection-tract definitions. People were

assigned to post-strata based on the return rate of tracts

defined using collection blocks. Now consider the case

where people are assigned to post-strata based on the

return rate of tracts defined using tabulation blocks. It

could be the case that the change in geography causes an

individual’s post-stratum assignment to change. For

example, suppose the return rate of a collection-tract is 80

percent and that the collection tract is split into two pieces

by a tabulation-tract. A person who belonged to the

collection-tract (with an 80 percent return rate) may now

belong to a tabulation-tract with a different return rate.

Changes in an individual’s post-stratum would also cause

changes in the dual system estimates, coverage correction

factors, and synthetic estimates. To avoid potential inconsistencies in the assignment of people to post-strata, there

was only one assignment of people to post-strata. The

assignment was based on collection-block geography,

which was consistent with the geography used in the

A.C.E. Further, this post-stratification assignment was

maintained for all estimation purposes.

Controlled Rounding

Synthetic estimates at any geographic level are not typically integer-valued. A controlled rounding program,

developed by the Statistical Research Division (SRD) of the

U.S. Census Bureau, was utilized that produces integervalued estimates. The theory of controlled rounding is

given in Cox and Ernst (1982). The problem is represented

as a transportation theory problem to minimize an objective function that measures the change due to controlled

rounding. In essence, the controlled rounding program

takes a two-dimensional matrix of numbers and rounds

each to an adjacent integer value based on an efficiency

algorithm. An optimal solution that minimizes the change

due to controlled rounding is guaranteed; there can, however, be more than one optimal solution. The two dimensions of the matrix are: 1) the post-strata for one level of

geography; and 2) totals for a lower level of geography.

The controlled rounding procedure ensures that the sum

of the synthetic estimates within a geographic level are

rounded up or down by an amount strictly less than one

person.

The overall goal of controlled rounding was to obtain an

integer number of persons for each post-stratum i within

each tabulation block b, reflecting the estimates of overcount and undercount. The controlled rounding program

could not be implemented in one step due to the size of

the post-strata by tabulation block matrix. As a result,

controlled rounding was implemented in steps such that

the rounded, adjusted synthetic estimates for blocks

sum to:

• the rounded, adjusted synthetic estimates for tracts,

• the rounded, adjusted synthetic estimates for counties,

and

• the rounded, adjusted synthetic estimates for states.

In other words, the block, tract and county rounded,

adjusted synthetic estimates would all be consistent with

each other. Also, the state-level synthetic estimates are

adjusted in order to guarantee that total population estimates at the state level sum to the national total population estimate.

A controlled rounding procedure for the U.S. can be implemented as follows:

8–2 Section I—Chapter 8 Model-Based Estimation for Small Areas

U.S. Census Bureau, Census 2000
1. Form the ratio of the control-rounded dual system

estimate (DSER

) to the unrounded DSE for post-stratum

i. It is written as

DSEi

R

DSEi

2. For each post-stratum i within state s, multiply the

state-level synthetic estimate by the ratio formed in

step 1. The superscript AS denotes an adjusted synthetic estimate. The resulting product is the adjusted

synthetic estimate for post-stratum i, within state s

written as

N

ˆ

i,s

AS  N

ˆ

i,s

S [ DSEiR  DSEi ] where N

ˆ

i,s

S  Ci,s CCFi .

3. Apply the controlled rounding procedure to the

adjusted state-level synthetic estimates to produce

rounded, state-level synthetic estimates, denoted N

ˆ

i,s

RS.

The superscript RS denotes a rounded, synthetic estimate. The two dimensions of this matrix are state s by

post-stratum i.

4. Calculate the ratio of the rounded state-level synthetic

estimate to the state-level synthetic estimate for poststratum i in state s.

5. For each post-stratum i within county c for state s,

multiply the county-level synthetic estimate by the

ratio formed in step 4. The resulting product is the

adjusted county-level synthetic estimate for poststratum i, written as

N

ˆ

i,c

AS  N

ˆ

i,c

S [Nˆ

i,s

RS  N

ˆ i,s

S ] where N

ˆ

i,c

S  Ci,c CCFi .

6. Apply the controlled rounding procedure to the

adjusted county-level synthetic estimates to produce

rounded, adjusted, county-level synthetic estimates,

denoted N

ˆ

i,c

RS. The two dimensions of this matrix are

county c (in state s) by post-stratum i (in state s).

7. Form the ratio of the rounded, adjusted, county-level

synthetic estimate to the county-level synthetic estimate for post-stratum i in county c in state s.

8. For each post-stratum i within tract t in county c for

state s, form the product of the tract-level synthetic

estimate and the ratio formed in step 7. This results in

the adjusted tract-level synthetic estimate for poststratum i, written as

N

ˆ

i,t

AS  N

ˆ

i,t

S [Nˆ

i,c

RS  N

ˆ

i,c

S ] where N

ˆ

i,t

S  Ci,t CCFi .

9. Apply the controlled rounding procedure to the

adjusted tract-level synthetic estimates to produce

rounded, adjusted tract-level synthetic estimates,

denoted N

ˆ

i,t

RS. The two dimensions of this matrix are

tract t (in county c in state s) by post-stratum i (in

county c in state s).

10. Calculate the ratio of the rounded, adjusted tractlevel synthetic estimate to the tract-level synthetic

estimate for post-stratum i in tract t in county c in

state s.

Post-stratum i

State 1 2 .. i ..

1

N

ˆ

i,s

AS

2

:

s

:

Post-stratum i

State 1 2 .. i ..

1

N

ˆ

i,s

RS

2

:

s

:

→

Post-stratum i in state s

County 1 2 .. i ..

1

N

ˆ

i,c

AS

2

:

c

:

Post-stratum i in state s

County 1 2 .. i ..

1

N

ˆ

i,c

RS

2

:

c

:

→

Post-stratum i in county c in

state s

Tract 1 2 .. i ..

1

N

ˆ

i,t

AS

2

:

t

:

Post-stratum i in county c in

state s

Tract 1 2 .. i ..

1

N

ˆ

i,t

RS

2

:

t

:

→

Model-Based Estimation for Small Areas Section I—Chapter 8 8–3

U.S. Census Bureau, Census 2000
11. For each post-stratum i within block b in tract t in

county c for state s, multiply the block-level synthetic estimate by the ratio formed in step 10. The

resulting product is the adjusted block-level synthetic estimate for post-stratum i, written as

N

ˆ

i,b

AS  N

ˆ

i,b

S [Nˆ

i,t

RS N

ˆ i,t

S ] where N

ˆ

i,b

S  Ci,b CCFi .

12. Again, apply the controlled rounding procedure to

the adjusted block-level synthetic estimates to produce rounded, adjusted block-level synthetic estimates, denoted N

ˆ

i,b

RS. The two dimensions of this

matrix are block b in tract t in county c in state s

by post-stratum i in tract t in county c in state s.

Record Replication for Coverage Correction

Once the rounded, adjusted block-level synthetic estimates were formed, they were compared with the census

counts for post-stratum i in tabulation block b. Person

records were then replicated at the post-stratum level to

reflect the coverage correction for the census blocks. No

attempt was made to place these persons in households.

Thus, for example, the number of persons per household

does not change due to coverage correction. The number

of records replicated depends on the value of the coverage

correction factor that is reflected in the rounded synthetic

estimate for post-stratum i and tabulation block b.

Coverage Correction Factors ≥1

When the coverage correction factor for post-stratum i was

greater than one, undercount person records were replicated to reflect the undercount in post-stratum i and block

b as follows:

Ui,b  N

ˆ

i,b

RS  Ci,b

If Ui,b = 0, then no additional records were necessary. If

Ui,b > 0, then we replicated Ui,b undercount person records

for post-stratum i in tabulation block b.

Undercount person records were replicated by randomly

selecting without replacement Ui,b records from the Ci,b

available person records in post-stratum i and tabulation

block b. The selected records were replicated and

appended to the file of person records. The undercount

person record for each of the replicated records was given

an effective weight of +1 for tabulations. This resulted in

an upward adjustment of people in post-stratum i in

tabulation block b.

Coverage Correction Factors <1

When the coverage correction factor for post-stratum i was

less than one, overcount person records were replicated

to reflect the overcount in post-stratum i and block b as

follows:

Oi,b  C i,b  N

ˆ

i,b

RS

If Oi,b > 0, then Oi,b overcount person records were replicated for post-stratum i in tabulation block b.

Overcount person records were replicated by randomly

selecting without replacement Oi,b records from the Ci,b

available person records in post-stratum i and tabulation

block b. The selected records were replicated and

appended to the file of person records. The overcount person record for each of the replicated records was given an

effective weight of -1 for tabulations, resulting in a downward adjustment of people in post-stratum i in tabulation

block b.

VARIANCE ESTIMATION FOR SMALL AREAS

Estimating the error due to sampling for any published

estimate is a policy of the Census Bureau. This policy

applies to synthetic estimates as well as the more traditional estimates. Due to the large number of estimates at

lower levels of geography, it is not feasible to provide

tables listing the standard error of each published estimate. Instead, a parameter, the generalized coefficient of

variation (GCV), is provided, that allows users to approximate the standard error for any desired estimate. The

coefficient of variation of an estimate is simply the ratio of

the estimate’s standard error to the estimate itself.

Small area variance estimation is a two-step process. The

first step consists of producing direct variance estimates

for the synthetic count estimates for small areas such as

census tracts. This process is explained under the heading

Direct Variance Estimates. The second step is to model the

direct variance estimates using the generalized coefficient

of variation, or GCV. This method is explained under the

heading Generalized Variance Estimates, along with an

example.

Variances calculated for small areas do not account for all

sources of synthetic error; they only reflect variations due

to sampling. Synthetic population bias can exist since the

same coverage correction factors are applied to areas with

different net census coverage. See Griffin and Malec

(2001) for details on estimating synthetic bias. In most

very small geographic areas such as blocks and tracts, the

Post-stratum i in tract t in county

c in state s

Block 1 2 .. i ..

1

N

ˆ

i,b

AS

2

:

b

:

Post-stratum i in tract t in county

c in state s

Block 1 2 .. i ..

1

N

ˆ

i,b

RS

2

:

b

:

→

8–4 Section I—Chapter 8 Model-Based Estimation for Small Areas

U.S. Census Bureau, Census 2000
biases are likely to be the principal source of errors. Sampling errors dominate the total error for larger areas such

as states, metro area, etc. Bias in the post-stratum-level

dual system estimates can stem from matching bias, data

collection errors, and correlation bias, among other

sources. Bell (2001) investigates and estimates correlation

bias in the A.C.E. dual system estimates by comparing

them to results from Demographic Analysis.

Direct Variance Estimates

During the post-stratum-level A.C.E. variance estimation

operation, a variance-covariance matrix of the A.C.E. coverage correction factors (CCFs) was produced. The estimated variance of any synthetic population estimate can

be computed using this matrix and the unadjusted census

counts, broken down by post-stratum and excluding outof-scope persons in the A.C.E. See Starsinic (2001) for

details. A synthetic household population estimate (Group

Quarters persons are not included) for tract t is written as

X

ˆ

t  

post-strata h

X

ˆ

th

 h1

416

Cth CCFh ́

where

Cth is the final, unadjusted census count for post-stratum

h in tract t.

There were 416 post-strata used to estimate coverage.

The variance for the synthetic household population estimate X

ˆ

t is

VarX

ˆ

t

  Var h1

416

X

ˆ

th

 h1

416

h ́ 1

416

CovX

ˆ

th,Xˆth ́

 h1

416

h ́ 1

416

CovCth CCFh, Cth ́ CCFh ́

 h1

416

h ́ 1

416

Cth Cth ́ CovCCFh, CCFh ́.

For a given data item j in tract t, the synthetic variance for

the synthetic household population estimate X

ˆ

jt is

expressed as

VarX

ˆ

jt  h1

416

h ́ 1

416

Cjth Cjth ́ CovCCFh, CCFh ́, (1)

where

Cjth is the final, unadjusted census count for data item j in

post-stratum h in tract t.

Here h and h ́ refer to particular post-strata and j refers to

a data item.

Generalized Variance Estimates

The generalized coefficient of variation (GCV) is the variance estimation methodology used for estimating variances of adjusted redistricting data and for estimates of

adjusted population counts for the thousands of geographic areas that can be tabulated using synthetic estimation. For a given count in a particular state, the coefficient of variation (CV) was calculated for all tracts in that

state that had population in the particular demographic

category. The CV of an estimate is estimated as the ratio

of the standard error of the estimate to the estimate itself,

i.e.

CV X

ˆ  =

SE X

ˆ 

X

ˆ .

The standard error in the numerator is the square root of

the variance estimate from (1). Tracts composed entirely

of persons out-of-scope for the A.C.E. sample had no sampling variance (and therefore a CV of 0) and were removed

from the processing. Also removed were tracts with a very

small population in the demographic category, as these

were shown in the Census 2000 Dress Rehearsal analysis

to have a disproportionate downward effect on the parameters. The process of removing tracts was controlled to

prevent removing an overly large fraction of ‘‘small’’ tracts

for any adjusted demographic data item. In addition, outliers were identified using the relative absolute deviation

(RAD) statistic for each data item j. Tracts with a RAD

value above the cutoff value were removed and a new

GCV was computed using CVs of remaining tracts. There

were four iterations of identifying and removing outliers.

Of the 286 unique demographic categories, GCVs were

calculated for the 50 states and the District of Columbia

for each of the 56 largest categories and 4 additional

‘‘catch-all’’ groups.

The average of the direct CVs for data items in a state is a

GCV parameter. The state-level GCV parameters can then

be used to estimate the standard error of a data item for

all geographic areas within that state. Consider the following table of GCV parameters for a given state.

Model-Based Estimation for Small Areas Section I—Chapter 8 8–5

U.S. Census Bureau, Census 2000
State Parameters for Calculating the Standard Error of A.C.E.–Adjusted Data

Demographic category

All persons Not Hispanic or Latino

All ages 18 and over All ages 18 and over

GCV GCV GCV GCV

All persons ............................................... 0.0063 0.0067 0.0066 0.0069

Hispanic or Latino . . ....................................... 0.0106 0.0115 X X

Population of one race .................................... 0.0064 0.0067 0.0066 0.0069

White alone ............................................ 0.0073 0.0077 0.0081 0.0083

Black or African American alone .......................... 0.0073 0.0083 0.0073 0.0083

American Indian and Alaska Native alone ................. 0.0143 0.0147 0.0188 0.0190

Asian alone . . .......................................... 0.0080 0.0085 0.0081 0.0086

Native Hawaiian and Other Pacific Islander alone . . . . ...... 0.0391 0.0495 0.0507 0.0545

Some Other Race alone ................................. 0.0109 0.0119 0.0126 0.0139

Population of two or more races ............................ 0.0070 0.0077 0.0071 0.0082

Population of two races . . ................................. 0.0071 0.0078 0.0071 0.0082

White; Black or African American ......................... 0.0103 0.0156 0.0103 0.0157

White; American Indian and Alaska Native ................. 0.0088 0.0092 0.0096 0.0100

White; Asian . .......................................... 0.0116 0.0131 0.0120 0.0133

Black or African American; American Indian and Alaska

Native ................................................ 0.0129 0.0140 0.0128 0.0140

Asian; Native Hawaiian and Other Pacific Islander .......... 0.0524 0.0560 0.0530 0.0566

All other combinations of two or more races ................. 0.0088 0.0095 0.0088 0.0099

Suppose a data user is interested in calculating the standard error of the population estimate of all Asians in a

given county. The data user would locate the GCV parameter that corresponds to the ‘‘Asian alone’’ demographic

category and the ‘‘All persons, All ages’’ classification in

the appropriate state table. For the table above, the GCV

parameter is 0.0080. Now assume that the population

estimate for all Asians in this county is 370 people. Users

are instructed to use the formula

SE X

ˆ  = GCV Xˆ ,

to calculate the estimated synthetic standard error, yielding 0.0080 × 370 = 2.96, or about 3 people in this

example. Similar calculations can be done for any geographic level and demographic category.

8–6 Section I—Chapter 8 Model-Based Estimation for Small Areas

U.S. Census Bureau, Census 2000
Appendix A.

Census 2000 Missing Data

INTRODUCTION

The Census Bureau used imputation in the 2000 Decennial

Census, as it has in prior censuses, to address the problem of missing, incomplete, or contradictory data, an

inevitable aspect of censuses and surveys. It is impossible

not to have missing data in an endeavor as massive and

complex as a decennial census. In Census 2000, the Census Bureau processed data for over 120 million households, including over 147 million paper questionnaires

and 1.5 billion pages of printed material. In the 2000 Census, the various situations that resulted in missing data

included incomplete or unavailable responses from housing units with previously confirmed addresses, conflicting

data about the same housing unit, and failures in the datacapture process. The various types of missing data

included characteristic data (information about an enumerated person, such as sex, race, age), population count

data (information about the number of occupants in an

identified housing unit), and housing unit status data

(whether the unit is vacant, occupied, or nonexistent). The

2000 Census used two primary types of imputation.

1. The first type, called ‘‘count imputation,’’ is imputation

of the number of occupants of a housing unit. Count

imputation applies when the Census Bureau is unable

to secure any information regarding a given address,

or when the Census Bureau has limited information

about the address and does not have definitive information on the number of occupants.

2. The second type, called ‘‘characteristic imputation,’’ is

imputation that supplies missing characteristic data

for a housing unit’s response, but does not involve the

number of occupants for a housing unit. For example,

if a given housing unit did not provide ages for the

individuals living in the housing unit, but supplied all

other information, age would be imputed for the individuals in that housing unit. Sometimes the household

size is known for the housing unit; however, none of

the characteristics about the people are known. In this

case all of the person’s characteristics are imputed.1

This appendix summarizes the methods used to impute

these types of missing data in the census. Some summary

statistics showing the degree of imputation for these categories is given in the last section of this appendix.

BACKGROUND

The census data collection activities started around midMarch of 2000, through the mail or directly using censusenumerators. From June to September, census staff conducted nonresponse follow-up (NRFU) and coverage

improvement follow-up (CIFU) operations to revisit

addresses for which census reports were not completed,

i.e. did not respond to mailout/mailback or early enumeration operations. Based on the results of these operations,

the Census Bureau was able to designate more than 99.5

percent of housing unit records as occupied, vacant, or

nonexistent housing unit addresses. To designate an

address as vacant or nonexistent required at least two

independent census operations. This was to ensure complete census coverage. The nonexistent housing units

were addresses of places used only for nonresidential purposes, or places that were uninhabitable and were not

included in the census counts.

To permit the production of census population counts, it

was necessary for each census address to have a status of

occupied/vacant/nonexistent and a household size if

occupied. To permit the production of the redistricting file

and other more detailed census products, it was also necessary to have information about each person such as age,

race, and sex. The count imputation covered status for

housing units with undetermined status and household

size for occupied units with an unknown number of occupants. The characteristic imputation was used to fill in the

missing person data.

Census housing units identified in the Accuracy and Coverage Evaluation ( A.C.E.) block clusters were defined as

the E-sample housing units. Persons residing in these

housing units were E-sample persons. It took several different census operations to establish a list of census housing unit records and a list of census person records. One

of these operations was the creation of a Hundred Percent

Census Unedited File (HCUF). At the housing unit level, all

housing units designated as occupied or vacant through

data collection or through imputation were included in the

HCUF. The file was used as a source file to identify the

E-sample housing units for the A.C.E. operations. At the

person level, the HCUF was used as a source file for person matching between the census and the A.C.E. (However, this does not include imputed persons, since they

were not sent to A.C.E. matching). Chapter 3 provides

detailed information on E-sample identification, while

Chapter 4 provides information on person matching.

1

This does not include geographic characteristics such as location, urban or rural residency etc., which are generally known for

all households.

Census 2000 Missing Data Section I—Appendix A A–1

U.S. Census Bureau, Census 2000
Persons imputed to an occupied unit with an unknown

number of occupants or persons with all their characteristics imputed were considered as non-data-defined persons

in the person Dual System Estimation (DSE). For datadefined persons, characteristic imputation filled in census

missing data, such as sex, age, ethnicity, and owner

/renter status for person DSE poststratification purposes.

COUNT IMPUTATION

The Census Bureau used count imputation for three categories of cases in Census 2000.

1. Household size imputation. The Census Bureau

imputed the number of occupants for a housing unit

when Census Bureau records indicated that the housing unit was occupied, but did not show the number

of individuals residing in the unit.

2. Occupancy imputation. When Census Bureau

records indicated that a housing unit existed, but not

whether it was occupied or vacant, the Census Bureau

imputed occupancy status (occupied or vacant). If the

unit was imputed to be occupied, the household size

was also imputed.

3. Status imputation. When the Census Bureau’s

records had conflicting or insufficient information

about whether an address represented a valid, nonduplicated housing unit, the Census Bureau first imputed

for the status of the unit (occupied, vacant, nonexistent), then, if occupied, the household size was

imputed.

Methodology

The Census Bureau used the nearest-neighbor hot deck

imputation methodology to perform the count imputation.

‘‘Nearest’’ was defined by the geographical closeness of

housing units. Group quarters addresses were included in

the measure of distance, although not otherwise involved

in count imputation. Census geographical identifiers, such

as tract number, block number, or map spot number, along

with street name, house number or apartment number

were used to describe geographical proximity of housing

records. To properly assign status and number of occupants to the housing units requiring imputation, limited

donor pools and expanded donor pools were developed

for each imputation category, which were further subdivided by type of structure.

All cases with missing status, occupancy or household

size went through intensive follow-up operations to

reduce the amount of imputation as much as possible.

This was the main purpose of the NRFU and CIFU for

mailout/mailback areas and enumerator visit in

list/enumerate or update/enumerate areas. To properly

represent these cases (donees), the primary donor pools

were also housing units from NRFU, CIFU or from other

enumerator visited cases. In the design phase, the Census

Bureau did develop a standby procedure to include all enumerations in an expanded donor pool. With 99.5 percent

of housing units having status and household size information available from data collection activities, the

expanded donor pools were never used. The chart below

characterizes the relationship between donees and the primary donor pool by imputation category.

Donors and Donees by Imputation Category

Imputation

categories Donees Donor pool

Household size

imputation:

a. Single units

b. Multiunits

Occupied with unknown

household population

Occupied units with known

population (in NRFU, or

CIFU,orfromlist/enumerate

orupdate/enumerateareas)

Occupancy

imputation:

a. Single units

b. Multiunits

Units known to be either

occupied or vacant

Occupied units with known

population or vacant units

(in NRFU, or CIFU, or from

list/enumerate or update/

enumerate areas)

Status Imputation:

a. Single units

b. Multiunits

Units with no status

information

Occupied units with known

population, vacant units,

or nonexistent units (in

NRFU, or CIFU, or from

list/enumerate or update/

enumerate areas)

In general, type of structure (multi or single), type of enumeration (mail or list/enumerate), and final stage of the

data collection for a housing unit (initial collection, NRFU,

or CIFU) determined whether a housing record could be

used as a primary donor. Each available donor could only

be used once. Most of the time, the nearest potential

donor was selected as the donor. Occasionally, a second

nearest neighbor was designated as the donor, because

the nearest donor had been taken by some previously processed donee. Whenever possible, the donor and donee

were to be in the same tract, or in the same multiunit if

the donee was located in a multiunit building.

To identify the nearest donor, a search was conducted in

both directions: forward and backward. Using the donee

as a reference point, potential donors surrounding the

donee record were searched, and the donor housing unit

geographically closest to the donee housing unit was

determined. The search was done separately for single

units and multiunits.

A–2 Section I—Appendix A Census 2000 Missing Data

U.S. Census Bureau, Census 2000
CHARACTERISTIC IMPUTATION

Characteristic imputation was the process of filling in

missing person characteristics, which include sex,

age/date of birth, relationship, Hispanic origin and race.

The Census Bureau used characteristic imputation for

three categories of cases in Census 2000.

1. Whole household imputation. The Census Bureau

imputed all of the characteristics for all of the persons

in the household when the household record did not

contain any data defined persons. To be data-defined,

a person record must contain two or more of the 100-

percent population data items, or a name.

2. Within household imputation. The Census Bureau

imputed all the 100-percent characteristics for any

non-data-defined persons in the household when the

household record contained at least one data-defined

person.

3. Within Person Imputation. Sometimes some of the

100-percent characteristic data for data-defined persons were missing and were imputed.

Methodology

The categories of characteristic imputation employ different methodologies. For whole household imputations, the

process replicates all of the 100-percent person data items

by substituting data from a hot deck nearest neighbor

donor pool record of the same household size. This process is sometimes referred to as substitution, since it

assigns all the characteristics for all of the persons in the

selected donor household to the household requiring

imputation. This substitution process is also used to

obtain the person characteristics for those housing units

that were imputed as occupied or had their household size

imputed during the count imputation process. By definition these households do not contain any data-defined

persons. However, the majority of whole household

imputations occur for cases where a census response on

household size was obtained.

For within household imputations as well as within person

imputations, the process allocates missing values for individual person characteristic data items on the basis of

other reported information for other persons in the household, or from other persons in households with similar

characteristics.

RESULTS

This section briefly summarizes the overall level of imputation for people whose 100-percent characteristics were

totally imputed in Census 2000 (within person imputations are excluded) for the U.S. population residing in

housing units.

Census 2000 Housing Unit Persons by

Imputation Category

(Excludes within person imputations)

Number of

persons

Percent of

total persons

Total housing unit population . ......... 273,643,272 100.00

100-percent characteristic

imputation not required ............ 267,869,007 97.89

100-percent characteristic

imputation required . . . ............ 5,774,266 2.11

Count imputations: ................... 1,172,144 0.43

Household size .................... 495,600 0.18

Occupancy ........................ 260,652 0.10

Status ............................ 415,892 0.15

Characteristic imputations ............. 4,602,122 1.68

Whole household1 ................. 2,269,010 0.83

Within household .................. 2,333,112 0.85

1

The count imputation cases (also requiring characteristic imputation) are not included in this figure to avoid duplication.

About 2 percent of persons residing in housing units

required imputations of all 100-person characteristics. The

majority of these cases , about 1.7 percent, occurred in

situations where a census response on household size was

obtained. Less than a half of a percent were situations

where household size or the status of the housing unit

was unknown.

Census 2000 Missing Data Section I—Appendix A A–3

U.S. Census Bureau, Census 2000
Appendix B.

Demographic Analysis

INTRODUCTION

The Census Bureau has used Demographic Analysis (DA)

to measure population coverage, trends between censuses, and differences in coverage by age, sex, and race

(Black, non-Black) at the national level in every census

since 1960 (Siegel and Zelnik (1966), Siegel (1974), Fay et

al. (1988), and Robinson et al. (1993)). DA produces estimates of the U.S. population through the use of data from

administrative records and other noncensus sources. It

has documented both the long-term reduction in the census net undercount rate and the persistent and disproportionate undercount of certain demographic groups, such

as Black men. One goal of Census 2000 was to reduce

these differential undercounts, which has been a continuing effort for the last several censuses.

The independence from the census and internal consistency of the DA estimation process allows us to compare

the results with the survey-based Accuracy and Coverage

Evaluation (A.C.E.) coverage estimates; in particular, the

consistency of the age-sex results can be assessed. DA

and A.C.E. use entirely different methodologies. Because

the sources and patterns of errors in the two estimates are

sufficiently different, any disagreement in the results can

shed light on both the quality of the census and potential

problems in methodology in the A.C.E. or the DA. Because

of data limitations, DA estimates and comparisons are

only possible at the national level and for certain large

demographic groups. A further discussion of DA limitations is found in the section ‘‘Limitations of DA Estimates’’

of this appendix.

The U.S. Census Bureau released two sets of DA results as

part of its evaluation of Census 2000 and the A.C.E. All DA

results in this section are from the revised values released

in October 2001. See Robinson (2001) for details.

DESCRIPTION OF THE DEMOGRAPHIC ANALYSIS

METHOD

Demographic Analysis represents a macro-level approach

for measuring coverage. Estimates of net undercount are

obtained by comparing census counts to independent estimates of the population derived from other measures

(mostly administrative data). In general, DA population

estimates are developed for the census date by combining

various types of demographic data that are independent

of the census and are highly reliable, such as administrative statistics on births, deaths, and Medicare data and

estimates of immigration and emigration. The difference

between the DA estimated population (P) and the census

count (C) provides an estimate of the net census undercount (u). Dividing the net undercount by the DA benchmark provides an estimate of the net undercount rate (r):

u  P C

r  uP  100

The particular analytic procedure used to estimate coverage nationally for the various demographic subgroups

depends primarily on the nature and availability of the

required demographic data. Two different demographic

techniques were used to produce the demographic analysis estimates for 2000, one for the population under age

65 and another for the population 65 and over.

Ages under 65. The Demographic Analysis estimates for

the population below age 65 are based on the compilation

of historical estimates of the components of population

change: births since 1935 (B), deaths to persons born

since 1935 (D), immigrants born since 1935 (I), and emigrants born since 1935 (E). Presuming that the components are accurately measured, the population estimates

(P0-64) are derived by the basic demographic accounting

equation applied to each birth cohort:

P064  B D  I E

The size of the component estimates used to develop

the DA population under age 65 for 2000 is shown in

Table B-1:

Table B-1. DA Estimates of the Components

of Change for the U.S. Resident

Population: April 1, 2000

Component Estimate

Total population . . ............................... 281,759,858

Under age 65 in 2000

+ Births since 1935 (B) ....................... 234,860,298

- Deaths to persons born since 1935 (D) ....... 14,766,736

+ Immigration of persons born since 1935 (I) .... 32,563,971

- Emigration of persons born since 1935 (E) .... 5,485,117

Ages 65 and over in 2000

Medicare-based population .................... 34,587,440

Demographic Analysis Section I—Appendix B B–1

U.S. Census Bureau, Census 2000
Clearly, births (234.9 million) represent by far the largest

component. The immigration component (32.6 million) is

second largest, followed by deaths (14.8 million) and emigrants (5.5 million).

The actual calculations are carried out for single-year birth

cohorts. For example, the estimate of the population age

40 on April 1, 2000 is based on births from April 1959 to

March 1960 (adjusted for under-registration), reduced by

deaths to the cohort in each year between 1959 and 2000,

and incremented by estimated immigration and emigration of the cohort over the 40-year period.

The components for births and deaths are compiled principally from vital statistics records augmented by correction

factors. The immigration component is estimated from its

subcomponents:

Table B-2. DA Estimates of the Components of

Immigration for the U.S. Resident

Population Under 65 Years of Age:

April 1, 2000

Component Estimate

Legally admitted permanent residents ............. 20,332,038

Other measured migration ....................... 2,249,001

Migrants from Puerto Rico . . ................... 905,698

Temporary migrants ........................... 776,002

Civilian citizen migration ....................... 891,940

Armed Forces overseas . ...................... -324,639

Residual foreign-born migration (includes unauthorized migrants) . ................................. 9,982,932

Age 65 and over. Administrative data on aggregate

Medicare enrollments are used to estimate the population

age 65 and over (P65+):

P65  M  m

where M is the aggregate Medicare enrollment and m is

the estimate of underenrollment in Medicare. The DA

population 65 and over is based on 2000 Medicare enrollments. Medicare is an administrative data set from the

Health Care Financing Administration. Although Medicare

enrollment is generally presumed to be quite complete,

adjustments are made to the basic data to account for

individuals who are omitted. An allowance is made for

the estimated 1.3 million not enrolled (3.9 percent).

Underenrollment factors are based on survey estimates of

Medicare coverage and data on age at enrollment in the

Medicare file. The DA population aged 65 and over (34.6

million) represents 12.3 percent of the total population in

2000.

The demographic component estimates for the population

under 65 are combined with the Medicare-based estimate

for the population 65 and over to produce the total DA

population estimate of 281.8 million as of April 1, 2000.

LIMITATIONS OF DA ESTIMATES

DA estimates for the total population are available only at

the national level and only for the broad categories Black

and non-Black. DA cannot provide estimates for subnational geographic areas like states or metropolitan

areas; or for other demographic groups, such as Hispanics. DA also cannot provide separate estimates for census

overcoverage and undercoverage, but is limited to estimating net undercount.

There are also certain inherent limitations on DA estimates

because of data quality. The race categories reflect the

race as assigned at the time of the event (e.g. birth or

Medicare enrollment), which for some persons will differ

from the race reported in the census. There is also considerable uncertainty in the quality of the data for some of

the components related to immigration, most importantly

the components which capture those who entered illegally

or temporarily, or whose legal status had not yet been

determined.

DA ESTIMATES

Compared to the Census 2000 count of 281.4 million, the

DA estimate of 281.8 million implies a net census undercount of 0.12 percent (see Table B-3). The net census

undercount in 2000 was dramatically different from that in

1990, which was 4.2 million, or 1.65 percent. However,

the fact that DA provides only a net undercount estimate,

not separate measures of gross undercount and overcount, is a limitation on its ability to shed light on specific

undercoverage or overcoverage problems in the census.

Table B-3. Demographic Analysis Estimate and

Net Census Undercount for the

Total Population: 1990 and 2000

Category 1990

Census

2000

Census

DA (millions) .......................... 252.9 281.8

Difference from Census . . . . . . . . . . . . . . . . 4.2 0.3

Percent difference ..................... 1.65 0.12

B–2 Section I—Appendix B Demographic Analysis

U.S. Census Bureau, Census 2000
The DA estimates indicate that the substantial reduction in

net census undercount from 1990 to 2000 was shared by

almost all demographic groups. The net census undercount of males and females each fell by about 1.5 percentage points (to an estimated net census undercount of 0.86

percent for males and estimated net census overcount of

0.60 percent for females in 2000). The estimated net

undercount rate dropped more for Blacks (estimated net

census undercount of 2.78 percent in 2000) than nonBlacks (estimated net census overcount of 0.29 percent in

2000), reducing the differential undercount of Blacks relative to non-Blacks from 4.4 percentage points in 1990 to

3.1 points in 2000.

Table B-4. Demographic Analysis Estimates of

Percent Net Census Undercount for

the Total Population and Selected

Demographic Groups: 1990 and

2000

Category 1990 DA 2000 DA

Total.................................. 1.65 0.12

Male ................................. 2.39 0.86

Female ............................... 0.93 -0.60

Black ................................ 5.52 2.78

Non-Black . . .......................... 1.08 -0.29

Black male, ages 20-64 ................ 11.31 8.44

Children, ages 0-4 . . ................... 3.72 3.84

(a minus sign denotes a net overcount)

Demographic Analysis Section I—Appendix B B–3

U.S. Census Bureau, Census 2000
Appendix C.

Weight Trimming

INTRODUCTION

This appendix contains a general overview of the Accuracy and Coverage Evaluation (A.C.E.) weight trimming

plan. The procedure was designed to protect against

undue influence from a small fraction of the sample. The

weight trimming criteria were established prior to the

completion of data processing operations to ensure that

there was no manipulation of the dual system estimates.

This procedure was implemented according to the prespecified criteria. Since only one cluster was trimmed, the

impact on the dual system estimates was very minimal.

The A.C.E. weight trimming procedure was designed to

reduce the sampling weights for clusters that potentially

could have had an extreme influence on the dual system

estimates and variances. The measure of cluster influence

was the net cluster error, the absolute difference between

the weighted estimate of nonmatches and the weighted

estimate of erroneous enumerations. When the net error

exceeded a pre-set maximum value, the sampling weights

were reduced. This approach reduced variance and may

have introduced some bias, but it is highly likely to have

reduced the mean square error for most items. If the net

error of the cluster did not exceed the pre-set maximum

value, the sampling weights were unchanged.

The net error criteria was examined after the A.C.E. person

matching operation was completed. If the criteria for

weight trimming was met, it was done for all sample cases

in a cluster even though a cluster contributed sample to

multiple post-strata. This was done prior to the missing

data process.

BACKGROUND

Weight trimming guards against the possibility of a certain

small number of clusters exerting an undue influence on

post-stratum estimates and variances. In the A.C.E., these

are expected to be due to a disproportionate number of

census nonmatches or census erroneous enumerations

within a few block clusters. Although extreme sampling

weights can also be a source of influence in surveys, the

A.C.E. sampling weights, the inverse of the probability of

selection, were reasonably controlled in the sample

design. These were not expected to be an important

source of variance in the A.C.E.

While the A.C.E. sample design helped minimize the occurrence of highly influential clusters, a weight trimming plan

was developed to reduce the effect of these potential

extreme clusters. The A.C.E. weight trimming plan was a

modification of the method used for the 1990 PostEnumeration Survey (PES). As in 1990, the weights for

extremely influential clusters were trimmed to yield a prespecified net error. The intention of the plan was to lessen

the impact of such clusters on the dual system estimates

and variances.

The plan did not redistribute the weights across the

remaining clusters to preserve totals. This would imply

treating the E and P samples differently to preserve these

separate totals, and contradicts the preference for consistent treatments of both samples. Since the primary interest was in the dual system estimation ratios, and not Eand P-sample totals, the weights were not redistributed.

A.C.E. WEIGHT TRIMMING METHODOLOGY

Each cluster was evaluated to determine if it contributed

disproportionately to the dual system estimates and variances. If the cluster was an outlier, the cluster sampling

weight was multiplied by a factor to decrease the influence of the cluster on the dual system estimates and variances.

Identify Outlier Clusters

A measure of the cluster influence was calculated for

each cluster. Then, based on pre-set criteria, a decision

was made whether the cluster should be identified as an

outlier.

Cluster Influence. The measure of cluster influence was

the net error. For purposes of weight trimming, the net

error was the absolute difference between the weighted

number of nonmatches and the weighted number of erroneous enumerations. The form of the weighted net error

was

Zi  | (Pi - Mi

) - (Ei - CEi) | (1)

where

Zi  the net error estimate for cluster i,

Pi  the weighted P-sample population estimate for

cluster i,

Mi  the weighted P-sample match estimate for cluster i,

Ei  the weighted E-sample population estimate for

cluster i, and

CEi  the weighted E-sample correct enumeration

estimate for cluster i.

The first term of equation (1) was the weighted number of

nonmatches in the ith cluster, while the second term was the

weighted number of erroneous enumerations in the ith

cluster.

Weight Trimming Section I—Appendix C C–1

U.S. Census Bureau, Census 2000
Outlier Criteria. The outlier criterion was the maximum

allowable net error for a single cluster. There were two different criteria based on the cluster geography. The nation

was classified into two levels of geography: American

Indian Reservations and the balance of the nation. The

American Indian Reservation clusters were sampled at disproportionately higher rates relative to the balance of the

country. In addition, separate American Indian on American Indian Reservation post-stratum estimates were

planned. If the American Indian Reservation clusters were

included with the rest of the nation, it is unlikely that an

influential cluster would be detected. The two outlier criteria are defined in Table C-1.

Table C-1. Outlier Cluster Criteria

Cluster geography Maximum

net error

American Indian Reservations . . . ................. 6,250

Balance of the United States ..................... 75,000

All clusters with net error greater than the maximum

allowable net error were considered influential clusters.

They were expected to disproportionately influence the

dual system estimates and variances. The sampling

weights of these clusters were decreased.

The maximum net error for the balance of the country was

based on experience in the 1990 PES. Since the A.C.E. was

roughly double the PES sample size, the maximum allowable net error was set to be half the 1990 value. For the

American Indian Reservation clusters, the maximum allowable value was a function of the average sampling rates.

The American Indian Reservation average P-sample cluster

sampling weight was approximately one-twelfth the balance of the U.S. average P-sample cluster sampling

weight. Because of this, the American Indian Reservation

maximum allowable net error was one-twelfth the balance

of the U.S. criteria.

Implementation Strategy. The outlier clusters were

identified after the person matching operation (Chapter 4)

was completed, but before the missing data process

(Chapter 6). The person matching results were the major

input into this process. The weight trimming estimate

used the best estimate of cluster net error at that time that

was operationally feasible. This timing had several implications:

• Only nonmovers and outmovers were used for deriving

the estimate of nonmatches above. For dual system estimation, if the number of outmovers in a post-stratum

was less than 10 then only the non-movers and

outmovers were used. Because of the small number

of movers expected in most clusters, this process

only used nonmovers and outmovers.

• Some nonmovers and outmovers had unresolved match

status and residence status. Some E-sample cases had

unresolved enumeration status. This meant the status of

unresolved cases had to be estimated to identify outlier

clusters. Information available at the time of the weight

trimming process was used to approximately estimate

the unresolved status cases. Since the weight trimming

process was done before the missing data process,

there was some information that the missing data process used to estimate unresolved status that was not

yet available.

• A P-sample noninterview adjustment was approximated

in the estimate of nonmatches. Information available

during the weight trimming process was used to

approximately estimate the noninterview adjustment for

each cluster. As with the unresolved cases, since the

weight trimming process was done before the missing

data process, there was some information that the missing data process used to do the noninterview adjustment that was not yet available.

• The targeted extended search results and sampling

rates were reflected in the estimate of nonmatches and

erroneous enumerations (Chapter 5).

Down-Weighting Outlier Cluster

All outlier clusters were down-weighted, so that no cluster

contributed more than the maximum allowable number of

net errors for the appropriate geography. A separate

down-weighting factor was computed for each outlier

cluster. The down-weighting factor was the ratio of the

outlier cluster criteria to the cluster net error computed

above.

Di  C

Zi

(2)

where

Di  the down-weighting factor for cluster i, and

C  the maximum net error from Table C-1 for

the appropriate level of geography, and

Zi  the net error estimate for cluster i from (1).

The cluster down-weighting factor was applied to the

P-sample and the E-sample weights of the outlier cluster.

The P-sample and E-sample weights for the remaining

clusters were unchanged.

C–2 Section I—Appendix C Weight Trimming

U.S. Census Bureau, Census 2000
A.C.E. WEIGHT TRIMMING RESULTS

Table C-2 shows the one cluster down-weighted by the

weight trimming process in the balance of the United

States. No clusters were trimmed on American Indian

Reservations.

Figures C-1 and C-2 show the distributions of net error

before weight trimming for the balance of the United

States and the American Indian Reservation areas.

Table C-2. A.C.E. Weighted Net Errors for DownWeighted Cluster

Geographic area

Before trimming After

trimming

Estimated

erroneous

enumerations

Estimated

weighted

nonmatches

Estimated

weighted

net error

Estimated

weighted

net error

Balance of the

United States ...... 79,371 1,396 77,975 75,000

Weight Trimming Section I—Appendix C C–3

U.S. Census Bureau, Census 2000
Figure C-1.

Distribution of Net Error for the Balance of the United States

U.S. Census Bureau, Census 2000

C–4 Section I—Appendix C Weight Trimming

(Number of clusters)

0

1000

2000

3000

4000

5000

6000

7000

8000

2,461

7,610

510

133 45 24 14 12 3 2 0 0 2 0 0 0 1

0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000

Net error before trimming
Figure C-2.

Distribution of Net Error for American Indian Reservations

U.S. Census Bureau, Census 2000

Weight Trimming Section I—Appendix C C–5

(Number of clusters)

0

50

100

150

200

250

300

186

262

510

29

3 2 1 1 1 1 0 0 0 0 0 0

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

Net error before trimming
Appendix D.

Error Profile for A.C.E. Estimates

INTRODUCTION

The Accuracy and Coverage Evaluation (A.C.E.) survey provided estimates of census coverage error that have been

considered for adjusting Census 2000. The estimation

used the PES-C version of dual system estimation with the

data collected by the A.C.E. The adjusted estimates are

subject to nonsampling error, as well as sampling error.

This appendix discusses the types of errors found in the

use of PES-C and the measurement of these errors.

OVERVIEW OF ADJUSTED ESTIMATES

Define the following notation for each post-stratum h.

Ch  census ‘‘count’’ for post-stratum h

IIh  number of persons imputed into the original

enumeration for post-stratum h

I

ˆ

E,h  estimated number of enumerations in post-stratum h

with insufficient information for matching1

E

ˆ

E,h  estimated number of erroneous enumerations in

post-stratum h

N

ˆ

E,h  estimated population size for post-stratum h from

the E sample

CEˆ

h  estimated population size for post-stratum h who

could possibly be matched

CEˆ

h  N

ˆ

E,h I

ˆ

E,h E

ˆ

E,h

N

ˆ

P,h  estimated size of the P-sample population

Mˆ

h  estimated number of the P-sample population enumerated in the census

The dual system estimator for the population size Nh in

post-stratum h is defined by

N

ˆ

h  Ch IIh)(CEˆhN

ˆ

E,h)(NˆP,hMˆh).

The 2000 A.C.E. used the PES-C formulation of the dual

system estimator which uses the number of inmovers to

estimate the number of outmovers, but uses the match

rate for the outmovers to obtain the estimate of the number of outmovers that match the census. The post-stratum

index h is suppressed in the following formula.

(Nˆ

PMˆ )  N

ˆ

n  N

ˆ

i

Mˆ

n  (Mˆ

oN

ˆ

o)Nˆi

).

where

N

ˆ

n  estimated number of nonmovers

N

ˆ

o  estimated number of outmovers

N

ˆ

i  estimated number of inmovers

Mˆ

n  estimated number nonmovers enumerated in the

census

Mˆ

o  estimated number outmovers enumerated in the

census

When a post-stratum had fewer than 10 outmovers, the

PES-A version of the dual system estimator that does not

use inmovers was employed as follows:

(Nˆ

P /Mˆ )  (Nˆn  N

ˆ

o)/(Mˆn + Mˆo)

The adjustment factor for post-stratum h is defined as

A

ˆ

h  N

ˆ

hCh. The unadjusted estimate for area j is

Nunadj, j  h

Ch, j and the adjusted estimate is N

ˆ

adj, j 

h

A

ˆ

hCh, j. The estimates of undercount in the population

size of area j is N

ˆ

adj, j Nunadj, j and the estimate of the corresponding undercount rate is Nˆ adj, j Nunadj, j N

ˆ

adj, j .

SOURCES OF ERROR IN ADJUSTMENTS

The adjusted estimates are subject to a variety of possible

sources of error: sampling error, data collection and survey operations error, missing data, error from exclusion of

late census data and data with insufficient information for

matching, contamination error, correlation bias, synthetic

estimation bias, inconsistent post-stratification, and balancing error.

P-Sample Matching Error and E-Sample Processing

Error

Source. The term ‘P-sample matching’ has been used to

describe the search of the census records for enumerations for P-sample respondents. The P-sample respondents

are designated as matching an enumeration in the census

or as not enumerated. The counterpart for the E sample is

called ‘‘E-sample processing’’ where census enumerations

are designated as correctly enumerated or erroneously

enumerated. When the status of a P-sample or E-sample

case can not be determined, it is designated as unresolved.

‘‘P-sample matching error’’ refers to the net effect of

errors that occur during the processing that affect the

determination whether a P-sample person matches a census enumeration. Likewise, the net effect of errors in

assigning enumeration status to E-sample enumerations

during the office processing is called ‘‘E-sample processing

error.’’ 1

Late enumerations are included with imputations in the original enumeration.

Error Profile for A.C.E. Estimates Section I—Appendix D D–1

U.S. Census Bureau, Census 2000
Errors may occur in either direction. P-sample people may

be designated as matching a census enumeration

although they are not in the census, called a ‘‘false match,’’

or people may be designated as not enumerated although

they are, called a ‘‘false nonmatch.’’ E-sample enumerations may be falsely assigned a correct enumeration status, called a ‘‘false correct enumeration,’’ or enumerations

may be incorrectly designated as an erroneous enumeration, a ‘‘false erroneous enumeration.’’

Matching error also encompasses errors in the size of the

P-sample population that may happen during the processing of the P-sample. These errors also may occur in either

direction. A person included as a member of a household

may really reside at another location or not be in the

population of interest. For example, the census residency

rules consider family members away at college to reside at

their college address. A family member in a nursing center

is considered to be in the group quarters population,

which is not part of the population of interest. Vice versa,

a person with two homes, may be designated as living at

the other home, but really live at the one in the sample.

In the application of PES-C, respondents have the potential

of many more statuses than was possible in the processing of the P-sample than in 1990. The reason is that a

P-sample respondent may be a nonmover, an outmover, an

inmover, or an out-of-scope person. The nonmovers and

outmovers have another characteristic, which is resident

or nonresident. A person who is living at the sample

address on Census Day is called a resident.

Errors in mover status may go in all directions. A person

designated as a nonmover may be an inmover or an outmover. All combinations of errors may happen and affect

the DSE in different ways.

Definition. P-sample matching error affects both the

estimates of nonmovers and inmovers in the estimate of

the size of the P-sample population. In addition, matching

error affects the estimates of the number of nonmover

matches, the number of outmovers and outmover

matches, and the number of inmovers in the estimate of

the number of matches. E-sample data collection error

affects the estimate of the number of erroneous enumerations. The post-stratum index h is suppressed in the following definitions.

mnms  net P-sample matching error in the nonmover component of Mˆ

momims  net P-sample matching error in the outmover and

inmover component of Mˆ

nnms  net P-sample matching error in the nonmover component of N

ˆ

P

nims  net P-sample matching error in the inmover component of N

ˆ

P

ees  net E-sample office processing error in CEˆ

Under the assumption that all other errors are zero, the

bias in the adjustment factors caused by P-sample matching error and E-sample processing error is defined as

B

ˆ

process,h  A

ˆ

h ChIIh

Ch



CEˆ

h B

ˆ

CEprocess,h

N

ˆ

E,h



[Nˆ

P,h B

ˆ

Pprocess,h]

Mˆ

h B

ˆ

Mprocess,h

.

The error component definitions include a ratio adjustment because they are estimated using the Evaluation

Sample. The ratio adjustment for components from the

P-sample is the ratio of the P-sample population total from

the A.C.E. to the P-sample population total based on the

Evaluation Sample N

ˆ

PF. The ratio adjustment for the components from the E-Sample is ratio of the two E-sample

totals defined comparably.

B

ˆ

Mprocess  [mnms  momims]  [NˆPN

ˆ

PF]

B

ˆ

Pprocess  [nnms]  [NˆPN

ˆ

PF]

B

ˆ

CE-process  [ees]  [NˆEN

ˆ

EF]

P-Sample and E-Sample Data Collection Error

Source. Errors may occur during the data collection.

While an interview is in progress, the respondent may

make an error in answering a question, or the interviewer

may make an error in asking a question or recording the

answer. Errors also occur when an interviewer goes to the

wrong address. Regardless of whether the error is caused

by the respondent, the interviewer, or a combination of

the two, such errors may cause the matching operation to

assign mover status, residency status, or match status

incorrectly to a person on the household roster. The A.C.E.

interviewer collects both a Census Day roster and an Interview Day roster. A person who resides at the household on

both days is classified as a nonmover. A person who lived

there only on Census Day is an outmover, while a person

who lived there only on Interview Day is an inmover. Persons classified as outmovers and nonmovers may or may

not have been a resident at the address on Census Day.

Errors in the mover status, residency status, or other

errors may cause the matching operation to fail to determine that a person was enumerated and to classify the

person as a nonmatch incorrectly.

Sometimes people listed on household rosters do not

exist. A more likely scenario is an interviewer who is having trouble contacting the residents of a housing units

may copy the name from a mail box and fill in the characteristics. This type of error is called ‘‘P-sample fabrication.’’

Usually fabricated households cause an underestimate of

the match rate, because they are smaller than the average

household size and do not match,

A special type of E-sample data collection error is the failure to identify duplicate enumerations. The processing

includes a search for duplicate enumerations within the

block cluster and the surrounding blocks. Duplicate enumerations outside the block cluster and surrounding

D–2 Section I—Appendix D Error Profile for A.C.E. Estimates

U.S. Census Bureau, Census 2000
blocks are more difficult to find. Identifying these duplications requires the respondent to provide information concerning another address where a household member may

also be enumerated. Errors may occur when the respondent does not understand the residency rules or is

unaware that a household member may be enumerated at

another address. The situations most prone to causing

duplicate enumerations are college students enumerated

at their family home and their college address, children in

joint custody agreements enumerated at both parents’

addresses, and people with two residences.

Another type of field error occurs during the listing of the

housing units for the census or for the P-sample. The

housing units listed as being in the sample block may be

in another block or vice versa. These types of errors are

called ‘‘geocoding error.’’ To account for minor geocoding

errors in 2000, the search for matches occurred within all

block-clusters and also in surrounding blocks for a sample

of the cases with geocoding errors recorded in the E

sample a design called ‘‘Targeted Extended Search (TES).’’

The variance estimates for the A. C. E. account for the TES

design. Flaws in the execution of the TES may result in

biases.

Definition. P-sample fabrication and data collection error

affect both the estimates of nonmovers and inmovers in

the estimate of the size of the P-sample population. In

addition, fabrication and data collection error affect the

estimates of the number of nonmover matches, the number of outmovers and outmover matches, and the number

of inmovers in the estimate of the number of matches.

E-sample data collection error affects the estimate of the

number of erroneous enumerations. Again, the poststratum index h is suppressed in the following definitions.

mnmr  net P-sample data collection error in the nonmover component of Mˆ

momimr  net P-sample data collection error in the outmover

and inmover component of Mˆ

nnmr  net P-sample data collection error in the non−

mover component of N

ˆ

P

nimr  net P-sample data collection error in the inmover

component of N

ˆ

P

eer  net E-sample data collection error in CEˆ

mnmfp  net P-sample fabrication error in the

nonmover component of Mˆ

momimfp  net P-sample fabrication error in the

outmover and inmover component of Mˆ

nnmfp  net P-sample data collection error in the

nonmover component of N

ˆ

P

nimfp  net P-sample data collection error in the inmover

component of N

ˆ

P

Under the assumption that all other errors are zero, the

bias in the adjustment factors caused by P-sample data

collection error and E-sample data collection error is

defined as

B

ˆ

collect,h A

ˆ

h Ch IIh

Ch



CEˆ

h B

ˆ

CEcollect,h

N

ˆ

E,h



[Nˆ

P,h B

ˆ

Pcollect,h]

Mˆ

h B

ˆ

mcollect,h

.

The error component definitions include a ratio adjustment because they are estimated using the Evaluation

Sample. The ratio adjustment for components from the

P-sample is the ratio of the P-sample population total from

the A.C.E. to the P-sample population total based on the

Evaluation Sample. The ratio adjustment for the components from the E-Sample is ratio of the two E-sample totals

defined comparably.

B

ˆ

Mcollect  [mnmr  mnmfp  momimr  momimfp]  [NˆPPF]

B

ˆ

Pcollect  [nnmr  nnmfp  nim]  [NPN

ˆ

PF]

B

ˆ

CEcollect  [eer]  [NˆEN

ˆ

EF]

Missing Data

Source. A.C.E. data may be missing for a variety of

reasons—some A.C.E. interviews fail to take place, some

households provide incomplete data on questionnaire

items, and in some cases the information for classification

as a match or nonmatch is ambiguous. The methods used

to compensate for missing data effectively assume that

the match status for the case with missing data is equal

on average to the status for cases that are similar, except

that they have complete data. Missing data on characteristics are imputed from otherwise similar cases with complete data. Nonresponse weighting adjustments are used

to account for sampled but noninterviewed households.

The P-sample matching and E-sample processing operation

assigns ‘‘unresolved’’ enumeration status to a case when

the available data is inadequate to determine whether the

person is enumerated in the census and a probability of

being correctly enumerated is imputed for such cases.

Also, error in the resolved cases causes error in the imputations, because the resolved cases are used to form the

imputations. Even if the imputation model were perfect,

the imputations will have error if the data used to fit the

model has error. This type of error is called ‘‘imputation

error due to data error.’’

Although one can consider the range of effects on the DSE

by considering extreme alternatives—e.g., all unresolved

matches truly are matches or truly are nonmatches—the

range is too wide to be informative about the likely bias.

The bias from the method used to compensate for missing

data can in principle be estimated from intensive

follow-up of cases with missing data, but in practice the

fraction completed by follow-up is too low. The Census

Bureau analyzed the missing-data bias by looking at the

changes in the DSE when alternative methods were used

to compensate for missing data.

Results from the Analysis of Reasonable Alternative Imputation Models are used to estimate the variance component. See Keathley et al. (2001) for details. The results of

Error Profile for A.C.E. Estimates Section I—Appendix D D–3

U.S. Census Bureau, Census 2000
Reasonable Alternative Imputation Models provided the

data for the calculation of the variance-covariance matrix

for adjustment factors the missing data component. The

missing data variance-covariance matrix was added to the

sampling variance-covariance matrix to obtain a variancecovariance matrix for the adjustment factors that contained the random error due to sampling and imputation

for missing data.

Definition. The Census Bureau models the error due to

imputation as a random effect and estimates its variancecovariance matrix. Modeling imputation error as a random

effect is motivated by practicalities. In principle, the bias

from the method used to compensate for missing data can

be estimated from intensive follow-up of cases with missing data, but in practice the fraction completed by

follow-up is too low. The variance component due to

imputation for missing data has three components.

VM  variance due to imputation  VRA  VB  VI

where

VRA  variance due to the imputation model selection

VB  variance due to the model parameter estimation

VI  within-person imputation variance.

The imputation variance components due to parameter

estimation and within person estimation are included in

the sampling error estimates, leaving the variance due to

model selection to be estimated separately. The missing

data variance-covariance matrix is added to the sampling

variance-covariance matrix to obtain a variance-covariance

matrix for the adjustment factors that contained the random error due to sampling and imputation for missing

data.

The components of imputation error due to data error

affect estimate of the number of nonmovers, the estimate

of the number of nonmovers enumerated, the estimate of

the match rate for the outmovers, and the estimate of the

number of erroneous enumerations. The post-stratum

index h is suppressed in the following definitions.

mnmi  net imputation error due to data error in the

nonmover component of Mˆ

momi  net imputation error due to data error in the

outmover match rate component of Mˆ

nnmi  net imputation error due to data error in the

nonmover component of N

ˆ

P

eei  net imputation error due to data error in CEˆ.

Under the assumption that all other errors are zero, the

bias in the adjustment factor A

ˆ

h caused by

imputation error due to data error is defined as

B

ˆ

impdata,h  A

ˆ

h Ch IIh

Ch



CEˆ

h B

ˆ

CEimpdata,h

N

ˆ

E,h



[Nˆ

P,h B

ˆ

Pimpdata,h]

Mˆ

h B

ˆ

Mimpdata,h

The error component definitions include a ratio adjustment because they are estimated using the Evaluation

Sample. The ratio adjustment for components from the

P-sample is the ratio of the P-sample population total from

the A.C.E. to the P-sample population total based on the

Evaluation Sample. The ratio adjustment for the components from the E Sample is the ratio of the two E-sample

totals defined comparably.

B

ˆ

Mimpdata  [mnmi  momi]  [Nˆ

PN

ˆ

PF]

B

ˆ

Pimpdata  [nnmi]  [NˆPN

ˆ

PF]

B

ˆ

CEimpdata  [eei

]  [Nˆ

EN

ˆ

EF]

Sampling Error

Source. Sampling error gives rise to random error, quantified by sampling variance, and to a systematic error

known as ratio-estimator bias. The sampling variance is

present in any estimate based on a sample instead of the

whole population. Ratio-estimator bias arises because

even if X and Y are unbiased estimators, X/Y typically is

biased.

Definition. The sampling variance and ratio-estimator

bias for the adjustment factors are

S2  sampling variance-covariance matrix for the

adjustment factors

B

ˆ

ratio,h  ratio-estimator bias in the adjustment factor A

ˆ

h

for post-stratum h.

Random sampling error is reflected in the estimated

variance-covariance matrix of the A

ˆ

h’s. The covariance

matrix is estimated by the Census Bureau’s sampling-error

software applied to the A.C.E. data. The software also can

be used to produce estimates of ratio-estimator bias.

Correlation Bias

Source. If there is variability of the enumeration probabilities for persons in the same post-stratum, or if there

is a dependence between enumeration in the census and

in the A.C.E. e.g., people less likely to be enumerated in

the census may also be less likely to be found in the

A.C.E., then correlation bias may arise. Correlation bias is

most likely a source of downward bias in the DSE. Evidence of correlation bias in national estimates is provided

by sex ratios (males to females) for adjusted numbers that

are low relative to ratios derived from demographic analysis of data on births, deaths, and migration.

The information from demographic analysis is insufficient

to estimate correlation bias at the post-stratum level, however, and alternative parametric models have been used to

allocate correlation bias estimates for national age-racesex groups down to post-strata. Estimates of correlation

bias at the national level provided by demographic analysis information also account for possible error from

groups whose probabilities of enumeration are so low that

the DSE will fail to account for them. The estimates of correlation bias based on sex ratios are affected by error in

the demographic-analysis sex ratios and by possible other

biases in the sex ratios in the DSE.

D–4 Section I—Appendix D Error Profile for A.C.E. Estimates

U.S. Census Bureau, Census 2000
The assumptions and model underlying the measurement

of correlation bias are discussed in detail in Bell

(2001,2001b), but are described briefly here. Although

there are several models for how correlation bias is distributed, the ‘two-group’ model was selected. The twogroup model relies on the basic assumptions listed below

for the estimation of correlation bias. In addition, sensitivity analyses assess the impact of variations in these

assumptions.

• The ratio of males to females measured in demographic

analysis is more reliable for the two racial groups, Black

and non-Black, than the A.C.E.

• There is no correlation bias present in the A.C.E. estimates for females.

• The relative correlation bias is equal across all A.C.E.

post-strata within an age-race category.

• The relative impact of other nonsampling errors is equal

for males and females at the national level.

The assumption with the two-group model of the relative

correlation bias being equal across post-strata within an

age-sex category has the advantage of permitting the estimation of correlation bias through a multiplicative factor

applied to the corrected DSE. Even more important, an

unbiased estimate of the factor is available under the

assumption that the relative impact of the other nonsampling errors is equal for males and females without

actually having to estimate the nonsampling errors.

Definition. Correlation bias usually causes the DSE to

underestimate the population size.

B

ˆ

correl,h  correlation bias in the adjustment factor A

ˆ

h for

post-stratum h.

Excluded-data Error from Reinstated Census

Enumerations

Source. The DSE treats late census data as nonenumerations. Thus, duplicate enumerations among the late data

do not contribute to census data, but valid enumerations

among the late data are treated as census misses and are

estimated by the DSE. If the late census data were

excluded from the entire adjustment process and estimation, no new source of error would be present. The

adjusted estimates do partially incorporate late census

data by including them in Ch, but excluding them from the

computation of N

ˆ

h. This use of late data affects the estimates for areas with disproportionately many or few late

adds, with an effect that is similar to synthetic estimation

error. In addition, the exclusion of late census data from

the E sample could bias the estimates at the post-stratum

level.

There are two conditions that have to be met for the

exclusion of the late adds from the processing of the

A.C.E. not to bias the dual system estimates at the poststratum level:

• The P sample covers the correct enumerations among

the late adds at the same rate as other correct enumerations.

• The late adds occur in the E sample at the same rate as

they occur in the census (excluding the imputations).

Definition. Error due to excluding the reinstated census

enumerations in the calculation of the DSE affects the estimate of the DSE and therefore the adjustment factor

directly.

B

ˆ

reinstate,h  bias in the adjustment factor A

ˆ

h for post-stratum

h due to excluding reinstated census enumerations.

Contamination Error

Source. Contamination occurs when the A.C.E. selection

of a given block cluster alters the implementation of the

census there and affects enumeration results, e.g, by

increasing or decreasing erroneous enumerations or by

increasing or decreasing coverage rates. Contact with residents of the sample blocks during the listing for the

P-sample may cause them to not respond to the census,

because they think that the listing contact is a response to

the census.

Definition. The bias in the adjustment factor for poststratum h from contamination is defined as follows.

B

ˆ

contam,h  bias in the adjustment factor A

ˆ

h for post-stratum h

due to contamination error.

Synthetic Estimation Bias

Source. The adjustment methodology relies on a method

called synthetic estimation to provide the same adjustment factor A

ˆ

h for all enumerations in a given poststratum, regardless of whether the enumerations are from

the same geographic area. Synthetic estimation bias arises

when the census from different areas but in the same

post-stratum should have different adjustment factors.

To assess synthetic estimation bias for a given area one

needs to develop an estimate based on data from the area

alone, which is rarely possible. Attempts to estimate synthetic estimation bias in undercount estimates from analysis of ‘‘artificial populations’’ or ‘‘surrogate’’ variables,

whose geographic distributions are known, are unconvincing. Therefore, sensitivity analyses have been conducted

to assess the impact of synthetic estimation bias. These

studies show that assuming synthetic estimation has a

minor effect on uses of the data is reasonable.

Definition. The synthetic estimates may cause a bias in

the adjusted estimates for area j. Error from synthetic estimation does not affect the dual system estimate for a

post-stratum, only areas within a post-stratum.

B

ˆ

syn, j  bias in the adjusted estimate N

ˆ

adj, j for area j due to

synthetic estimation error.

Error Profile for A.C.E. Estimates Section I—Appendix D D–5

U.S. Census Bureau, Census 2000
Inconsistent Post-stratification

Source. The computation ofˆCEhN

ˆ

E,h requires census enumerations to be assigned to post-strata, and the computation of N

ˆ

P, hMˆh requires P-sample enumerations to be

assigned to post-strata. When the assignments are not

made consistently for the two samples, error arises in the

ratio N

ˆ

P, hMˆh. Inconsistent assignments to post-strata may

be caused by mis-reporting of characteristics used in poststratification.

Cases that are most prone to inconsistent classification

are those where there is a different respondent for the

household in the census and the A.C.E. For example, a

household member’s age or race may be reported differently in a self-response than when another household

members responds for the person. Such inconsistencies

also may be due to computer processing errors, as well as

inconsistent reporting.

The matches in the A.C.E. sample provide a source of data

for estimating the error due to inconsistent post-stratification. An estimate of the error for a post-stratum may be

formed by assuming the inconsistency rate observed in

the matches also holds for those not matched.

Definition. Error due to inconsistent post-stratification

affects the estimate of the DSE and therefore the adjustment factor directly.

B

ˆ

inconsist,h  bias in the adjustment factor A

ˆ

h for post-stratum

h due to inconsistent post-stratification.

Error from Estimating Outmovers with Inmovers

Source. This error is unique to the PES-C model used in

the A.C.E. For the PES-C model, the members of the

P-sample are the residents of the housing units on Census

Day. There is some difficulty in identifying all the residents

of all the housing units on Census Day because some

move prior to the A.C.E. interview. The A.C.E. interview

relies on the respondents to identify those who have

moved out, the outmovers. Since the outmovers are identified by proxies, many of the outmovers are not recorded.

Therefore, the estimate of outmovers is too low. PES-C

uses the number of inmovers to estimate the number of

outmovers. The inmovers are those who did not live in the

sample blocks on Census Day, but moved in prior to the

A.C.E. interview. Theoretically the number of inmovers in

the whole country should equal the number of outmovers.

However, the number of inmovers may not equal the number of outmovers in a post-stratum because of circumstances such as economic conditions causing more people

to move out of an area than to move into an area.

Definition. The error due to using the inmovers to estimate the outmovers affects the estimates of the size of

the P-sample population and the number of matches.

mio,h  net P-sample data collection error in the mover

component of Mˆ

h in post-stratum h

nio,h  net P-sample data collection error in the mover

component of N

ˆ

P, h in post-stratum h.

Under the assumption that all other errors are zero, the

bias in the adjustment factors caused by P-sample matching error and E-sample processing error is defined as

B

ˆ

inout,h A

ˆ

h Ch IIh

Ch



CEˆ

h

N

ˆ

E,h



[Nˆ

P,h B

ˆ

Pinout,h]

Mˆ

h B

ˆ

Minout,h

.

The error component definitions include a ratio adjustment because they are estimated using the Evaluation

Sample. The ratio adjustment for components from the

P-sample is the ratio of the P-sample population total from

the A.C.E. to the P-sample population total based on the

Evaluation Sample. The post-stratum index h is suppressed in the following definitions.

B

ˆ

Minout  [mio]  [NˆPN

ˆ

PF]

B

ˆ

Pinout  [nio]  [NˆPN

ˆ

PF]

Balancing Error

Source. Balancing error must be addressed in the design

of the search areas used to search for E-sample correct

enumerations and P-sample matches. Limiting the search

for correct enumerations and matches is necessary

because the matching operation cannot search the entire

census. By limiting the search area, a small percentage of

correct enumerations will not be found and a small percentage of matches will not be found. This causes an

underestimate of the correct enumerations and an underestimate of the matches. However, the estimate of the net

error is not biased as long as the percentage error in the

correct enumerations equals the percentage error in the

matches. The A.C.E. design avoids balancing error by

choosing the same block clusters for the E-sample and the

P-sample and drawing the search areas consistently.

Definition. There is not a separate measurement of balancing error. Any balancing error that may arise during the

implementation of the A.C.E. will be included in the measurement of data collection error.

D–6 Section I—Appendix D Error Profile for A.C.E. Estimates

U.S. Census Bureau, Census 2000
Section I.

References

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References Section I—References 1

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Kostanich, D., Griffin, R., and Fenstermaker, D. (1999).

‘‘Census 2000 Accuracy and Coverage Evaluation Survey:

Sample Allocation and Post-stratification Plans,’’ DSSD Census 2000 Procedures and Operations Memorandum Series

#R-2.

Marks, E. (1979). ‘‘The Role of Dual System Estimation in

Census Evaluation,’’ in K. Krotki (Ed.), Developments in

Dual System Estimation of Population Size and Growth,

Edmonton: University of Alberta Press, 156-188.

Nash, F. (2000). ‘‘Overview of the Duplicate Housing Unit

Operations,’’ Census 2000 Information Memorandum

Number 78.

National Center for Health Statistics (1968). ‘‘Synthetic

State Estimates of Disability,’’ P. H. S. Publication 1759,

U.S. Government Printing Office, Washington, D.C.

Raglin, D. and Bean, S. (1999). ‘‘Outmover Tracing and

Interviewing,’’ Census 2000 Dress Rehearsal Evaluation

Results Memorandum Series #C-3.

Rao, J.N.K. and Shao, J. (1992). ‘‘Jackknife Variance Estimation with Survey Data Under Hot Deck Imputation,’’

Biometrika, 79, 811-822.

Reynolds v. Simms, 377 U.S. 533 (1964).

2 Section I—References References

U.S. Census Bureau, Census 2000
Robinson, J. G. (2001). ‘‘ESCAP II: Demographic Analysis

Results,’’ Executive Steering Committee for A.C.E. Policy II,

Report 1.

Robinson, J. G., Ahmed, B., Gupta, P., and Woodrow, K.

(1993). ‘‘Estimation of Population Coverage in the 1990

United States Census Based on Demographic Analysis,’’

Journal of the American Statistical Association, 88, 1061-

1071.

Schindler, E. (1998). ‘‘Allocation of the ICM Sample to the

States for Census 2000,’’ Proceedings of the Survey

Research Methods Section, American Statistical Association.

Schindler, E. (1999). ‘‘Comparison of DSE C and DSE A,’’

Census 2000 Dress Rehearsal Evaluation Memorandum

# C-8a.

Schindler, E. (2000). ‘‘Accuracy and Coverage Evaluation

Survey: Post-stratification Preliminary Research Results,’’

DSSD Census 2000 Procedures and Operations Memorandum Series #Q-23.

Sekar, C. C. and Deming, W. E. (1949). ‘‘On a Method of

Estimating Birth and Death Rates and the Extent of Registration,’’ Journal of the American Statistical Association,

44, 101-115.

Siegel, J. (1974). ‘‘Estimates of Coverage of Population by

Sex, Race, and Age: Demographic Analysis,’’ 1970 Census

of Population and Housing: Evaluation and Research Program, PHC(E)-4, U.S. Bureau of the Census, Washington,

D.C.

Siegel, J. and Zelnik, M. (1966). ‘‘An Evaluation of Coverage in the 1960 Census of Population by Techniques of

Demographic Analysis and by Composite Methods,’’ Proceedings of the Social Statistics Section, American Statistical Association.

Starsinic, M. (2001). ‘‘Accuracy and Coverage Evaluation

Survey: Specifications for Covariance Matrix Output Files

from Variance Estimation for Census 2000,’’ DSSD Census

2000 Procedures and Operations Memorandum Series

#V-4.

Starsinic, M. and Kim, J. (2001). ‘‘Accuracy and Coverage

Evaluation: Computer Specifications for Variance Estimation for Census 2000 - Revision,’’ DSSD Census 2000 Procedures and Operations Memorandum Series #V-5.

U.S. Bureau of the Census (1985). Evaluating Censuses of

Population and Housing, Statistical Training Document,

ISP-TR-5, Washington, D.C.

West, K. (1991). ‘‘Final Report for PES Evaluation Project

P4: Quality of Reported Census Day Address - Evaluation

Follow-up,’’ 1990 Coverage Studies and Evaluation Memorandum Series #D-2.

Winkler, W. (1994). ‘‘Advanced Methods for Record Linkage,’’ Proceedings of the Survey Research Methods Section, American Statistical Association.

Wolfgang, G. (1999). ‘‘Request for Dress Rehearsal Surrounding Block Files for A.C.E. Research,’’ unpublished

Census Bureau Memorandum.

Wolter, K. (1986). ‘‘Some Coverage Error Models for Census

Data,’’ Journal of the American Statistical Association, 81,

338-346.

Woltman, H., Alberti, N., and Moriarity, C. (1988). ‘‘Sample

Design for the 1990 Census Post Enumeration Survey,’’

Proceedings of the Survey Research Methods Section,

American Statistical Association.

ZuWallack, R. (2000). ‘‘Sample Design for the Census 2000

Accuracy and Coverage Evaluation,’’ Proceedings of the

Survey Research Methods Section, American Statistical

Association.

References Section I—References 3

U.S. Census Bureau, Census 2000
Accuracy and Coverage Evaluation

of Census 2000:

Design and Methodology

Section II

A.C.E. Revision II March 2003

U.S. Census Bureau, Census 2000
Chapter 1.

Introduction to A.C.E. Revision II

INTRODUCTION

The Accuracy and Coverage Evaluation (A.C.E.) survey was

designed to measure and possibly correct net coverage

error in Census 2000. However, because A.C.E. failed to

measure a significant number of erroneous enumerations,

A.C.E. did not meet these objectives. The Census Bureau’s

Executive Steering Committee for A.C.E. Policy (ESCAP)

recommended twice NOT to correct the census counts.1

There are, however, concerns about differential coverage

error in Census 2000 data. While the Census 2000 data

products will not be corrected, it is possible that improvements could be made to the post-censal population estimates used for survey controls. This is the Census

Bureau’s motivation for correcting errors in the A.C.E. data

and developing improved estimates of the net undercount.

The improved estimates are called A.C.E. Revision II estimates. These revised estimates provide a better picture of

Census 2000 coverage and will help us design a better

coverage measurement program for 2010. This part of the

document provides a description of the methodology used

to produce the A.C.E. Revision II estimates. A comprehensive technical description of the methodology used to produce the original

estimates of net undercount released in March 2001 is

presented in the first half of this publication.

This chapter summarizes the history of the two adjustment decisions and discusses key findings and limitations.

It also introduces the key components of the revision and

describes the major errors being corrected. The next

chapter provides an overview of the revision process and

subsequent chapters provide detailed methodology as

follows:

Chapter 2: Summary of A.C.E. Revision II

Methodology

Chapter 3: Correcting Data for Measurement Error

Chapter 4: A.C.E. Revision II Missing Data Methods

Chapter 5: Further Study of Person Duplication in

Census 2000

Chapter 6: A.C.E. Revision II Estimation

Chapter 7: Assessing the Estimates

BACKGROUND

The original A.C.E. estimates were available in February

of 2001, in time to allow for the possibility of correcting

Census 2000 redistricting files. The Census Bureau’s

ESCAP recommended in March 2001 not to correct the

Census 2000 counts for purposes of redistricting (ESCAP I,

2001). The Secretary of Commerce concurred. Given the

information available at this time, this decision was not

based on any clear evidence that the census counts were

more accurate, but rather concern that there was some yet

undiscovered error in the A.C.E. The A.C.E estimate of a

3.3 million net undercount was much larger than the

Demographic Analysis (DA) estimate of only 340,000.

Further evaluations were conducted over the next 6

months to examine the reasons for the discrepancy and to

determine if other Census 2000 data products should be

corrected. The Census 2000 redistricting files were the

first of many Census 2000 data products scheduled for

public release. See the Census Bureau’s Web site,

www.census.gov, for released data products. The question

remained as to whether these other Census 2000 data

releases should be corrected.

In October 2001, the ESCAP again decided not to correct

the census counts for other Census 2000 data products.

Analysis of A.C.E. evaluation data and a study of duplicates in the census revealed that the A.C.E. failed to

measure large numbers of erroneous census enumerations

(ESCAP II, 2001). This error called into question the quality

of the A.C.E. survey results. Some of the key findings from

the analyses are:

• An evaluation by Krejsa and Raglin (2001) was the first

indication that A.C.E. seriously underestimated erroneous enumerations. This analysis revealed an additional

net 1.9 million erroneously enumerated persons for

those cases that could be resolved. These results are

based on an independent reinterview and matching of

about 70,000 E-sample persons. Because of the serious

implications of this finding, a further Review Study was

conducted.

• The findings from the Review Study by Adams and

Krejsa (2001) showed that A.C.E. underestimated erroneous enumerations by a net of 1.45 million persons,

which was smaller than the evaluation figure but still a

significantly large amount. This figure does not include

unresolved cases, so the estimated amount is probably

somewhat higher. This study was based on a sample of

1

The ESCAP recommendations, supporting analyses, technical

assessments, and limitations can be found on the Census Bureau’s

Web site at www.census.gov/dmd/www/EscapRep.html.

Introduction to A.C.E. Revision II Section II—Chapter 1 1–1

U.S. Census Bureau, Census 2000
about 17,000 persons selected from the 70,000 person

evaluation follow-up E sample. The most experienced

analysts reviewed these cases using both the original

A.C.E. person follow-up interviews as well as the reinterview results to determine their enumeration status.

• Mule (2001) showed that Census 2000 suffers from a

large number of duplicate enumerations, i.e., persons

who were double counted. Mule computer-matched

census enumerations in A.C.E. block clusters to those

across the entire country. The matching used by Mule

was conservative in picking up census duplicates given

his requirement for exact matching at the first stage.

Within the A.C.E. block clusters, Mule found only 38

percent of the in-scope duplicates that A.C.E. found,

leading us to believe that his matching algorithm was

underestimating duplicates in the census. Note that

A.C.E. was not designed to estimate duplicates outside

the search area, and this, itself, was not a design flaw.

A.C.E. was, however, expected to determine which

census enumerations were erroneous because they were

reported at the wrong residence. The design of A.C.E.

Revision II accounts for duplicates outside the search

area. Mule’s study did not distinguish which of the

duplicate pair was correct and which was erroneous,

but one could easily speculate that half of these should

be correct and half should be erroneous.

• Feldpausch (2001) examined the A.C.E. enumeration

status for E-sample cases identified by Mule (2001) as

duplicates outside the search area. Only 14 percent of

the E-sample persons that were duplicates of a person

in a housing unit were coded as erroneous by A.C.E.

This was much lower than the expected 50 percent,

indicating that A.C.E. underestimated erroneous enumerations due to not perceiving that these E-sample

persons should have been counted at other residences.

Note that these results suggest measurement error in

the original A.C.E. figures released.

• Fay (2001, 2002) then compared the enumeration status

for the E-sample Review Study cases to the duplicates

identified by Mule (2001) outside the search area. Only

19 percent of the review cases that were duplicates of a

person in a housing unit were coded as erroneous by

the Review Study. Again, this was much less than the

expected 50 percent, indicating that the evaluation data

and the special review did not identify all the erroneous

enumerations. Using these data, Fay then produced a

lower bound on the level of unmeasured erroneous

enumerations of 2.9 million.

• There was also evidence that similar problems may

have affected the population sample (P sample) which is

used to measure the omission rate. A.C.E. evaluation

data from Raglin and Krejsa (2001) show that there are

measurement errors in determining residency and

mover status.

Using Fay’s lower bound on the level of unmeasured erroneous enumerations, Thompson et al. (2001) produced a

‘‘Revised Early Approximation’’ of undercount for three

race/Hispanic origin groups. These estimates were

intended to be illustrative of net undercount and possible

coverage differences. The same methodology and data

were later used to expand the calculations to seven

race/Hispanic origin groups. See Fay (2002) and Mule

(2002) for details. These preliminary estimates show a

very small net undercount. The data also indicate that the

differential undercount has not been eliminated. These

results are limited to the extent that they only provide

information at the national level for broad population

groups. Furthermore, these preliminary approximations

were based on a small subset of A.C.E data and only partially correct for errors in measuring erroneous enumerations. Potential errors in measuring omissions were not

accounted for.

In summary, the A.C.E. results were not acceptable

because A.C.E. failed to measure large numbers of erroneous census enumerations. This was the reason for not

using the A.C.E., but this does not mean that there were

no other errors in the A.C.E. In particular, there was concern about P-sample cases that matched to enumerations

suspected of being duplicates. If the E-sample case was

erroneous, then that match cannot be valid. The extent of

this problem was not quantified at the time of the ESCAP II

decision. The level of other errors was small by comparison, and therefore, was not a major factor in this decision.

See Hogan et al. (2002) and Mulry and Petroni (2002) for

further information.

Plans for Revising the 2000 A.C.E. Estimates

Even though the ESCAP recommended twice not to correct

the census counts, they had concerns about differential

coverage error in Census 2000 data. They thought it possible that further research resulting in revised estimates of

coverage could potentially be used to improve the postcensal estimates. In addition, revised estimates would

provide a better understanding of Census 2000 coverage

error that could be used to improve census operations for

2010 and would help in developing better methodologies

for the 2010 coverage measurement program.

The major objective was to produce improved estimates of

the household population that could be used to measure

net coverage error in Census 2000. This meant obtaining

better estimates of erroneous census enumeration from

the E sample and obtaining better estimates of census

omissions from the P sample. Furthermore, since the

national net undercount, as indicated by both DA and the

1–2 Section II—Chapter 1 Introduction to A.C.E. Revision II

U.S. Census Bureau, Census 2000
‘‘Revised Early Approximations,’’ was very close to zero

and the census included large numbers of erroneous enumerations in the form of duplicates, it was imperative that

the revised methodology carefully account for both overcounts and undercounts. Hogan (2002) summarized the

major revision issues in the form of the following five

challenges:

1. Improve estimates of erroneous census enumerations

2. Improve estimates of census omissions

3. Develop new models for missing data

4. Enhance the estimation post-stratification

5. Consider adjustment for correlation bias

There were no field operations associated with the A.C.E.

Revision II process. Because of the late date, it was not

feasible (or practical) to revisit households for additional

data collection. Consequently, the revisions were based on

data that had already been collected. One aspect of the

strategy for revising the coverage estimates involves correcting measurement error using information from the

A.C.E. evaluation data. This is referred to as the recoding

operation. Another aspect of these corrections involves

conducting a more extensive person duplicate study to

correct for measurement error that was not detected by

A.C.E. evaluations. This is referred to as the Further Study

of Person Duplication (FSPD). The estimation method,

discussed briefly in Chapter 2 and more fully in Chapter 6,

is designed to handle overlap of errors detected by both

of these studies to avoid overcorrecting for measurement

error.

The recoding operation was designed to improve estimates of erroneous census enumerations and census

omissions. It uses the original A.C.E. person interview (PI)

and person follow-up (PFU), the evaluation follow-up interview (EFU), the matching error study (MES), and the

PFU/EFU Review Study2 to correct for measurement error

in enumeration status, residence status, mover status and

matching status. This effort involved extensive recoding

of about 60,000 P-sample cases and more than 70,000

E-sample cases.3 An automated computer algorithm was

used to recode most of the cases, but many required a

clerical review by experienced analysts at the National

Processing Center. The analysts had access to the questionnaire responses, as well as interviewer notes that put

them in a better position to resolve apparent discrepancies. It was not possible to completely code all cases

because of missing or conflicting information; however,

the number of conflicting cases was relatively small.

The duplicate study was designed to further improve

estimates of erroneous census enumerations and census

omissions. This study used computer matching and modeling techniques to identify E- and P-sample cases that link

to census enumerations across the entire country, including group quarters, reinstated, and deleted census cases.

For the E-sample links, this study does not identify which

enumeration is correct and which is the duplicate. For

P-sample links, this study does not identify whether the

correct Census Day residence is at the P-sample location

or the census location. This information is used to model

the probability that an E-sample linked case is a correct

enumeration or that a P-sample case is a resident on

Census Day.

New missing data models were developed to reflect the

different types of missing data now possible as a result of

the recoding operation. There were three new types of

missing data to deal with:

1. P-sample households that were originally considered

interviews, but the recoding determined that there

were no valid Census Day residents,

2. cases with unresolved match, enumeration, or residency status because of incomplete or ambiguous

interview data, and

3. cases with conflicting enumeration or residency status, because contradictory information was collected

in the A.C.E. PFU and EFU interviews.

It was impossible to determine which data were valid for

these cases. A household noninterview weighting adjustment using new cell definitions was used for type 1

above. Imputation cells and donor pools were developed

for the second type of missing data based on detailed

responses to the questionnaire. For the conflicting cases

in type 3 above, there were no applicable donor pools,

and probabilities of 0.5 were imputed for correct enumeration status and Census Day residency status. Fortunately,

the recoding operation resulted in a relatively small number of these cases.

The revision effort incorporates separate post-strata for

estimating census omissions and erroneous census enumerations because the factors related to each of these are

likely to be different. The research effort focused on determining variables related to erroneous enumerations. This

was because much of the previous work on developing

post-strata focused only on the census omissions, and by

default, the same post-strata were applied to the erroneous inclusions. For the E sample, some of the original

post-stratification variables have been eliminated and

additional variables have been included. Variables such as

2

The PFU/EFU Review Study was not a planned evaluation. It

was a special study conducted in a subsample of the evaluation

data to resolve discrepancies between enumeration status in the

PFU and EFU. 3

These are probability subsamples of the original A.C.E. P and

E samples and in the context of A.C.E. Revision II are called revision samples, but they are in fact equivalent to the evaluation

follow-up samples.

Introduction to A.C.E. Revision II Section II—Chapter 1 1–3

U.S. Census Bureau, Census 2000
region, Metropolitan Statistical Area/type of census enumeration area, and tract-level return rate were replaced by

proxy status, type and date of census return, and household relationship and size. For the P sample, only the age

variable was modified to define separate post-strata for

children aged 0 to 9 and those 10 to 17. This was done

because the DA estimates suggested different coverage

for these groups. The estimated correct enumeration rates

and estimated match rates are used to calculate Dual

System Estimates (DSEs) for the cross-classification of the

E and P post-strata.

The A.C.E. Revision II DSEs include an adjustment for

correlation bias. Correlation bias exists whenever the

probability that an individual is included in the census is

dependent on the probability that the individual is

included in the A.C.E. This form of bias generally has a

downward effect on estimates, because people missed in

the census may be more likely to also be missed in the

A.C.E. Since the intent of the A.C.E. Revision II is to estimate the net coverage error, it is important to carefully

account for errors of omissions and errors of erroneous

inclusions. In previous coverage measurement surveys,

the erroneous inclusions were assumed to be much

smaller than omissions. Consequently, not adjusting for

correlation bias had the effect of understating the net

undercount and relative to the census was a correction

that was in the right direction, but just not big enough. In

the presence of large numbers of overcounts, this assumption is no longer valid and it’s possible that a correction

might not even be in the right direction when the estimate

is close to zero. For example, if there is a small true net

undercount, it’s possible to estimate an overcount because

the DSE would underestimate population in the presence

of correlation bias. Estimates of correlation bias were calculated using the ‘‘two-group model’’ and sex ratios from

DA. The sex ratio is defined as the number of males

divided by the number of females. This model assumes no

correlation bias for females or for males less than 18 years

of age, and that Black males have a relative correlation

bias that is different from the relative correlation bias for

non-Black males. The correlation bias adjustment is also

done by three age categories: 18-29, 30-49, and 50 and

over with the exception of non-Black males 18 to 29 years

of age. This is because the A.C.E. Revision II sex ratios for

non-Blacks 18-29 exceed the corresponding modified DA

sex ratio and is likely a result of a data problem. This

model further assumes that relative correlation bias is

constant over male post-strata within age groups.

The DSEs, adjusted for correlation bias, are used to produce coverage correction factors for each of the crossclassified post-strata. These factors are applied or carried

down within the post-strata to produce estimates for

geographic areas such as counties or places. This process

is referred to as synthetic estimation. The key assumption

underlying this methodology is that the net census

coverage, estimated by the coverage correction factor, is

relatively uniform within the post-strata. Failure of this

assumption leads to synthetic error.

1–4 Section II—Chapter 1 Introduction to A.C.E. Revision II

U.S. Census Bureau, Census 2000
Chapter 2.

Summary of A.C.E Revision II Methodology

INTRODUCTION

The original A.C.E. estimates were found to be unacceptable because they failed to detect significant numbers of

erroneous census enumerations. There were also suspicions that the A.C.E. may have included residents in its P

sample that were actually nonresidents. Thus, the major

goal in revising the A.C.E. estimates included a correction

of these measurement errors. One aspect of these corrections involved correcting a subsample of the A.C.E. data.

Another aspect involved correcting measurement errors

that could not be detected with the information available

in the subsample. These additional errors were identified

via a duplicate study. The purpose of this chapter is to

present a high-level overview of the process used to produce A.C.E. Revision II estimates of the population coverage of Census 2000. Further details concerning the methodology and procedures are included in subsequent

chapters.

Background

The chronology of events leading to the corrected A.C.E.

Revision II results were as follows:

1. The A.C.E. estimates produced in March 2001 were

based on the Full E and P samples, which were probability samples of over 700,000 persons in 11,303

block clusters.

2. The Matching Error Study (MES) and the Evaluation

Follow-up (EFU) were two programs that evaluated the

March 2001 A.C.E. estimates. The MES measured

errors introduced when the census and A.C.E. interviews were matched. The EFU, which was designed to

study unusual living situations, entailed another interview. It evaluated the Census Day residency, enumeration status and mover status assigned during the

A.C.E. interview and A.C.E. Person Follow-up (PFU)

interview. The MES and EFU were conducted in a subsample of 2,259 block clusters selected from the original 11,303 block clusters. A further subsample of persons within these block clusters was selected for the

EFU evaluation.

3. The PFU/EFU Review occurred next; it was not part of

the planned evaluations. It was done in order to

resolve major discrepancies in enumeration status

between the EFU and PFU results. Thus, the Review

E sample was a subsample of the EFU E sample.

4. At this point the A.C.E. Revision II program commenced. The Revision E and P samples were developed for purposes of producing A.C.E. Revision II estimates. They are each comprised of about 70,000

sample persons. These samples were essentially the

same as the evaluation E and P samples for EFU, but

the data have undergone a major recoding to correct

for measurement error. These data, along with other

measurement error corrections identified by the duplicate study, were used to adjust the Full E and P

samples to produce A.C.E. Revision II estimates.

The A.C.E. Revision II process is presented below. First, the

corrections for measurement error (undetected erroneous

enumerations and P-sample nonresidents) in the Revision

Samples are explained. Then, a discussion is given of the

missing data methods applied to cases whose match, residency or enumeration status had changed in the Revision

Samples. Next, the process for identifying census duplicates across the entire nation is discussed. An applicable

dual system estimation formula that incorporates these

changes and accounts for correlation bias is presented.

Finally, synthetic estimation was employed to produce

A.C.E. Revision II results. See Kostanich (2003) for a summary of the methodology.

CORRECTING MEASUREMENT ERROR

IN THE REVISION SAMPLES

As previously stated, the original A.C.E. process (step 1.

above) failed to detect significant numbers of erroneous

census enumerations (EEs). These undetected EEs (one

part of ‘‘measurement error’’ in the A.C.E.) were uncovered

during the evaluations of the A.C.E. (step 2. above).

In general, the original A.C.E. Person Interview (PI) and

PFU, the EFU interview, the MES, and the PFU/EFU Review

results were used to correct for measurement error in the

enumeration, residency, mover, and match statuses for

subsamples of the Full A.C.E., called the Revision E and P

samples. No additional data were collected in this measurement error correction process.

The Revision Samples underwent extensive recoding using

all available data indicated above. This recoding included

the original interview and matching results, the evaluation

interview and matching results, as well as the recoding

done for the PFU/EFU Review.

The A.C.E. Revision II recoding operation was an extension

of the PFU/EFU Review clerical recoding, which was used

to examine discrepancies between enumeration status in

Summary of A.C.E. Revision II Methodology Section II—Chapter 2 2–1

U.S. Census Bureau, Census 2000
the original A.C.E. and the Evaluation Follow-up (EFU).

Given the information available, the recoding that was

done on the 17,500 cases in the Review E sample was

considered to have negligible error, since these data were

reviewed and recoded by expert matchers using rules

consistent with census residence rules.

An automated coding algorithm based on specific

responses to the PFU and the EFU questionnaires was used

to determine an appropriate code for each case. This was

done for both the PFU interview and the EFU interview.

The automated coding also assigned a ‘Why’ code that

described the reason why the particular code was

assigned.

A three-step process was followed to assign final codes to

each case:

1. Validation. Determine, for categories of ‘Why’ codes,

if the automated coding was of high quality based on

level of agreement with the Review data.

2. Targeting. Target only those ‘Why’ code categories

that had codes produced by automated coding that

had low levels of agreement with the Review data.

3. Clerical coding. Clerically recode only cases in the

targeted ‘Why’ code categories. The clerical recoding

took advantage of handwritten interviewer comments.

In general, cases did not go to clerical review if both the

PFU and EFU automated codes agreed, the mover statuses

also agreed, and the ‘Why’ code category was deemed to

be of high enough quality.

After the A.C.E. Revision II recoding operation corrected

for enumeration, residency, and mover status, the results

of the MES were used to correct for false matches and

false nonmatches. Some matching errors were a result of

incorrect residency status coding and had been corrected

as part of the recoding operation discussed above. To

determine the correct match status, each of the possible

combinations of match status was reviewed to determine

the appropriate match status for each type of case. In general, the MES match status was assigned when there were

changes from a match to a nonmatch or changes from a

nonmatch to a match. For other situations the match

status from the EFU coding was assigned. See Krejsa and

Adams (2002) for further details.

ADJUSTMENT FOR MISSING DATA

As with all survey data, it is not possible to obtain interviews for all sample cases, nor is it possible to obtain

answers to all interview questions. For the Full A.C.E. E

and P samples, household noninterview adjustments were

used to adjust for noninterviewed households. In addition,

imputation methods were used to adjust for missing characteristics such as age or tenure, as well as enumeration,

residency, and match status. For the A.C.E. Revision II

work, these missing data adjustments for the Full A.C.E. E

and P samples were essentially unchanged from those

used to produce the March 2001 A.C.E. estimates.

For the Revision E and P samples, however, there were

three new types of missing data to deal with:

1. Noninterviewed households: Revision P-sample households that were considered interviews in the A.C.E. P

sample, but were identified as noninterviews in the

Revision coding because it was determined that there

were no valid Census Day residents;

2. Revision E- or P-sample cases with unresolved match,

enumeration, or residency status because of incomplete or ambiguous interview data;

3. Revision E- or P-sample cases with conflicting enumeration or residency status. This occurred when contradictory information was collected in the A.C.E. PFU

and the EFU interviews and it could not be determined

which was valid.

Household Noninterview Adjustment

for the Revision P Sample

For the original March 2001 A.C.E. estimates, the household noninterview adjustment generally spread the

weights of the Full P-sample noninterviewed housing units

over interviewed housing units in the same block cluster

with the same housing unit structure type. The methodology for the Revision P-sample household noninterview

adjustment for Interview Day was essentially unchanged

from that used for the Full P sample. There was, however,

an important change for the noninterview adjustment for

Census Day residency. A separate cell was defined for new

noninterviews due to whole households of persons determined to be inmovers or nonresident outmovers based on

the recoding that was done to correct for measurement

error.

Imputation for Revision E- or P-Sample

Unresolved Cases

In the Full A.C.E. P sample, persons with unresolved Census Day residency or match status came about in two

ways. First, the person interview (PI) may not have provided sufficient information for matching and follow-up.

Second, the Person Follow-up (PFU) may not have collected

adequate information to determine a person’s Census Day

residency status or their match status. The imputation

method differed by how the case came to be unresolved.

Revision P-sample persons with insufficient information

for matching and follow-up tended also to have had insufficient information in the original coding of the Full P

sample, except for some rare coding changes. These persons with insufficient information were not sent out for an

Evaluation Follow-up interview.

2–2 Section II—Chapter 2 Summary of A.C.E. Revision II Methodology

U.S. Census Bureau, Census 2000
For the Revision P sample, the imputation of Census Day

residency was improved upon by defining finer imputation

cells that included whether or not the housing unit was

matched, not matched, or had a conflicting household.

The probability of a match was imputed based on the

overall match rate for five groups defined by mover status, housing unit match status as in the original A.C.E.,

and also on conflicting household status.

For Revision P- and E-sample persons who were unresolved because of ambiguous or incomplete follow-up

information, the situation was more complicated because

there were two follow-up interviews to consider, the PFU

and EFU.

For the Full E and P samples, imputation cells were based

mostly on information obtained before any follow-up was

conducted. For the Revision E and P samples, imputation

cells relied on the after follow-up information. This change

was the single most important improvement in the missing data methodology.

Imputation for Revision E- or P-Sample

Conflicting Cases

When the A.C.E. PFU and EFU interviews had contradictory

information, the case was assigned a code of conflicting.

All cases determined to be conflicting based on the

automated recoding were sent to analysts for further

clerical review. By examining the handwritten notes of

interviewers, the analysts could often determine which of

the interviews was better and assign an appropriate code.

There were some cases where the interviews appeared to

be of equal quality, such as both respondents were household members or both respondents were of equal caliber

proxy. For these conflicting cases, the interviews seemed

equally valid based on the expertise of the analysts.

Therefore, probabilities of 0.5 were imputed for correct

enumeration for Revision E-sample conflicting cases and

for Census Day residency for Revision P-sample conflicting

cases.

FURTHER STUDY OF PERSON DUPLICATION

Earlier work showed that correcting measurement error by

recoding was not going to correct all the missed erroneous enumerations. Evaluations of the March 2001 A.C.E.

coverage estimates indicated the A.C.E. failed to detect a

large number of erroneous census enumerations. One type

of census erroneous enumerations was duplicate census

enumerations; that is, census enumerations included in

the census two or more times. The A.C.E. was not specifically designed to detect duplicate census enumerations

beyond the A.C.E. search area (the area where census and

A.C.E. person matching was conducted). However, there

was an expectation that the A.C.E. would detect that these

E-sample enumerations had another residence and that

roughly half the time this other residence was the usual

residence. Feldpausch (2001) showed this expectation was

not met.

For purposes of constructing A.C.E. Revision II estimates,

the study of person duplication used matching and modeling techniques to identify duplicate links between the Full

E and P samples to census enumerations. Links to group

quarters, reinstated, deleted and E-sample eligible records

throughout the entire nation were allowed. The matching

algorithm used statistical matching to identify linked

records. Statistical matching allowed for the matching

variables not to be exact on both records being compared.

Because linked records may not refer to the same individual even when the characteristics used to match the

records were identical, modeling techniques were used to

assign a measure of confidence, the duplicate probability,

that the two records refer to the same individual.

Matching Algorithm

The matching algorithm consisted of two stages. The first

stage was a national match of persons using statistical

matching. Statistical matching links records based on similar characteristics or close agreement of characteristics.

Statistical matching allowed two records to link in the

presence of missing data and typographical or scanning

errors. The second stage of matching was limited to

matching persons within households that contained a link

from the first stage.

The second stage of matching was limited to matching

persons within linked households. The first stage established a link between two housing units. The second stage

was a statistical match of all household members in the

sample housing unit to all household members in the census housing unit.

Modeling Techniques

The set of linked records consists of both duplicated enumerations and person records with common characteristics. Using two modeling approaches, the probability that

the linked records were the same person was estimated.

One approach used the results of the statistical matching

and relied on the strength of multiple links within the

household to indicate person duplication. The second

relied on an exact match of the census to itself and the

distribution of births, names, and population size to indicate if the individual link was a duplicate. These two

approaches were combined to yield an estimated duplicate

probability for the linked records from the statistical

matching of the Full E and P samples to the census. See

Chapter 5 for a full discussion on the person duplication

study.

THE A.C.E. REVISION II DSE FORMULA

With the correction of measurement error in the Revision E

and P samples, the adjustment for missing data in the

Revision E and P samples, and the determination of census

Summary of A.C.E. Revision II Methodology Section II—Chapter 2 2–3

U.S. Census Bureau, Census 2000
duplicate links between the Full E and P samples and census enumerations, the dual system estimation formula can

be applied. The following sections explain the formula and

its adjustment for the A.C.E. Revision II work.

Using procedure C for movers and different post-strata for

the E and P samples, the DSE formula can be written as:

DSEC

ij  Cen ́ij  II ́ij

[

CEi

Ei

]

[

Mnm,j  [

Mom,j

Pom,j

]Pim,j

Pnm,j  Pim,j

]

The A.C.E. Revision II DSE formula using procedure C for

movers, separate E and P post-strata, measurement error

corrections from the E and P Revision Samples, and duplicate study results is:

ReDSEC

ij  Cen ́ij  II ́ij

[CEi

ND f1,i ́CEi

D

Ei

]

[

Mnm,j ND f2,j ́  M

nm,j D  [

Mom,j f3,j ́

Pom,j f4,j ́

]Pim,j f5,j ́  gPnm,j D - Pnm,j D 

Pnm,j ND f6,j ́  P

nm,j D  Pim,j f5,j ́  g Pnm,j D - Pnm,j D 

]

Recall that the II ́ term excludes the late census adds.

Notation

Terms CE Correct enumerations

E E-sample total

M Matches

P P-sample total

f Adjusts for measurement error

g Adjusts nonmovers to movers due to

duplication

Subscripts i, j Full E and P post-strata

i ́, j ́ Revision E and P measurement error

correction post-strata

nm, om, im nonmover, outmover, inmover

Superscripts C DSE Procedure C for movers

ND Not a duplicate to census enumeration

outside search area

D Duplicate to census enumeration outside search

area

∼ Includes probability adjustment for residency

given duplication

Adjustment for Duplicates using the Duplicate

Study

The first task was to adjust the usual dual system estimate

formula for those cases that have a link to a census enumeration outside the A.C.E. search area. P- and E-sample

cases with links to census enumerations were assigned a

nonzero probability of being a duplicate. P- and E-sample

cases without duplicate links were assigned a probability

of zero.

When estimating terms in the A.C.E. Revision II DSE involving nonduplicates, those indicated by a superscript ND, it

was necessary to include the probability of not being a

duplicate in the tallies. This probability of not being a

duplicate was included in all of the terms involving the ND

superscript.

Although the duplicate study identified E- and P-sample

cases linking to census enumerations outside the A.C.E.

search area, this study could not determine which component of the link was the correct one since there were no

additional data collected to determine this. On the

E-sample side, this study does not identify whether the

linked E-sample case is the correct enumeration. On the

P-Sample side, this study does not identify whether the

linked P-sample case is a resident on Census Day. Thus, it

was necessary to estimate two conditional probabilities,

which are reflected for the E sample in CEi

D. In the P

sample, these probabilities are reflected in the nonmover

terms P



nm,j D and M



nm,j D .

Adjustment for Measurement Error Using the

Revision E and P Samples

Next, an adjustment is made for other measurement

errors not accounted for by the duplicate study. This

adjustment was applied only to nonduplicate terms to

avoid over-correction due to any overlap between the

duplicate study and correction of measurement error.

In support of the A.C.E. Revision II program, the Revision

Samples have undergone extensive recoding using all

available interview data and matching results. Missing

data adjustments have also been applied to the Revision

Samples. This recoded data from the Revision Samples

were used to correct for measurement error in the original

Full E and P samples.

The ratio adjustments that correct for measurement error

were based on the E or P Revision Sample and were a ratio

of an estimate using the Revision coding to the estimate

using the original coding. These adjustments were done

by measurement error correction post-strata i ́ or j ́ and are

denoted by the f terms in the A.C.E. Revision II DSE formula.

The term g adjusts the number of inmovers for those Full

P-sample nonmovers who are determined to be nonresidents because of duplicate links. Some of these nonresidents are nonresidents because they are inmovers and

should be added into the count of inmovers. The term

Pnm,j D - Pnm,j D is an estimate of nonresidents among nonmovers with duplicate links.

Adjustment for Correlation Bias Using

Demographic Analysis

Next, the A.C.E. Revision II DSE estimates are adjusted to

correct for correlation bias. Correlation bias exists whenever the probability that an individual is included in the

2–4 Section II—Chapter 2 Summary of A.C.E. Revision II Methodology

U.S. Census Bureau, Census 2000
census is not independent of the probability that the individual is included in the A.C.E. This form of bias generally

has a downward effect on estimates, because people

missed in the census may be more likely to also be missed

in the A.C.E. Estimates of correlation bias are calculated

using the ‘‘two-group model’’ and sex ratios from Demographic Analysis (DA). The sex ratio is defined as the number of males divided by the number of females. This

model assumes no correlation bias for females or for

males under 18 years of age; and that Black males have a

correlation bias, which is different than the relative correlation bias for non-Black males. The correlation bias

adjustment is also done by three age categories: 18-29,

30-49, and 50 and over. This model further assumes that

relative correlation bias is constant over male post-strata

within age groups. The Race/Hispanic Origin Domain variable is used to categorize Black and non-Black.

The DA totals are adjusted to make them comparable with

A.C.E. Race/Hispanic Origin Domains. Black Hispanics are

subtracted from the DA total for Blacks and added to the

DA total for non-Blacks. This is done because the A.C.E.

assigns Black Hispanics to the Hispanic domain, not the

Black domain. The second adjustment deletes the group

quarters (GQ) people from the DA totals using Census

2000 data. The reason for making this adjustment is that

the GQ population is not part of the A.C.E. universe. A

final adjustment that could have been made would have

been to remove the remote Alaska population from the DA

totals, since it too is not part of the A.C.E. universe. Since

this population is small, the DA sex ratios would not be

affected in any meaningful way. See U.S. Census Bureau

(2003) for technical details.

SYNTHETIC ESTIMATION

The coverage correction factors for detailed post-strata ij

were calculated as:

CCFij  R

eDSEC

ij

Cenij

where:

R

eDSEij

C’s are the correlation bias adjusted DSEs for

post-strata ij.

Cenij’s are the census counts for post-strata ij,

including late census adds.

A coverage correction factor was assigned to each poststratum. The post-strata excluded persons in group quarters or in remote Alaska. Effectively, these persons have a

coverage correction factor of 1.0. In dealing with duplicate

links to group quarters persons, the person in the group

quarters was treated as if (s)he was a correct enumeration

or as if this was their correct residence on Census Day. A

synthetic estimate for any area or population subgroup b

is given by:

N

 b  

ijb

Cenb,ij CCF ij

Summary of A.C.E. Revision II Methodology Section II—Chapter 2 2–5

U.S. Census Bureau, Census 2000
Chapter 3.

Correcting Data for Measurement Error

INTRODUCTION

The original A.C.E. estimates were found to be unacceptable because they failed to detect significant numbers of

erroneous census enumerations. There were also suspicions that the A.C.E. may have included residents in its P

sample that were actually nonresidents. Thus, the major

goal for the A.C.E. Revision II estimates includes a correction of these measurement errors. One aspect of these

corrections involves correcting a subsample of the A.C.E.

data. Another aspect involves correcting measurement

errors that cannot be detected with the information

available in the subsample. These additional errors, which

are identified via a duplicate study, are discussed in

Chapter 5.

To understand the measurement error correction process,

it is important to be familiar with the various sources of

available information. These are summarized in the following table.

The A.C.E estimates produced in March 2001 were based

on the Full E and P samples, which are probability samples

of over 700,000 persons in 11,303 block clusters. The

Matching Error Study (MES) and the Evaluation Follow-up

(EFU) were two programs that had been planned to evaluate the March 2001 A.C.E. estimates. These evaluations

were conducted in a subsample of 2,259 block clusters

selected from the original 11,303 block clusters. A further

subsample of persons within these block clusters was

done for the EFU evaluation. The probes used for EFU were

designed to capture unusual living situations. The

PFU/EFU Review was not part of the planned evaluations.

It was conducted in order to resolve major discrepancies

in enumeration status between the EFU and PFU results.

Thus, the Review E sample is a subsample of the EFU E

sample. The Revision E and P samples are referred to as

such for purposes of producing A.C.E. Revision II estimates. These samples are essentially the same as the

Evaluation E and P samples for EFU, but the data have

undergone a major recoding to correct for measurement

Table 3-1. Overview of A.C.E. Revision II Data Sources

Program Sample Sample size What & when

Decennial census Spring 2000

A.C.E. Full E and P samples E & P: About 700,000 persons in

11,303 block clusters

A.C.E. Person Interviewing

(PI), Summer 2000

A.C.E. Person Follow-up (PFU), Fall 2000

Matching Error Study

(MES)

Evaluation E and P samples E & P: About 170,000 persons in

2,259 block clusters

Rematching Operation, December 2000

Evaluation Follow-up

(EFU)

EFU E and P samples1 E: About 77,000 persons in

2,259 block clusters

Evaluation Person Follow-up (EFU),

January - February, 2001

P: About 61,000 persons in

2,259 block clusters

PFU/EFU Review Review E sample E: About 17,500 persons in

2,259 block clusters

Recoding Operation, Summer 2001

A.C.E. Revision II Revision E and P samples E: About 77,000 persons in

2,259 block clusters

Recoding Operation, Summer 2002

P: About 61,000 persons in 2,259 block

clusters

1

The number of sample cases included in the Evaluation Follow-up is less than those selected to be in this sample. Cases were

excluded from follow-up for certain situations such as insufficient information or a duplicate enumeration.

Correcting Data for Measurement Error Section II—Chapter 3 3–1

U.S. Census Bureau, Census 2000
error. This chapter discusses the measurement error corrections made to the E- and P- Revision samples. These

corrected data, along with other measurement error corrections identified by the duplicate study, were used to

adjust the Full E and P samples to produce A.C.E.

Revision II estimates.

GOALS AND BACKGROUND

The goal for A.C.E. Revision II was to correct as much measurement error as possible in the original A.C.E. estimates,

given resource and timing constraints.2 The primary

sources of measurement error were determining residence

and enumeration status, match status, and mover status.

Residence and Enumeration Status. The original

A.C.E. did not detect all of the erroneous enumerations.

See Adams and Krejsa (2001) and Fay (2002) for documentation. The Evaluation Follow-up (EFU) detected approximately 1.4 million additional erroneous enumerations in

the E sample. Since the coding of enumeration status in

the E sample was identical to the coding of residence status in the P sample, similar results for P-sample residence

status coding were expected (i.e., additional nonresidents

were expected to be found as a result of the EFU). To correct for the residence status errors, the A.C.E. Revision II

utilized a recoding of the Evaluation Follow-up Interview in

combination with the original A.C.E. to determine the best

residence or enumeration status for each person in the

Revision sample.

Matching Error. The Matching Error Study showed a net

difference in match codes between the original March

2001 matching results and the evaluation matching

results of 0.41 percent in the E sample and 0.20 percent in

the P sample. Bean (2001) suggested this net difference

translated into an increase in the dual system estimate of

483,938 people. To correct for matching error, results of

the Matching Error Study and the A.C.E. Revision II recoding were used in conjunction to determine the appropriate

match status for each person.

Mover Status. Raglin and Krejsa (2001) estimated a 2.6

percent gross difference rate in the mover status between

the original A.C.E. and the Evaluation Follow-up. This

translated into a negative bias of 465,000 in the DSE

(assuming no other biases). Results of the Evaluation

Follow-up were used to correct for mover status errors.

The EFU questionnaire contained questions designed to

probe for a person’s mover status. This information was

captured during the clerical recoding and during the initial

coding of the Evaluation Follow-up form. These types of

measurement errors were corrected either by computer or

clerically.

Two other sources of error were not part of the measurement error recoding portion of the A.C.E. Revision II.

These errors included geocoding errors and duplicates

outside the search area. Certain geocoding errors detected

by various geocoding evaluations were not included in the

A.C.E. Revision II.3 Within the P sample, 245,926 production nonmatched residents were found outside the search

area4 and 195,321 production correct enumerations in the

E sample were found outside the search area. See Adams

and Liu (2001). Some of the correct enumerations outside

the search area were identified by the EFU interview and,

hence, were reflected in the revised coding.5 Duplicates

found outside the search area as a result of computer

matching (see Chapter 5) were not handled by clerical coding. They were accounted for in the dual system estimator

using estimation techniques. See Chapter 6 for a full

description of the estimation techniques.

RESIDENCE STATUS AND ENUMERATION STATUS

As already noted, the original March 2001 A.C.E. underestimated the number of erroneous enumerations. To correct

for this, the best residence status code was based on

available field follow-up data. Duplicates were corrected

using a separate process. The following data were available for measurement error correction:

• Person Interview (PI). The PI was the original A.C.E.

enumeration of the P sample. It was a ComputerAssisted Personal Interview questionnaire designed to

fully enumerate persons in the A.C.E. It was conducted

by either phone or personal visit between April and

September, 2000.

• Person Follow-up (PFU). The PFU was the follow up

used to assign residence and enumeration status, whenever those items were not determined, after the before

follow-up matching (Childers, 2001). It was conducted

by personal visit in October and November, 2000,

approximately 6-7 months after Census Day.

• Evaluation Follow-up (EFU). The EFU was an evaluation of the A.C.E. designed to detect unusual living situations using additional probes and additional interviewing techniques (e.g., flashcards). It was conducted by

personal visit in January and February, 2001, approximately 9-10 months after Census Day.

2

In order to complete the A.C.E. Revision II estimates on time,

12 weeks were allotted for coding. Analysts at the National Processing Center were expected to code approximately 25,000

cases in this time frame.

3

As part of the A.C.E., several evaluations of geocoding error

were conducted on various subsamples of the A.C.E., most notably Targeted Extended Search 2 (TES2) and Targeted Extended

Search 3 (TES3). Results of these evaluations can be found in

Adams and Liu (2001). 4

For the 2000 A.C.E., the search area, or area in which a person can be considered a correct enumeration or match, was the

cluster and any census block touching the cluster. 5

Some of the cases in TES2 were evaluated using the Evaluation Follow-up questionnaire. For these cases, results of the geocoding evaluation were included in the Evaluation Follow-up; however, if a case was in TES2, but not in the Evaluation Follow-up, no

geocoding evaluation results were included.

3–2 Section II—Chapter 3 Correcting Data for Measurement Error

U.S. Census Bureau, Census 2000
Results of the Person Interview were used to assign A.C.E.

residence status by computer to all people in A.C.E. who

did not need follow-up. In contrast, the PFU was used to

assign residence status for anyone who was eligible for

follow-up (Childers, 2001). The PFU is similar to the PI.

The PFU process interviewed both P-sample and E-sample

people. The EFU followed up a sample of people sent to

PFU and a sample of those not sent to PFU. This allowed

the residence/enumeration status of a representative

sample of people eligible for field follow up to be

evaluated.

There were measurement errors in both the A.C.E. PFU and

EFU resulting from limitations of their respective interviews. These errors are documented in Bean (2001) and

Adams and Krejsa (2001), respectively. Also, the EFU was

not strictly coded according to census residence rules. To

evaluate the E sample for ESCAP II, the Census Bureau conducted the PFU/EFU Review in the summer of 2001. Expert

matchers reviewed a subsample of the EFU E sample and

applied consistent census residency rules. These analysts

were assumed to make negligible errors; therefore, the

PFU/EFU Review was considered to be free of coding error,

given available data.

For A.C.E. Revision II, this high-quality coding was needed

for subsamples of the A.C.E. P and E samples that were

large enough to provide accurate subgroup estimates of

net coverage. Twelve weeks coding time were allotted to

clerically code approximately 25,000 cases. However,

there were over 100,000 cases needing codes. To assign

the highest quality codes, while meeting a demanding

schedule, keyed data from both the PFU and EFU forms

were used to augment clerical coding procedures. An

automated coding algorithm, based on specific responses

to the PFU and EFU questionnaires, was used to determine

an appropriate code for each case. This was done for both

the PFU interview and the EFU interview. The automated

coding also assigned a ‘Why’ code that describes the reason why the particular code was assigned. There were

more than 60 possible ‘Why’ code categories. A final code

was assigned to each case using the following three-step

process:

• Validation. Determine for each category of ‘Why’ code

if the automated coding is of high quality using the

PFU/EFU Review as a truth deck.

• Targeting. Target only those ‘Why’ code categories that

have low levels of agreement between the automated

coding and the PFU/EFU Review data.

• Clerical Review. Clerically recode only those cases in

the targeted ‘Why’ code categories. The clerical recoding

takes advantage of handwritten interviewer comments.

Validation of Keyed Data

To validate the quality of coding produced by the keyed

data algorithm, skip patterns for both questionnaires were

programmed to determine an appropriate match code and

‘Why’ code for each case. Then, for both the PFU and EFU

forms, the percentage agreement with the original coding

(either production coding or the coding of the EFU form)

for the respective form, the percentage agreement with

the PFU/EFU Review, and the residual risk were examined.

That is, the following calculations were performed twice -

once for PFU and once for EFU.

The residual risk of disagreement (i.e. potential bias) represented the number of cases at risk for being coded

wrong due to accepting the automated code for categories

defined by questionnaire responses. Cases subject to risk

were those where the automated code and original code

agreed. If they disagreed, the automated code was

rejected and the case was sent for clerical review. The risk

for the cases agreeing is calculated as follows:

risk = AgreeK − AgreeRev

where

AgreeK = The weighted number of cases whose code

from the keyed data agreed with the original production code.

AgreeRev = Of those cases where the code from the

keyed data agreed with the original production code,

the weighted number of cases whose code from the

keyed data agreed with the PFU/EFU Review code.

The term risk, rather than an error, is used because some

potential coding changes may not have had an effect on

the DSE. For example, people who were in group quarters

have a residual risk of 26,517 after computer coding.

These represent cases that probably should have been

coded as erroneous enumerations, but were not. However,

some of the 26,517 cases could be unresolved, which

have a probability less than one of being correct.

The automated coding results for a given ‘Why’ code category were rejected if the residual risk was too high or if

there were not enough cases to make an informed decision. The exception to this rule was the category consisting of cases without any indication of living in a group

quarters or other residence. This group was, by far, the

largest category for both the PFU and EFU, so a higher

residual risk6 was expected.

Targeting Cases for Clerical Review

After the decision was made to accept or reject the automated code for each ‘Why’ code category, cases were targeted for clerical review. Analysts, who were the highest

level of clerical matchers, performed the clerical review.

Due to their experience and additional training, they were

assumed to make negligible errors in coding.

6

Absolute risk, rather than relative risk, is used. Therefore,

larger categories tended to have higher risks.

Correcting Data for Measurement Error Section II—Chapter 3 3–3

U.S. Census Bureau, Census 2000
In general, cases did not go to clerical review if both the

PFU and EFU automated codes agree, the mover statuses

agree, and the ‘Why’ code category was deemed to be of

high enough quality. In some instances, cases are exempt

from clerical review because they could be coded based

on information available in data files. For many of these

situations, consistent and complete data were obtained

from both the PFU and EFU interviews. These cases

included:

• Census Usual Home Elsewhere. If the person

claimed a Usual Home Elsewhere on certain types of

census forms, they were counted as a correct7 enumeration within the cluster and did not need clerical review.

• Geocoding Errors from Initial Housing Unit

Matching. If a case should not have been sent to PFU

or EFU and was only sent due to clerical error in the initial production matching, then it did not need clerical

review.

In contrast, some cases are automatically sent to clerical

review. For example, this includes cases in the PFU/EFU

Review that resulted in a conflicting status, noninterview

cases, or cases where mover dates could not be determined from the EFU keyed data. Some of the cases that

went to clerical review did so because the original A.C.E or

PFU results did not agree with the EFU results. Most of the

cases went to clerical review because the automated coding process was not reliable for that ‘Why’ code category.

For P-sample inmovers, there was no validation data.

Cases where the original EFU mover status did not match

the mover status from the keyed data, or the residence

status from the keyed data did not match the original EFU

residence status, were sent to clerical review. Noninterview cases or cases where mover dates could not be

determined from the keyed data were also sent to clerical

review.

Cases with the following attributes were sent to clerical

review:

• the code from the keyed data for either form was not

accepted for that case.

• the code from the keyed data was accepted for both

forms, but at least one of the codes from the keyed data

did not agree with its original code (i.e., the PFU code

from the keyed data did not agree with production or

the EFU code from the keyed data did not agree with the

original EFU code).

• for P-sample people, the mover status from the keyed

data did not agree with mover status assigned during

the EFU coding.

• there was write-in information in open-ended questions

on the form that could not be coded.

• the case was a possible match in before follow-up

matching and the production and original EFU code disagreed.

• the case was a duplicate in either the original EFU coding or production after follow-up coding.

• the case was not yet flagged for clerical review and the

PFU code from the keyed data did not agree with EFU

code from the keyed data, and one of the cases was not

unresolved for certain reasons.

• the case was in the PFU/EFU Review and was conflicting

or had a mover status disagreement between the keyed

data and the original EFU mover status.

Clerical Review

The clerical review for A.C.E. Revision II was an analystonly operation. The following data were collected:

• Match Code for each form

• ‘Why’ Code for each form

• Respondent for each form

• Whether the respondents are the same for the two interviews

• Best Code. A code indicating which form is the better of

the two forms

• Smooshed Code. Information from both forms combined to make a code to represent the true situation

• Mover Status. Mover Status from the EFU form for

P-sample people

The match codes were assigned using the census residence rules to construct coding rules for the flow of the

questionnaire.

The best code could be one of four values:

• Both = The enumeration statuses were the same

• PFU = The PFU form provided better information

• EFU = The EFU form provided better information

• Conflicting = Similar caliber respondents (e.g., husband

and wife; two neighbors) provided contradictory information for the case

To ensure reproducibility, computer edits were applied to

the best code. If the analyst did not follow pre-specified

rules, then the analyst had to review the case again or

leave a note indicating the situation.

7

A person can claim a usual home elsewhere if he or she is

enumerated on certain types of census forms in group quarters

(e.g. military, shipboard, and certain types of special places like

shelters). If a person on one of these forms claims a usual home

elsewhere, then that person is counted at the address they indicate is their usual home. These people are part of the E sample

because they are part of the housing unit universe.

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U.S. Census Bureau, Census 2000
CORRECTION OF MOVER STATUS ASSIGNMENT

ERRORS

For each P-sample case, mover status was based on the

EFU. This was used to determine whether or not the person needed clerical review.

CORRECTION OF MATCHING ERRORS

After the A.C.E. Revision II recoding operation corrects for

enumeration, residence, and mover status, the results of

the Matching Error Study (MES) were used to correct for

false matches and false nonmatches. Some matching

errors were a result of incorrect residence status coding

and have been corrected as part of the recoding operation

discussed above. To determine the correct match status,

each of the possible combinations of match status was

reviewed to determine the appropriate match status for

each type of case. In general, the MES match status was

assigned when there were changes from a match to a nonmatch or changes from a nonmatch to a match. For other

situations, the match status from the EFU coding was

assigned.

DATA OUTPUTS

After the clerical operation was completed, two files were

assembled - one for the P sample and another for the E

sample. The files contain match codes and ‘Why’ codes

(where appropriate) for original March 2001 A.C.E., EFU,

PFU/EFU Review, Keyed Data, and A.C.E. Revision II Clerical Review. A final code is also assigned in the following

hierarchy: A.C.E. Revision II Clerical Review, PFU/EFU

Review, Keyed Data. This code reflects the final match,

residence, and enumeration status for the A.C.E. Revision

II process.

LIMITATIONS

There were several limitations on the data for the A.C.E.

Revision II:

• Sample Size. The sample used to estimate measurement error is 2,259 clusters, containing about 10 percent of the persons in the sample used in the production A.C.E. Due to the smaller sample size, some

subgroup estimates are subject to higher variances

compared to those for the original March 2001 A.C.E.

• Conflicting Cases. Conflicting cases occurred when

the PFU and EFU interviews had respondents of the

same caliber (either both nonproxy or proxy respondents who were in the position to have similar knowledge about the household, e.g. two neighbors) who

gave contradictory information. Since an additional field

follow-up was not possible, these cases were coded as

conflicting, were reviewed separately, and imputed.

• Data Collection Error. Cases were coded as best as

possible. However, there was no attempt to correct for

any residual data collection error. Any remaining respondent and interviewer errors could not be rectified without an additional field follow-up.

Correcting Data for Measurement Error Section II—Chapter 3 3–5

U.S. Census Bureau, Census 2000
Chapter 4.

A.C.E. Revision II Missing Data Methods

BACKGROUND

Missing data arises because it is not possible to obtain

interviews for all sample cases or to obtain answers to all

interview questions. This was as true for the A.C.E. Revision II, as it was for the A.C.E. To put the A.C.E. Revision II

missing data methods in perspective, a brief summary of

the A.C.E. missing data adjustments is presented. For the

A.C.E. P sample, a household noninterview adjustment

compensated for noninterviewed households. Imputation

methods were implemented to handle missing characteristics such as age or tenure. Further, match and residency

probabilities were assigned when the respective match

and residency statuses could not be definitively determined. There was no noninterview adjustment for the

A.C.E. E sample, nor was there an imputation for missing

characteristics as the census imputations were used. However, E-sample cases with unresolved enumeration status

were assigned probabilities of correct enumeration. See

Ikeda and McGrath (2001) for details on the A.C.E. missing

data methodology.

As will be discussed in Chapter 6, the A.C.E. Revision II

estimation utilizes both the original A.C.E. coding results

on the Full E and P samples and the Revision coding

results on the smaller Revision Samples. Note that the

A.C.E. Revision II subsample of the A.C.E. is referred to as

the Revision Sample and the new coding operation is

called the Revision coding. The missing data adjustments

for the A.C.E. E and P samples were unchanged from those

used to produce A.C.E. estimates, with the exception of

the imputation for missing age. It was necessary to impute

age again for the Full A.C.E. P sample because the A.C.E.

Revision II post-strata had different age groupings.

The Revision P sample used the same imputations for

missing characteristics that the A.C.E. did, including the

new age imputation. However, since A.C.E. Revision II

measurement methodology had important differences

from the A.C.E. measurement methods, it was necessary

to develop new missing data methods. The A.C.E. Revision

II missing data confronted three general types of new

missing data problems:

1. New noninterviewed households: Revision P-sample

households that were considered interviews in the

A.C.E. were identified as noninterviews in the Revision

coding when it was determined that none of the

P-sample people there were valid Census Day residents.

2. Revision E- and P-sample cases with unresolved

match, enumeration, or residency status, because of

incomplete or ambiguous interview data from the Person Follow-up (PFU) or the Evaluation Follow-up (EFU).

3. Revision E- or P-sample cases with conflicting enumeration or residency status because contradictory

information was collected in the PFU and the EFU interviews and it could not be determined which was valid.

AGE IMPUTATION

For the original A.C.E., P-sample people with missing age

were assigned to age categories defined by the poststratification plan. The A.C.E. Revision P-sample poststratification divided the original A.C.E. post-stratification

group of 0-17 year olds into two age groups: 0-9 and

10-17. Those people with missing age who had been

assigned to the 0-17 group were reassigned to either the

0-9 or the 10-17 group. This reassignment assumed that

the age distribution of people missing age was uniform

within the 0-17 age grouping. Other people with unresolved age remained in the age group they had been originally assigned to.

HOUSEHOLD NONINTERVIEW ADJUSTMENT

The A.C.E. household noninterview adjustment generally

spread the weights of P-sample noninterviewed housing

units over interviewed housing units in the same block

cluster with the same housing unit structure type. Housing

units were determined to be noninterviews in two ways:

1) an interview was not conducted during the A.C.E. person interview operation, and 2) based on the results of the

A.C.E. PFU, it was determined that a whole household of

P-Sample people should not have been listed in the first

place, and that another household may have been residents at that housing unit. Separate household noninterview adjustments were implemented for Census Day and

A.C.E. Interview Day.

The A.C.E. Revision II noninterview adjustment methodology for A.C.E. Interview Day was essentially unchanged

from the A.C.E. There was, however, an important change

from the A.C.E. methodology for the noninterview adjustment for Census Day residency. In A.C.E. Revision II, a new

imputation cell was defined. It included new noninterviews due to whole households of A.C.E. nonmovers who

were determined to be inmovers or nonresident outmovers by the Revision coding. The new noninterview cell

A.C.E. Revision II Missing Data Methods Section II—Chapter 4 4–1

U.S. Census Bureau, Census 2000
spread the weights of these noninterviewed units over

housing units with at least one person who: 1) indicated

he/she lived at another address, or 2) was identified as

potentially fictitious in the A.C.E. These new noninterviews were assumed to have both a low match rate and a

low residency rate similar to this group. Otherwise, the

noninterview adjustment for Census Day used methodology similar to that of the A.C.E.

ASSIGNMENT OF PROBABILITIES OF CORRECT

ENUMERATION, CENSUS DAY RESIDENCY, AND

MATCH STATUS

In the A.C.E., P-sample people with unresolved Census Day

residency or match status occurred in one of two ways.

Firstly, the A.C.E. person interview may not have provided

sufficient information for match and follow-up. Secondly,

the A.C.E. PFU may not have collected adequate information for determining a person’s Census Day residency status or their match status. Inadequate data collection can

also result in unresolved enumeration statuses for A.C.E.

E-sample people. In the A.C.E. Revision II, the EFU was also

the source of unresolved cases. How a case was imputed

depended on how it became unresolved.

Imputation for People with Insufficient

Information for Match and Follow-Up

The Revision P-sample people with insufficient information

for match and follow-up tended to be the same people

who had insufficient information for match and follow-up

in the A.C.E., except for some rare cases with coding

changes. Note that people who had insufficient information in the A.C.E. were not sent to EFU. There were about

three million weighted people with insufficient information for match and follow-up in both the Full and Revision

P samples.

In the A.C.E., P-sample people with insufficient information for match and follow-up were assigned a probability

of Census Day residency equal to the residency rate of

P-sample people who went to PFU. This methodology was

improved in the A.C.E. Revision II by defining finer imputation cells that accounted for whether or not the housing

unit was matched, nonmatched, or had a conflicting

household. A conflicting household existed when the Pand E-sample households had no people in common.

The probability of match was assigned based on the overall match rate, divided into groups based on mover status

and housing unit match status, as was done in the A.C.E.,

and additionally on conflicting household status.

Imputation for People with Incomplete or

Ambiguous Follow-Up

In contrast to P-sample people with insufficient information, the residency status for Revision P-sample people

and the correct enumeration status for Revision E-sample

people often changed from what it was in the A.C.E. These

statuses changed because the Revision coding processed

new information from the EFU, in addition to the original

information from the PFU. Thus, while the EFU information

resolved many cases that were unresolved in the A.C.E.

because of the PFU, EFU cases with incomplete or ambiguous information were a new source of unresolved cases.

There were about the same number of weighted E-sample

unresolved cases in the Revision sample as in the A.C.E.,

more than six million, with about half of these representing new unresolved cases. In contrast, the Revision coding

generated substantially more P-sample unresolved cases

than the A.C.E., 4.6 million compared to 2.7 million. This

increase was due to the fact that all Revision P-Sample

cases (except those with insufficient information) went to

EFU, including whole households of nonmatched people

who had not gone to PFU. These people were assumed to

be resolved in the A.C.E. and could have become unresolved because of the EFU.

The original A.C.E. missing data plan based the imputation

cells on information obtained before any follow-up was

conducted. An ad hoc fix to the A.C.E. missing data methodology was implemented using information from the

PFU. See Cantwell and Childers (2001) for details. Based

on the PFU keyed data, after follow-up groups for ‘potential fictitious’ and ‘lived elsewhere on Census Day’ were

created. The new cells used information highly relevant to

resident or enumeration status. Further, they showed

greater discrimination in assigning probabilities of correct

enumeration and residency. In A.C.E. Revision II, the

before follow-up imputation cells were abandoned and the

cells were defined based on after follow-up information.

This change was the single most important improvement

in the A.C.E. Revision II missing data methodology.

The after follow-up group definitions were based on keyed

responses to the PFU and EFU questionnaire checkboxes

and the ‘Why’ codes. ‘Why’ codes were clerically-applied

codes that reflected responses in the questionnaire checkboxes, as well as handwritten notes. See Adams and

Krejsa (2002) for a detailed description. The keyed results

and ‘Why’ codes helped identify the following:

• unresolved cases with the same history, i.e., the recipient cells.

• resolved follow-up cases with the same history up to

the point of being unresolved, i.e., the donor pool.

PFU after follow-up groups were defined for those cases

that were unresolved as a result of the PFU.

Similarly, EFU after follow-up groups were defined for

those cases unresolved because of the EFU. It was necessary to define separate groups for the PFU and EFU,

because their interviews and questionnaires were different. However, the same after follow-up groups were

4–2 Section II—Chapter 4 A.C.E. Revision II Missing Data Methods

U.S. Census Bureau, Census 2000
employed for the P- and E-sample unresolved cases, as the

PFU and EFU questions about Census Day residency were

the same as the PFU and EFU questions about enumeration

status.

It is useful to distinguish between uninformative and informative unresolved cases:

• uninformative unresolved: the follow-up was a noninterview or an incomplete interview, though there was no

evidence of an erroneous enumeration or nonresident.

• informative unresolved: a follow-up interview was conducted, and there was evidence of an erroneous enumeration or nonresident.

Note that when one interview was uninformative unresolved, but the other interview was resolved, the Revision

coding selected (i.e., the code was based on) the resolved

interview. On the other hand, when the unresolved interview was informative, the Revision coding could choose

the unresolved interview over the resolved one. See

Adams and Krejsa (2002) for details of the Revision coding.

It often happened that both the PFU and EFU interviews

were unresolved. To assign this case to an imputation cell,

the unresolved interview that was more informative was

selected. When both interviews had the same level of

information, the EFU was typically selected over the PFU,

because questions on the EFU questionnaire were more

sharply defined.

Consider the following example of an after follow-up

group. One cell of unresolved E-sample people or recipients was defined as people with evidence from the EFU

interview that they had moved in since Census Day, or

moved out before Census Day, though the EFU interview

did not provide the address they moved to or from. It was

impossible to determine the enumeration status of these

people, since it was unclear if their Census Day address

was in the A.C.E. cluster. The corresponding donor pool

consisted of those resolved people who indicated in the

EFU that they had moved in after Census Day or moved

out before Census Day. Generally, these people provided

their mover address in the EFU. An analogous after followup group was formed for people unresolved because they

indicated they were movers in the PFU interview. These

groups are characterized as informative, because the

follow-up provided evidence of an erroneous enumeration.

Table 4-1 shows the nine EFU after follow-up groups, while

Table 4-2 shows the nine PFU after follow-up groups.

People who moved in after Census Day or moved out

before Census Day were the largest informative after

follow-up group. Another important informative after

follow-up group consisted of people who, according to the

follow-up, had another residence such as a vacation home,

though the follow-up did not indicate whether the other

residence or the sample address was the Census Day residence. The noninterview groups and ‘didn’t answer other

residence questions’ group were the larger uninformative

groups.

Table 4-1. EFU After Follow-up Groups

Informative groups

The followed up person ‘Lived elsewhere’ or at an ‘other residence,’ but

the address was not given.

Followed up person moved in after Census Day or out before Census

Day, but Census Day address not given.

Respondent indicated the followed-up person ‘Never lived here’ at the

sample address, but did not provide the Census Day address.

The followed-up person had an ‘other residence,’ but did not indicate

whether the sample address or other residence was the Census Day

residence.

Followed up person moved in or moved out, but no move dates given.

Uninformative groups

The respondent indicated the followed up person ‘Lived here’ at the

sample residence, but did not answer the ‘other residence’ question.

The respondent answered the current residence question, but did not

answer the group quarters and ‘other residence’ questions.

The respondent did not answer the usual residence question, nor the

group quarters and ‘other residence’ questions.

Potentially fictitious person, no respondents knew of the followed up

person.

Some of the larger EFU groups were subdivided by A.C.E.

operational variables, such as whether or not the household went to PFU, or whether the household was conflicting. The uninformative after follow-up groups tended to

have imputed probabilities of correct enumeration or residence close to one, typically in the range of 0.92 to 0.99.

In contrast, the informative after follow-up groups had

smaller probabilities, often less than 0.25. The probability

of correct enumeration is calculated as the weighted proportion of correct enumerations in the donor pool. For

example,

Probability of correct enumeration  Weighted CE’s in Donor Pool

Weighted Resolved Enumerations in Donor Pool .

For the P sample, probabilities of residency and match status were calculated analogously.

A.C.E. Revision II Missing Data Methods Section II—Chapter 4 4–3

U.S. Census Bureau, Census 2000
Table 4-2. PFU After Follow-up Groups

Informative groups

The followed up person ‘Lived elsewhere’ or at an ‘other residence,’ but

the address was not given.

Followed up person moved in after Census Day or out before Census

Day, but Census Day address was not given.

The respondent indicated the followed up person ‘did not live here’ at

the sample address, but did not indicate the other address and did not

answer the group quarters and ‘other residence’ questions.

The followed up person had an ‘other residence,’ but did not indicate

where the usual residence was.

Uninformative groups

The respondent indicated the followed up person ‘Lived here’ at the

sample residence, but did not answer the ‘other residence’ question.

The respondent answered the usual residence question, but did not

answer the group quarters and ‘other residence’ questions.

The ‘lived here’ question is Don’t Know/refused, and the group quarters

and ‘other residence’ questions were not answered.

Blank questionnaire.

Potentially fictitious person, no respondents knew of the followed up

person.

Imputation for Conflicting Coding Cases

When the A.C.E. EFU and PFU interviews had contradictory

information, the Revision coding procedure assigned the

case a conflicting code. Note that a conflicting code is different than a conflicting household. All conflicting cases in

the Revision coding process were sent to analysts for clerical review. By examining the handwritten notes of interviewers, analysts could often determine which of the two

interviews was better and assign the appropriate code.

There were some cases where the interviews appeared to

be of equal quality, such as when both respondents were

household members or both respondents were proxies of

equal caliber. For these conflicting cases, the interviews

seemed equally likely to be correct based on the analyst’s

expertise. Therefore, the probability of correct enumeration for Revision E-sample conflicting cases and the probability of Census Day residency status for Revision

P-sample conflicting cases were assigned to be 0.5. It

should be noted that the Revision coding resulted in considerably fewer conflicting cases than the PFU/EFU Review

Sample. According to Adams and Krejsa (2001), the

PFU/EFU Review Sample had about 2.6 million weighted

conflicting people in contrast to only about 100,000

weighted conflicting people in the Revision Samples.

4–4 Section II—Chapter 4 A.C.E. Revision II Missing Data Methods

U.S. Census Bureau, Census 2000
Chapter 5.

Further Study of Person Duplication in Census 2000

INTRODUCTION

Evaluations of the March 2001 coverage estimates indicated the A.C.E. failed to detect a large number of erroneous census enumerations. One type of these census erroneous enumerations was duplicate census enumerations;

that is, census enumerations included in the census two or

more times. The A.C.E. was not specifically designed to

detect duplicate census enumerations beyond the search

area. However, there was an expectation that the A.C.E.

would detect that these E-sample enumerations had

another residence, and that, roughly half the time

this other residence was the usual residence.

Feldpausch (2001) showed this expectation was not met.

For purposes of constructing A.C.E. Revision II estimates,

matching and modeling techniques were used to identify

duplicate links between the Full E and P samples to census

enumerations. The matching algorithm used statistical

matching to identify linked records. Statistical matching

allowed for the matching variables not to be exact on both

records being compared. Because linked records may not

refer to the same individual, even when the characteristics

used to match the records are identical, modeling techniques were used to assign a measure of confidence, the

duplicate probability, that the two records refer to the

same individual. These duplicate probabilities were used

in the A.C.E. Revision II estimates.

This chapter documents the matching and modeling methods that were used to identify duplicate links and to produce duplicate probabilities. Note that this study was not

intended to identify which enumeration was in the correct

location. Chapter 6 describes how to compute the conditional probability that the sample case was in the correct

location given that it had a link to a census enumeration

outside the A.C.E. search area. This calculation impacts

the correct enumeration status in the E sample and the

residence status in the P sample. A full discussion of the

estimation components is given in Chapter 6.

BACKGROUND

Mule (2001) reported results for initial attempts at measuring the extent of person duplication in Census 2000. This

work was conducted by an inter-divisional group as part

of the further research to inform the ESCAP II decision on

adjusting census data products. This study is referred to

as the ESCAP II duplicate study in this chapter. The ESCAP

II duplicate study used conservative computer matching

rules to minimize the number of false matches that could

be introduced when doing a nationwide search, since

there was no clerical review of the results. As a consequence of the matching rules, comparisons to benchmarks

indicated that the ESCAP II duplicate estimates were a

lower bound. Specifically, comparing the ESCAP II results

within the A.C.E. sample area to the A.C.E. clerical matching results showed that only 37.8 percent of the census

duplicates were identified. Fay (2001, 2002) estimated the

matching efficiency at 75.7 percent when accounting for

the census records out-of-scope for the A.C.E. duplicate

search. The out-of-scope records were those that were

reinstated and deleted from the Housing Unit Duplication

Operation, documented in Nash (2000).

The ESCAP II matching was a two-step process. First, the

sample of census records were matched to the full census

on first name, last name, month of birth, day of birth and

computed age. Age was allowed to vary by one year.

Middle initials and suffixes being scanned into the first

name field were accounted for; however, the other characteristics had to be exact matches at this stage. This firststage match established a link between households. In the

second stage, all person records in the linked households

from the first stage were statistically matched using first

name, middle initial, last name, month of birth, day of

birth, and computed age. The matching parameters used

in the statistical matching were borrowed from other Census 2000 matching operations. Mule (2001) describes this

matching algorithm in more detail.

To reduce the impact of false matches, particularly with

respect to persons with common names and the same

month and day of birth, model weights were applied to

each set of linked records as a measure of confidence that

the linked records were indeed duplicates. Due to schedule constraints, a national, Poisson model was used in lieu

of a probability model.

The ESCAP II census duplicate methodology satisfied the

intended project goals and provided a valuable evaluation

of the census by showing that person duplication existed.

However, limitations of the methodology made it difficult

to estimate the magnitude of person duplication in the

census.

OVERVIEW OF THE DUPLICATE STUDY PLAN

Like the ESCAP II study, the A.C.E. Revision II duplicate

plan involved matching the Full E and P samples to the

census to establish potential duplicate links. Then, modeling techniques were used to identify the links most likely

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U.S. Census Bureau, Census 2000
to be duplicate enumerations and to assign a measure of

confidence that the links are duplicates. Key differences

with the ESCAP II study include extending the use of statistical matching and developing models to assign a duplicate probability to the links. An advantage of duplicate

probabilities over the Poisson model weights used in the

ESCAP II study is that all duplicate links outside the A.C.E.

search area could be reflected in the A.C.E. Revision II estimates. Fay (2001, 2002) used a subset of the ESCAP II

duplicate links to produce a lower bound on the level of

erroneous enumerations that the A.C.E. did not measure.

Estimates of census duplication were based on matching

and modeling E-sample cases to the census. For purposes

of A.C.E. Revision II estimation, the P sample was also

matched to the census. However, these results did not

contribute to estimates of person duplication in the census. The A.C.E. Revision II estimation methodology

adjusted the A.C.E. correct enumeration rate for E-sample

cases with links outside the A.C.E. search area. Further,

the A.C.E. Revision II estimation methodology adjusted the

A.C.E. match rate for P-sample cases that linked to census

cases outside the search area.

The matching algorithm consisted of two stages. The first

stage was a national match of persons using statistical

matching as described in Winkler (1995). Statistical matching attempted to link records based on similar characteristics or close agreement of characteristics. Exact matching

required exact agreement of characteristics. Statistical

matching allowed two records to link in the presence of

missing data and typographical or scanning errors.

Six characteristics common to both files, called matching

variables, were used to link records in the Full E and P

sample with records in the census. Matching parameters

associated with each matching variable were used to measure the degree to which the matching variables agreed

between the two records, ranging from ‘‘full agreement’’ to

‘‘full disagreement.’’ The measurement of the degree to

which each matching variable agreed was called the variable match score. The overall match score for the linked

records was the sum of the variable match scores.

Full agreement of at least four characteristics was required

to be considered a duplicate link. Because this study was a

computer process without the benefit of a clerical review,

this limitation of the statistical matching was necessary in

order to minimize linking records with similar characteristics that represented different people. This was a particular concern when looking for duplicate enumerations

across the entire country. The need to use statistical

matching at the first stage was apparent after the limited

success of the ESCAP II exact matching procedure to identify A.C.E. duplicates in the A.C.E. sample areas. The statistical matching yielded better identification of the A.C.E.

duplicates, but to identify all of the A.C.E. duplicates

would have required fewer characteristics to be exact

matches. This could potentially lead to a high number of

false links.

The search for duplicate links between the Full E and P

samples and the census was limited to those pairs that

agreed on certain identifiers, or blocking criteria. Blocking

criteria were sort keys that were used to increase the computer processing efficiency by searching for links where

they were most likely to be found. For instance, to search

only for duplicates when the first and last names agreed,

both the sample and census files would have been sorted

by the blocking criteria of first and last name. Then, all

possible pairs within each first name/last name combination would have been searched for duplicate links.

Although true matches can be missed by using blocking

criteria, multiple sets of blocking criteria minimize the

number of missed matches. The A.C.E. Revision II duplicate study utilized four sets of blocking criteria.

At the first stage of matching, it was possible for one

sample case to link to multiple census records. All of these

links were retained for the second stage of matching.

The second stage of matching was limited to matching

persons within households. If an E- or P-sample case

linked to a census record in a group quarter, the case did

not go to the second stage. Using results from the first

stage of matching, a link between two housing units was

established. The second stage was a statistical match of

all household members in the sample housing unit to all

household members in the census housing unit. The

second-stage matching variables were the same as the

first stage; however, the matching parameters differed.

Using a subset of the first-stage links, the second-stage

matching parameters were derived using the ExpectationMaximization (EM) algorithm. See Winkler (1995) for a

more detailed explanation. A key difference between the

first- and second- stage parameters was the reduced

emphasis on requiring last names to agree in the second

stage. This intuitively makes sense, since second stage

matching was within a given household.

The household was the only set of blocking criteria used

at the second stage of matching. Sample records were

allowed to link to only one census record within the

household. As a consequence, this limited the ability to

identify within-household duplicate links. Each link had an

overall match score based on the second-stage matching.

The set of linked records from the second-stage matching

and the links to group quarter enumerations from the first

stage consisted of both duplicate enumerations and person records with common characteristics. Two modeling

approaches were used to estimate the probability that the

linked records were duplicates. One approach used the

results of the statistical matching and relied on the

strength of multiple links within the household to indicate

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person duplication. The second relied on an exact match

of the census to itself and the distribution of births,

names and population size to indicate if the individual link

was a duplicate. These two approaches were referred to as

the statistical match modeling and the exact match modeling, respectively. These two approaches were combined so

that each sample case with a link to a census enumeration

had an estimated probability of being a duplicate.

The statistical match modeling was used when two or

more duplicate links were found between housing units in

the second stage. After the second-stage matching, each

duplicate link between a sample household and census

household had an overall match score. So, for each sample

household, a set of match scores was observed. For any

resulting set of match scores, a probability of not observing this set of match scores was estimated. See the attachment for details. The higher this probability, the more

likely that the set of linked records in the household were

duplicates.

The estimate of the probability of not observing this set of

match scores assumed independence of the individual

match scores within each household. This assumption was

based on using the EM algorithm to determine the secondstage matching parameters. The probability of observing

the individual match scores was estimated from the

empirical distribution of individual match scores resulting

from the second-stage matching. Further, this measure

accounted for the number of times that a unique sample

household was matched to different census households

within a given level of geography. The probability of not

observing this set of match scores was translated into a

‘‘statistical match’’ duplicate probability of 0 or 1 based on

critical values that varied by level of geography.

The exact match modeling relied on an exact match of the

census to itself. The methodology accounted for the overall distribution of births, frequency of names, and population size in a specific geographic area. Duplicate probabilities were computed separately by geographical distance of

the links. Further, duplicate links were modeled separately

by how common the last name was, as well as for Hispanic names.

The two approaches were combined to assign an estimated probability that the linked records were duplicates.

The duplicate probability for the links to group quarters in

the first stage and one-person household links were from

the exact match modeling. For all other links, the duplicate probability was the larger of the two model estimates. For nonexact matches, this was always from the

statistical match modeling. For exact matches, adjustments were made to account for the integration of these

two methods.

Based on the results of this matching and modeling, an

overall estimate of census duplicates was derived from the

E-sample links. Further, for each Full E- and P-sample person who linked outside the A.C.E. search area, these

results provided the probability that they were in fact the

same person. These duplicate probabilities were used in

the A.C.E. Revision II estimates.

MATCHING ALGORITHM

Efforts to increase matching efficiency over the ESCAP II

duplicate study included implementing statistical matching of persons at the first stage and the use of more discriminating matching parameters at the second stage.

Inputs

Both the Full E and P samples were matched to the census

records. The E-sample records reflected any updates made

by the clerical staff during the A.C.E. matching operation

when the census characteristics were incorrectly transcribed or scanned. The P sample included all nonmovers,

outmovers, and inmovers. The same matching algorithm

was used for the Full E and P samples.

The census files consisted of data-defined person records

for both the household and group quarters populations.

Both the reinstated and deleted records from the Housing

Unit Duplication Operation described in Nash (2000) were

included in the matching, so these links could be reflected

in the A.C.E. Revision II estimates.

First Stage: Person-Level Matching

The first stage was a statistical match of the Full E and P

samples to the census. This was a national match where

each Full sample case was compared with census records

across the nation to assess how well the matching variables agreed.

The matching variables were first name, last name, middle

initial, month of birth, day of birth, and computed age.

The matching variables and parameters are given in Table

5-1. The agreement weight and the disagreement weight

are the matching parameters of each variable. Standard

matching parameters were used at the first stage. The

relationship of the agreement and disagreement parameters translated into the match score for each variable. For

example, the full agreement value for first name was

2.1972; whereas, the full disagreement match score was

-2.1972. The sum of the variable match scores was the

total match score. When the match score was 9.4006, this

indicated full agreement of all variables. A match score of

-9.4006, on the other hand, indicated full disagreement.

Further Study of Person Duplication in Census 2000 Section II—Chapter 5 5–3

U.S. Census Bureau, Census 2000
Table 5-1. First-Stage Matching Parameters

Matching variables Type of

comparison

Matching parameters Match score

Agreement

weight (m)

Disagreement

weight (u)

Agreement

ln (m/u)

Disagreement

ln ((1-m)/(1-u))

First name String (uo) 0.9 0.1 2.1972 –2.1972

Last name String (uo) 0.9 0.1 2.1972 –2.1972

Middle initial Exact 0.7 0.3 0.8473 –0.8473

Month of birth Exact 0.8 0.2 1.3863 –1.3863

Day of birth Exact 0.8 0.2 1.3863 –1.3863

Computed age Age (p) 0.8 0.2 1.3863 –1.3863

Total 9.4006 –9.4006

The type of comparison indicated the statistical matching

method for comparing the variables. For example, the

string comparitor was used for first name and last name.

This method addressed typographical errors in names. For

example, ‘‘Tim’’ and ‘‘Tum’’ can yield a positive agreement

score. An exact match algorithm would have treated these

as a disagreement. For age, the age values could have

been off by ± one year and still receive a full agreement

score on computed age.

The Statistical Research Division matching software called

BigMatch documented in Yancey (2002) was used in the

first stage. This software allowed a sample record to link

to more than one census record. This capability was

important, since it was possible for there to be more than

two enumerations of the same person in the census.

Four blocking criteria were used. Blocking restricted the

comparisons of records to only those that exactly agreed

on certain values. Most records that did not agree on the

values below are probably not duplicates. The blocking

criteria were:

• First name, last name

• First name, first initial of last name, age groupings

(0-9, 10-19, 20-29, etc.)

• Last name, first initial of first name, age groupings

(0-9, 10-19, 20-29, etc.)

• First initial of first name, first initial of last name,

month of birth, day of birth

All possible links within each blocking criteria were compared. For each comparison, the variable match score and

the total match score were computed. The first-stage

matching decision rules were as follows. First, a match

must have had at least four of the match variables in full

agreement. This meant that four of the variables had to

have a match score equal to the agreement match score in

Table 5-1. The one exception was the middle initial. When

the middle initial was blank, it was considered to be in full

agreement in this study since the middle initial was often

missing on the sample and census records. In this case,

the middle initial score was zero. Second, the total match

score had to be 4.7 or greater. This minimum score was

about half the total score for full agreement of all matching variables.

Table 5-2 shows the distribution of A.C.E. links within

cluster that were identified by the resulting number of

matching variables in full agreement. There were a total of

10,559 duplicate links identified by the A.C.E. clerical staff

that agreed on the first letter of the first and last name.

The table shows the number of identified A.C.E. duplicates

as the number of matching variables in full agreement

decreased. The table also displays the number of total

links that were identified. The percent of A.C.E. links in

each row of the table decreases as the number of matching variables in full agreement decreases.

By requiring at least four matching variables to be in full

agreement, 68.4 percent of these A.C.E. duplicates were

identified. On the other hand, when only four of the six

variables fully agreed, only 30.4 percent of the total links

identified by this criteria were A.C.E. Revision II duplicates.

Note that it was tempting to require that only three variables be in full agreement, since this would increase the

number of A.C.E. duplicates by 20 percent. However, this

change would substantially increase the number of false

matches.

Table 5-3 shows that introducing a minimum total score

greatly increased the density of A.C.E. links identified.

Note that some A.C.E. duplicate links were dropped by

using this criteria. This was a consequence of applying

rules that reduced the false link rate.

Second Stage: Household-Level Matching

The second stage of matching was restricted to the household population. The person links from the first stage

established a link between two housing units. The second

stage was a statistical match of the household members

from the two housing units. A sample household was

included in the second stage multiple times, if the samplehousehold had persons with links to multiple census

households in the first stage. This was the same approach

used for the ESCAP II duplicate study.

5–4 Section II—Chapter 5 Further Study of Person Duplication in Census 2000

U.S. Census Bureau, Census 2000
Table 5-2. Distribution of Links Within A.C.E. Clusters by Full Agreement

[Percentages may not add due to rounding]

Number of variables

in full agreement

A.C.E. links

Total

links

Percent of A.C.E.

Count Percent Cumulative percent links in row

6 2,348 22.2 22.2 2,451 95.8

5 2,895 27.4 49.7 3,983 72.7

4 1,983 18.8 68.4 6,520 30.4

3 2,211 20.9 89.4 40,891 5.4

2 954 9.0 98.4 180,324 0.5

1 164 1.6 99.9 601,370 <0.1

0 4 <0.1 100 350,987 <0.1

Total 10,559 100 100 1,186,526 0.9

Table 5-3. Distribution of A.C.E. and Total Links Within A.C.E. Clusters

[Only include links with score ≥ 4.7]

Number of variables in

full agreement A.C.E. links Total links

Percent of A.C.E.

links in row

6 2,348 2,451 95.8

5 2,868 3,763 76.2

4 1,680 2,670 62.9

3 0 0 n/a

2 0 0 n/a

1 0 0 n/a

0 0 0 n/a

Total 6,896 8,884 77.6

Table 5-4. Second-Stage Matching Parameters

Matching variables Type of

comparison

Matching parameters Match score

Agreement

weight (m)

Disagreement

weight (u)

Agreement

ln (m/u)

Disagreement

ln ((1-m)/(1-u))

First name String (uo) 0.9500 0.0125 4.3307 –2.9832

Last name String (uo) 0.9600 0.5700 0.5213 –2.3749

Middle initial Exact 0.0840 0.0220 1.3398 –0.0655

Month of birth Exact 0.6000 0.0600 2.3026 –0.8544

Day of birth Exact 0.3000 0.0200 2.7081 –0.3365

Computed age Age (p) 0.9750 0.1325 1.9959 –3.5467

Total 13.1984 –4.1948

The matching variables were the same as the first stage:

first name, last name, middle initial, month of birth, day of

birth, and age. Table 5-4 gives the matching parameters.

The data in this table have similar meaning as that for the

first stage parameters in Table 5-1. Using a subset of the

first-stage links, the second-stage matching parameters

were derived using the EM algorithm as described in Winkler (1995). These parameters were anticipated to be more

discriminating than the set used for the ESCAP II study.

Since the first-stage matching established a link between

two housing units, first name had more discriminating

power than last name in the second stage. When first

name fully agreed, it contributed 4.3307 toward the total

score, while last name only contributed 0.5213 when it

was in full agreement. Further, month of birth and day of

birth were more powerful than computed age. This was

expected since adults in a housing unit often have similar

ages, but not the same month and day of birth.

The Statistical Research Division Record Linkage software

described in Winkler (1999) was used for the second

stage. Each sample record was linked to only one census

record within the household, a one-to-one matching. There

was no additional blocking criteria beyond household; all

possible links within households were compared. Each link

had a total match score ranging from -4.1948 to 13.1984.

This second-stage match score was used for the modeling.

Further Study of Person Duplication in Census 2000 Section II—Chapter 5 5–5

U.S. Census Bureau, Census 2000
All links with a second-stage match score greater than

0.3419 were retained as input to the modeling.

Reverse Name Matching

Occasionally, first and last name was captured in reverse

order on the data files. The first name was in the last

name field and the last name was in the first name field.

When the data was in reverse-order on one file but not the

other, it was difficult to identify these duplicate links since

the variable match scores for first and last name disagreed

for both the first and second stage. To attempt to identify

these cases, the first and last name fields were reversed

and then matched to the census files a second time. The

duplicate links from both runs, name in the usual order

and in reverse order, were input to the modeling. When

both methods identified the same duplicate link, the

higher of the two match scores was retained and used in

the modeling.

MODELING LINKS

Since the goal of this study was to provide duplicate information for calculating A.C.E. Revision II estimates, it was

important to provide a measure of confidence that could

be incorporated into the estimation methodology. Consequently, modeling efforts focused on methods for estimating the probability that two linked records were duplicate

enumerations. An advantage of duplicate probabilities

over the Poisson model weights used in ESCAP II was that

all duplicate links outside the A.C.E. search area could be

reflected in the A.C.E. Revision II estimates. The statistical

and exact match modeling approaches were combined to

yield an estimated duplicate probability for the linked

records from the statistical matching of the E and P

samples to the census.

Statistical Match Probability

The statistical match modeling was used when the second

stage matching resulted in two or more duplicate links.

After the second-stage matching, each duplicate link

between a sample household and census household had

an overall match score. So, for each sample housing unit

to census housing unit match, a set of match scores was

observed. For any resulting set of match scores, a probability of not observing this set of match scores, Pr(NT),

was estimated for each link within the sample household.

The higher this probability, the more likely that the set of

linked records in the household were duplicates.

Since a sample housing unit could have been matched to

more than one census housing unit during the second

stage, there were multiple sets of duplicate links and

match scores for each sample housing unit. Each set of

duplicate links for a sample housing unit was assigned a

separate Pr(NT) since the match scores differ for each

matching attempt. Further, the Pr(NT) for each set of duplicate links for a sample housing unit varied because of the

geographic distance of the duplicate links. As shown in

the attachment, Pr(NT) was estimated by

Pr NT [1 

p



d1

Pr Xd  xd]

n

where

Pr(Xd ≥ xd) was the probability of getting a total match score Xd

greater than or equal to xd,

p was the number of duplicate links in the sample household,

and

n is the number of census housing units the sample household

was matched with in the second stage within a given geographic area.

The estimate of the probability of not observing this set of

match scores assumed independence of the individual

match scores within each household. This assumption was

based on using the EM algorithm to determine the secondstage matching parameters. The probability of observing

the individual match scores was estimated from the

empirical distribution of individual match scores resulting

from the entire second-stage matching. Further, this measure accounted for the number of times that a unique

sample household was matched to different census households within a given level of geography. The geographical

levels were block, tract, same county (outside tract), same

state (outside county), and different state.

For the E sample, this analysis was done at the E-sample

household level. For the P sample, a household consisted

of any combination of nonmovers, outmovers, and inmovers. To account for this, the duplicate links were analyzed

separately by mover status when looking at patterns of

match scores.

The probability of not observing this set of match scores

was translated into a ‘‘statistical match’’ duplicate probability of 0 or 1 based on critical values that varied by

level of geography. Table 5-5 shows the minimum value of

Pr(NT) for assigning a statistical match duplicate probability of 1 for E and P samples.

Table 5-5. Minimum Value for Assigning

Statistical Match Probability

Geographic distance of linked records

Minimum Pr(NT)

E sample P sample

Same block ........................... 0.00 0.25

Same tract (different block) . ............ 0.70 0.35

Same county (different tract) ............ 0.97 0.60

Same state (different county) ........... 0.97 0.60

Different state . . ....................... 0.97 0.60

5–6 Section II—Chapter 5 Further Study of Person Duplication in Census 2000

U.S. Census Bureau, Census 2000
Duplicate links with a Pr(NT) greater than or equal to the

minimum value in Table 5-5 were assigned a statistical

match duplicate probability of 1. All other links were

assigned a statistical match duplicate probability of 0.

Exact Match Probability

Given exact matching of the census to itself, duplicate

probabilities were assigned to linked records by taking

into account the overall distribution of births, frequency of

names, and population size in a specific geographic area.

Duplicate probabilities were computed separately by links

within county, links within state and different county, and

different states. Further, duplicate links were modeled

separately by how common the last name was, as well as

for Hispanic names. Fay (2002b) gives the model and preliminary results. The following are excerpts from Fay

(2002b) to give the reader a general idea of the approach.

Like the Poisson model, the new approach uses frequencies of occurrences of combinations of first and last name.

The result is an estimated probability of duplication for

most matches, except for matches of frequently occurring

names, where the probability of duplication is low and difficult to estimate with high relative precision.

This work results in a series of probability models, with

parameters that can be estimated statistically from

observed census data. A core model characterizes probabilities of duplication, triple enumeration (apparent enumeration of the same person three times), and other forms

of multiple enumeration within a given geographic area.

The other models account for duplication across domain.

The first part of the core model expresses the probability

of coincidentally sharing a birthday. A second set of

expressions, a model for census duplication, is built on

top of the model for coincidental sharing of date of birth.

The core model combines the two models to account for

observed patterns of exact computer matches of census

enumerations. The core model provides a basis to estimate a probability that a given computer match links the

same person instead of two persons coincidentally sharing

a birthday. An approximate argument allows the core

model to be extended to nested geographic categories,

such as (1) counties, (2) other counties within state, and

(3) other states.

The result of the exact match model is a duplicate probability greater than or equal to zero, but less than one for

census records that agree exactly on first name, last

name, month and day of birth and two-year age intervals.

Combining the Two Models

The two approaches were combined to give one duplicate

probability to each E- and P-sample duplicate link. Table

5-6 summarizes the results of combining the two models.

The duplicate probability for the links to group quarters in

the first stage and one-person household links were from

the exact match modeling. For all other links, the duplicate probability was the larger of the two model estimates, as indicated by the shaded cells in Table 5-6. For

nonexact matches, the duplicate probability assignment

was always based on the statistical match modeling.

For exact matches in sample households with two or more

persons, adjustments were made to account for the integration of these two methods. The exact match probabilities were determined conditionally, requiring a downward

adjustment of the exact probabilities for the links, which

the statistical match modeling assigned a probability of

zero. The amount of the downward adjustment was based

on the upward adjustment made when using the statistical

match probability of one instead of the exact match probability.

Table 5-6. Combining the Two Modeling

Results

Type of Link

Size of

sample

HU

Type of

match

Statistical

match

probability

Exact

match

probability

Housing Unit 1 Exact – [0, 1)

Nonexact – –

2+ Exact 1 [0, 1)

Exact 0 [0, 1)

Nonexact 1 –

Nonexact 0 –

Group Quarter Exact – [0, 1)

Nonexact – –

– Modeling did not assign a value.

The results of this modeling provided, for each Full E- and

P-sample person who linked to a census person outside

the A.C.E. search area, the probability that they were in

fact the same person. These probabilities, referred to as pt

in Chapter 6, were used to obtain A.C.E. Revision II estimates.

Reinstated and Deleted Census Records

For the exact match modeling, separate probabilities were

computed based on population distributions with and

without the reinstated and deleted records. One computed

duplicate probability allowed sample records to link to

reinstated and deleted census records, while a second

duplicate probability did not allow links to reinstated and

deleted records. Under this second scenario, any links to

reinstated or deleted records were assigned a duplicate

probability of zero. The duplicate probabilities used in the

A.C.E. Revision II estimation were those that allowed links

to reinstated and deleted census records.

ASSESSMENT OF LINKS

Throughout the development of the Further Study of Person Duplication in Census 2000, the A.C.E. duplicate links

found during production were the benchmark used to

Further Study of Person Duplication in Census 2000 Section II—Chapter 5 5–7

U.S. Census Bureau, Census 2000
gauge whether the matching algorithm did a good job of

finding true duplicates and minimizing the number of

false links found within the block cluster.

This study and the ESCAP II duplicate study documented in

Fay (2001, 2002) utilized the same method for estimating

efficiency for the E sample. Basically, the method estimated the effectiveness of identifying A.C.E. clerical duplicates within the A.C.E. sample area and accounted for

duplicate links to reinstated and deleted records that were

out-of-scope for A.C.E. Instead of producing one overall

efficiency measure, several measures were computed for

various levels of detail including size of sample household

and number of links between the units.

FORMING ESTIMATES OF DUPLICATES

Estimates of census duplicates were formed by summing

the product of the sampling weight for the E-sample person, the duplicate probability, and the multiplicity factor.

Since a sample of the census (E sample) was matched to

the census, a naive approach would treat each duplicate

link of A to B as one duplicate. However, had a different

sample been drawn, it could have contained the B to A

link. Applying a multiplicity factor of 1/2 in this simple

case ensured that the estimate of this example was only

one duplicate. See Mule (2002b) for more details on the

computation of the multiplicity factor.

5–8 Section II—Chapter 5 Further Study of Person Duplication in Census 2000

U.S. Census Bureau, Census 2000
Attachment.

Probability of Not Observing a Set of Match Scores

Each E-sample household had a set of duplicate links to a

particular census household. Each duplicate link had a corresponding overall match score from the second-stage

matching resulting in a pattern of match scores for the

sample household. The task was to assess whether this

observed set of match scores occurred because the links

were duplicates or because the records had characteristics

in common but were different people.

Objective: To estimate the probability of not observing

this set of match scores or better for each

E-sample household.

The hypothesis is that the higher the probability of not

observing this set of match scores or better, the more

likely the links represent duplicate enumerations.

Suppose a particular E-sample household has p ≥ 2 duplicate links with observed match scores x1, x2, ..., xp.

Define Pr(NT) to be the probability of not observing the set

of match scores or better, (X1  x1, X2  x2, ..., Xp  xp.

This probability can be expressed as

PrNT [1  PrX1  x1,X2  x2,....,X p  xp]

n (1)

where n was the number of different census housing units

that the E-sample housing unit was linked to during the

second-stage match. This calculation accounted for the

fact that the more times the E-sample housing unit

matched to different housing units, the greater the chance

of obtaining this outcome.

Individual match scores X1, X2, ..., Xp were assumed to be

independent, since the second-stage matching parameters

gave more emphasis to first name rather than last name.

Further, the parameters gave more emphasis to month and

day of birth rather than age. Under the independence

assumption, (1) can be written as follows:

PrNT [1 

p



d1

Pr Xd  xd]

n

(2)

The probability of observing a match score Xd greater than

or equal to xd, Pr(Xd ≥ xd), was obtained from the empirical distribution of second-stage match scores. The probability in (2) was used for the P-sample households as

well.

Further Study of Person Duplication in Census 2000 Section II—Chapter 5 5–9

U.S. Census Bureau, Census 2000
Chapter 6.

A.C.E. Revision II Estimation

The A.C.E. Revision II Dual System Estimate (DSE) methodology was developed with the following objectives in

mind:

• Integration of the corrections for measurement errors so

that measurement errors identified by both the evaluations and the duplicate study are not over-corrected.

• Separate estimation for both E- and P- sample persons

based on whether or not they linked to a census enumeration outside the search area.

• Flexibility in the post-stratification design, because the

factors that affect correct enumeration (as measured by

the E sample) were not necessarily the same as those

that affect coverage (as measured by the P sample).

• Adjustment for correlation bias.

This chapter presents how this additional information was

incorporated into the DSE for A.C.E. Revision II estimates.

The reader is assumed to be familiar with the basic dual

system model and how it was used to produce the March

2001 A.C.E. estimates. See Haines (2001) for a detailed

description of this methodology and Davis (2001) for the

original dual system estimation results. This chapter

describes the approach to A.C.E. Revision II dual system

estimation. The chapter discusses estimation of the term

accounting for persons in the census who are not in the E

sample. The correct enumeration rate from the E-sample

data is described. Then, the estimation of the match rate

from the P-sample data is addressed. The census,

E-sample, and P-sample data are combined to form a

single DSE formula. Next, the post-stratification variables

used for the A.C.E. Revision II Full and Revision Samples

are defined. The chapter then discusses adjustment for

correlation bias using demographic analysis sex ratios and

concludes with a discussion of synthetic estimation.

DUAL SYSTEM ESTIMATION

The basic form of the dual system estimate (DSE) is:

DSE  Cen ́  II ́  

CE

E



P

M (1)

where

Cen ́ = the census count, excludes late adds

II’ = non-data-defined census records,

excludes late adds

LA = ‘‘late additions’’ to the census, i.e. records

included too late for A.C.E. processing;

primarily reinstated cases from the housing

unit duplication operation

CE = E-sample weighted estimate of census correct

enumerations

E = E-sample weighted estimate of census total

enumerations (includes insufficient

information for matching and followup cases,

excludes non−data−defined cases and late adds)

P = P-sample weighted estimate of total persons

M = P-sample weighted estimate of matches to

census persons

DSEs were computed separately within post-strata. A poststratum is a group of people defined by demographic and

geographic characteristics who are assumed to have the

same probabilities of inclusion in the census. Post-strata

can also be defined to have equal probabilities of correct

enumeration in the census.

The DSE in (1) can be written as a function of the final census count, Cen, which includes late adds and the following

three rates:

DSE  Cen  rDD  rCE

rM

(2)

where

rDD  (Cen ́  II ́ )/Cen is the census data-defined

rate. The numerator excludes

late adds, but the denominator

includes late adds.

rCE = CE / E is the E-sample correct enumeration rate

rM  M/P is the P-sample match rate.

The three rates can be interpreted as estimates of probabilities. Thus, within post-stratum,

• rDD estimates the probability that a census person

record has sufficient (and timely) information for

inclusion in A.C.E. processing,

• rCE estimates the probability that an E-sample universe person is a correct enumeration, and

• rM estimates the probability that a person in the

P sample is included in the census.

A.C.E. Revision II Estimation Section II—Chapter 6 6–1

U.S. Census Bureau, Census 2000
The interpretation of rM may be less obvious than the

other two; it is the sample-weighted proportion of

P-sample persons who were also found in the census. The

general independence assumption underlying DSE is that

either the census or the A.C.E. inclusion probabilities are

the same (both are not required). Assuming causal independence, the match rate rM estimates the probability of

census inclusion for the post-stratum.

Equation (2) also gives an interpretation of how the DSE

constructs population estimates within a post-stratum.

• Multiply the census count (Cen) by the data-defined

rate, rDD , to estimate the number of census persons

who are data-defined and, therefore, eligible for inclusion in the E sample.

• Reduce this product by multiplying it by the estimated

probability of correct enumeration, rCE

• Increase this result by dividing it by the estimated probability of census inclusion, rM

The primary tasks in developing DSEs at the post-stratum

level are the estimation of the three rates involved. The

estimate rDD is straightforward because it is based on

100-percent census tabulations. More detail is provided

for the estimates rCE and rM, since they are more challenging.

The different estimation tasks can be tackled one term at a

time. Basically, the goal is to estimate the numerators and

denominators of the terms rCE and rM. Since E, the estimated number of total census data-defined enumerations,

is a simple, direct sample-weighted estimate, the challenges relate mostly to developing the estimates CE, P,

and M. The estimation challenges for A.C.E. Revision II

focus on accounting for: (i) information from the revised

coding of the A.C.E. Revision Sample, (ii) information from

the A.C.E. Revision II study of census duplicates, and (iii)

different post-stratification schemes for the Full E and P

samples. The most difficult issue is (ii).

Before proceeding to a detailed discussion of the A.C.E.

Revision II DSE components, consider the general nature

of the estimator. While the basic DSE shown in equation (1)

was applied in the 1990 PES (Hogan, 1993), the March

2001 A.C.E. incorporated the modification called PES-C

estimation. See Haines (2001) and Mule (2001b) for

details. This DSE had the general form:

DSEC  Cen ́  II ́  

CE

E



Pnm  P im

Mnm 

Mom

Pom

Pim

(3)

where the following quantities are all P-sample weighted

estimates for the given post-stratum:

Mnm = estimate of matches to census persons for

nonmovers

Mom = estimate of matches to census persons for

outmovers

Pnm = estimate of total nonmovers

Pom = estimate of total outmovers

Pim = estimate of total inmovers

Nonmovers, outmovers, and inmovers were defined with

reference to their status in the period of time between

Census Day (April 1, 2000) and the A.C.E. interview. Nonmovers were those who did not move during this period,

outmovers were those persons who moved out of a

sample block during this period, and inmovers are those

who moved into a sample block during this period. Equation (3) estimated P-sample matches (M) as the sum of

estimated matches among nonmovers (Mnm) and estimated matches among movers. The number of mover

matches was estimated as the product of an estimated

number of movers (Pim) and an estimate of the mover

match rate (Mom / Pom). Thus, P-sample outmovers were

used to estimate the mover match rate while P-Sample

inmovers were used to estimate the number of movers.

This approach implies that Pnm + Pim should be used for

the estimated total of P-sample persons (P).

Equation (3) can be further expanded to include poststratification subscripts. The Full E- and P-sample poststrata are denoted by subscripts i and j, respectively. The

census term was calculated for the cross-classification of i

and j post-strata, denoted ij. The DSE formula, using procedure C for movers, with different post-strata for the E

and P samples is:

DSEC

ij  Cen ij  rDD, ij 

[

CEi

Ei

]

[

Mnm,j  [

Mom,j

Pom,j

]Pim,j

Pnm,j  Pim,j

]

ESTIMATION OF rDD

Recall the general form of the DSE in equation (2). This

section discusses the estimation of the data-defined rate,

or ‘‘DD-rate.’’

The DD-rate estimate (rDD) is defined as (Cen ́  II ́   Cen

for a given detailed ij post-stratum, where Cen ́, II ́, and

Cen are defined from 100-percent census tabulations. At

the post-stratum level, Cen  rDD reduces to Cen ́  II ́.

This suggests that an alternative to computing rDD at a

post-stratum level is to compute Cen ́  II ́ for all levels

(e.g., demographic post-stratum groups within small geographic areas) for which estimates were to be computed,

and then to adjust these quantities by the appropriate

rCE / rM factors. This approach may be problematic, especially when applied to very small areas.

The problem with direct computation of Cen ́  II ́ for very

small areas can be seen with the following hypothetical

example. Suppose a particular small geographic area (e.g.,

6–2 Section II—Chapter 6 A.C.E. Revision II Estimation

U.S. Census Bureau, Census 2000
a collection of blocks) has a high rate of imputation in the

census, say 15.0 percent. Imputation rates will vary geographically, and high rates could result from a number of

factors, such as difficulties getting access to housing units

in secure communities or difficulties in hiring and retaining census enumerators in a particular area. In this hypothetical example, removing all imputations from the census count for the area by computing Cen ́  II ́ would

reduce the census count by 15.0 percent. Subsequent multiplication by the rCE  rM factors and summing the resulting DSEs over post-strata may increase the population estimate from this base, but perhaps by no more than two or

three percent (depending on the post-stratum composition

of the area). The net synthetic DSE would, thus, be 12.0 or

13.0 percent lower than the census count. While this estimate could make sense if almost all the housing units for

which persons were imputed were actually vacant (and

this fact were not discovered in the census enumeration),

it would not make sense if most of the units were occupied and the high rate of imputation resulted from other

factors such as those suggested above. Calculating rDD for

post-strata and applying it synthetically avoids such problems in small area estimates, though perhaps incurring

some error for larger areas for which the direct tabulation

of Cen ́  II ́ would be sensible.

The data-defined rates, rDD , are computed at the detailed

post-stratum obtained as the intersection of the E- and

P-sample post-strata.

ESTIMATION OF rCE

This section discusses the estimation of the correct enumeration rate, rCE = CE/E. The Full E-sample post-strata

are denoted by the subscript i. The Revision E sample has

post-strata denoted by i ́, where i ́ is based on collapsed

post-strata i. This means that the Revision Sample poststrata were obtained by collapsing the Full Sample poststrata i. The correct enumeration rate is written:

rCE, i  CEi

ND f l, i ́  CE ̃ i

D

Ei (4)

Note that the numerator term separates the E-sample enumerations with a duplicate link to a census enumeration

outside the A.C.E. search area, as identified in the duplicate study, from those enumerations without a link. As

discussed in Chapter 5, the duplicate study used

computer-based record linkage techniques to match the

Full P- and E-samples to census enumerations outside the

search area. The census enumerations included those enumerations that were added too late to be included in the E

sample, as well as those enumerations that were determined to be duplicates and, therefore, were never

included in the census.

The term CE i

ND estimates the number of correct enumerations in the Full E sample without duplicate links in poststratum i. This term includes the probability of not being a

duplicate, 1-pt

.

The component CE ̃ i

D represents the estimated number of

correct enumerations in the Full E sample with duplicate

links in post-stratum i, which are retained after unduplication. This term includes the probability of being a duplicate, pt

, as well as the conditional probability that an

E-sample case is a correct enumeration given that it is a

duplicate to another census enumeration outside the

A.C.E. search area.

The total weighted number of persons in post-stratum i in

the E sample are denoted by Ei

.

The double-sampling ratio factor f1, i ́ corrects for measurement error based on the Revision E sample. It is a ratio of

an estimate that uses the revised coding (indicated by *)

to an estimate that uses the original coding. These adjustments, which are calculated for measurement error poststrata i ́, are represented by:

f l, i ́ 

CE i ́

ND*

Ei ́

ND

CEi ́

ND

Ei ́

ND

 CEi ́

ND*

CEi ́

ND .

P- and E-sample cases with duplicate links were assigned a

nonzero probability of being a duplicate, pt . P- and

E-sample cases without duplicate links were assigned a pt

value of zero. This probability is usually 0 or 1 for E- and

P-sample cases, but some duplicate links have a value in

between, indicating less confidence that the link is representing the same person. These probabilities are also

transferred to the E- and P- Revision Samples.

Although the duplicate study identified E- and P-sample

cases linking to census enumerations outside the A.C.E.

search area, this study could not determine which component of the link was the correct one since no additional

data were collected for this purpose. Assuming that the

linked person does exist, the goal is to determine which of

the two locations is the appropriate place to count the person. Since linked persons may be geographically close or

far apart, this has implications for the degree of synthetic

error. On the E-sample side, this study does not identify

whether the linked E-sample case is the correct enumeration. Thus, it is necessary to estimate the following conditional probability:

zt the probability that an E-sample case is a correct

enumeration given that it is a duplicate to another

census enumeration outside the A.C.E. search area.

E-Sample Links

From the duplicate study, an estimate of correct census

enumerations can be derived by considering the situation

of the linked enumerations, as well as assuming that each

link represents one correct enumeration. This assumes, of

course, that the link consists of true duplicates. These

A.C.E. Revision II Estimation Section II—Chapter 6 6–3

U.S. Census Bureau, Census 2000
assumptions are used to estimate the contribution to correct enumerations from Full E-sample cases with duplicate

links, including those originally coded as correct, as well

as those originally coded as erroneous. This contribution

to correct enumerations is given by the term: CE ̃

i

D. To estimate this term, the E-sample links are first classified

according to the characteristic of the linked situation and

the original coding of the E sample. Attachment 1 summarizes this classification and the rules for assigning zt

’s.

First, linked situations are identified where one component of the link is thought to be correct and the other

incorrect. If a person in a housing unit links with a person

in a group quarters, such as a college dormitory, the person in the housing unit is taken to be incorrect and

assigned a zt of zero. See Linked Situation 1. in Attachment

1. If a linked person 18 years of age or older is listed in

only one of the households as a child of the reference person, this person is assumed to be incorrectly included

with their parents and correctly included in the other

household, unless A.C.E. had already determined them to

be an erroneous inclusion. An example of this might be a

college student that was listed with their parents and also

listed in an off-campus apartment. This is represented by

Linked Situations 2a. and 2b. in Attachment 1.

For other Linked Situations, the choice of which person is

correct is not clear. Consider links between whole households where all household members are duplicated

(Linked Situation 3.). This includes families that might

have moved some time around Census Day and were inadvertently included at both places or this might involve

households with multiple residences with a helpful, but

perhaps, uninformed proxy respondent. Another situation,

Linked Situation 4., involves children ages 0 to 17, perhaps of divorced parents, that are linked between two different households. For these and all other situations, it is

assumed that only half of these census enumerations with

duplicate links are correct. To estimate the conditional

probability, zt , that the E-sample person is the correct enumeration, controls cells are defined for Linked Situations

3., 4., and 5., as indicated in Attachment 1, by:

• 3 Race/Hispanic Origin Domains

• Tenure

These resulting control cells are given in Attachment 2.

Within each control cell the zt

’s are determined such that

duplicate E-sample cases, originally coded correct or unresolved, will weight up to one half the number of census

duplicates identified, including the erroneous enumerations. This is calculated as:

z

ˆ

t 

0.5 t

Wt pt

t

Wt pt Pr CE

The summations are over the links in a control cell regardless of the original E-sample coding.

The components of equation (4) are defined below.

CE ̃

i

D  t 	 i

W


E

, t pt z t PRce
, t

is the estimated number of correct enumerations with

duplicate links in post-stratum i who were retained after

unduplication.

CEi

ND  t 	 i

W 
, t E 1  pt

 PRce
, t

is the number of correct enumerations without duplicate

links in post-stratum i, where the summation is taken over

all enumerations in the A.C.E. E sample in post-stratum i.

W
, t E is the production A.C.E. sampling weight for

E-sample person t.

pt is the probability that person t has a duplicate

link outside the search area. This is usually 0 or

1, but could be between these two values for

probability matches, where the accuracy of the

link was uncertain.

PRce
, t is the probability that person t is a correct enumeration in the original production coding. This

is either 0 or 1 unless it was not possible to code

the E-sample case a correct or erroneous enumeration. In these cases, a probability of correct

enumeration was imputed.

fl, i ́  CEi ́

ND*

CEi ́

ND 

t 	 i ́

WRR, t E 1  pt

 PRceR, t

t 	 i ́

WR
, t E 1pt

 PRce
, t

where

WRR,t E is the A.C.E. Revision Sample weight for person t to be used for Revision Sample coding.

WR
, t E is the A.C.E. Revision Sample weight for person t to be used with production coding.

These two weights could differ slightly

depending on TES status and noninterview

adjustment.

PRceR, t is the probability that person t is a correct

enumeration in the A.C.E. Revision Sample

coding.

Ei  t 	 i

W
, t E

is the total weighted number of persons in the E sample in

post-stratum i.

ESTIMATION OF rM

This section discusses the estimated match rate in equation (2). E-sample post-strata are indexed by i, while the

P-sample post-strata are indexed by j. The match rate for

post-stratum j is represented as:

rM, j 

Mnm, j ND f 2, j ́ M ̃

nm, j D  [ Mom, j f 3, j ́

Pom, j f 4, j ́

] (Pim, j f 5, j ́  g (Pnm, j D  P

 ̃

nm, j D ))

Pnm, j ND f 6, j ́  P

 ̃

nm, j D  Pim, j f 5, j ́  g (Pnm, j D  P

 ̃

nm, j D )

(5)

6–4 Section II—Chapter 6 A.C.E. Revision II Estimation

U.S. Census Bureau, Census 2000
The residence status of P-sample movers was adjusted for

coding error. The computer matching results were not

used. Outmovers in the P sample were collected by a

proxy interview, which made it difficult to obtain date of

birth and age information. Since date of birth and age

were important characteristics used in the computer

matching, the movers were only adjusted for coding error.

Although the duplicate study identified E- and P-sample

cases linking to census enumerations outside the A.C.E.

search area, this study could not determine which component of the link was the correct one, since there were no

additional data collected to determine this. Assuming that

the linked person does exist, the goal is to determine

which of the two locations is the appropriate place to

count the person. Since linked persons may be geographically close or far apart, this has implications for the

degree of synthetic error.

On the P-sample side, this study does not identify whether

the linked P-sample case is a resident on Census Day.

Thus, it is necessary to estimate the following conditional

probability:

ht is the probability that a P-sample case is a resident on

Census Day given that it links to a census enumeration outside the A.C.E. search area.

P-Sample Links

Unlike the E-sample side, the duplicate study does NOT

provide an estimate of the number of correct Census Day

residents in the P sample. In order to estimate ht the probability that a P-sample case is a resident on Census Day

given that it links to a census enumeration outside the

search area, it is necessary to borrow the resulting zt

’s

from the E-sample links. Attachment 1 summarizes how

the ht

’s borrow information from the zt’s.

First, the P-sample links to census enumerations outside

the search area are identified for situations where it can be

determined which component of the link is the correct

residence. The Linked Situations and rules for assigning

ht

’s are the same as those used for comparable types of

E-sample links. For example, consider a P-sample person

18 years of age or older, listed as a child of the reference

person who links with a census enumeration in a household where they are not listed as a child. This P-sample

person would be assigned an ht of zero regardless of how

A.C.E. coded this person. Thus, it is assumed that this person should not have been included in the P sample.

For the other Linked Situations 3., 4., and 5., there once

again is no information to determine whether the P sample

had the person at the correct location or whether the census had them at the correct location. Additionally, there is

no reasonable assumption about how many of these

linked P-sample persons should be at the correct location.

To overcome this obstacle, it is assumed that the error in

identifying correct residence is similar to the error in identifying correct enumeration for similar situations. Therefore, the ht for P-sample persons is set equal to the zt determined for the E sample for comparable linked situations

as identified by the control cells in Attachment 2. The ht

’s

are then included in the weighted tallies, along with the pt

,

to calculate the duplicate contribution to the Full P-sample

nonmovers and nonmover matches.

The terms in equation (5) are defined below. Summation

t 	 j denotes summation over A.C.E. Full P-Sample poststratum j, while summation t 	 j ́ denotes summation over

Revision Sample post-stratum j ́. The summation notation

also indicates whether the sum is taken over nonmovers,

outmovers, or inmovers, and if the Production (
) or Revision (R) Sample coding is used.

Mnm, j ND   W
, t P (1pt

) PRres
,t PRm
, t

t	j

t nonmover

production

where

W
, t P is the P-sample production weight of person t.

pt is the probability that person t has a duplicate

link outside the search area.

PRm
, t is the probability that person t is a match in the

production coding.

PRres
, t is the probability that person t is a resident in the

production coding.

f 2, j ́  Mnm, j ́ ND*

Mnm, j ́ ND 

 W RR, t P 1  p t

 PRresR, t PRmR,t

t 	 j ́

t nonmover

revision

 W R
, t P 1 pt

 PRres
, t PRm
,t

t 	 j ́

t nonmover

production

is the double-sampling adjustment for nonmover matches.

PRmR, t is the probability that person t is a match in the

Revision Sample coding.

PRresR, t is the probability that person t is a resident in

the Revision Sample coding.

W RR, t P is the A.C.E. Revision Sample weight for person t

to be used for Revision Sample coding.

W R
, t P is the A.C.E. Revision Sample weight for person t

to be used with production coding. These two

weights could differ slightly depending on TES

status and the noninterview adjustment.

Mom, j   W
, t P PRres
, t PRm
, t

t 	 j

t outmover

production

is the number of matched outmovers in the Full Sample in

post-stratum j.

A.C.E. Revision II Estimation Section II—Chapter 6 6–5

U.S. Census Bureau, Census 2000
f 3, j ́  Mom,j ́ *

Mom, j ́



 WRR, t P PRresR, t PRmR, t

t 	 j ́

t outmover

revision

 WR
, t P PRres
, t PRm
, t

t 	 j ́

t outmover

production

is the double-sampling ratio for matched outmovers for

post-stratum j ́.

Pom, j   W 
, t P PRres
, t

t	, j

t nonmover

production

is the number of outmovers in the Full Sample for poststratum j.

f 4, j ́  Pom, j ́ *

P om, j ́



 WRR, t P PRresR, t

t 	 j ́

t outmover

revision

 WR 
, t P PRres
, t

t	 j ́

t outmover

production

is the double-sampling ratio for outmovers for poststratum j ́.

Pim, j   W 
, t P

t 	 j

t nonmover

production

is the number of inmovers in the Full Sample post-stratum

j.

f 5, j ́  Pim, j ́ *

P im, j ́



 WRR, t P PRinmoverR, t

t 	 j ́

t inmover

revision

 WR 
, t P

t 	 j ́

t inmover

production

is the double-sampling ratio for inmovers for post-stratum

j ́.

PRinmoverR, t is the probability that person t in the Revision Sample is an inmover.

g (P nm, j D  P

 ̃ nm, j D )

The term g adjusts the number of inmovers for those Full

P-sample nonmovers who are determined to be nonresidents

because of duplicate links. Some of these nonresidents are

nonresidents because they are inmovers and should be added

to the count of inmovers.

The term P nm, j D  P

 ̃ nm, j D is an estimate of nonresidents among

nonmovers with duplicate links. This term is multiplied by g,

which is an estimate of the proportion of originally-coded nonmovers with duplicate links who are true nonresidents that have

moved in since Census Day. The term g is estimated using the

Revision Sample and both the original A.C.E. and the revision

coding as follows:

g  P nm, im* D

Pnm, nr* D

Pnm, im* D is an estimate of persons (using the Revision P

sample) with a duplicate link who were originally

coded as nonmovers but the revision coding determined them to be inmovers (a subset of nonresidents).

P nm, nr* D is an estimate of persons (using the Revision P

sample) with a duplicate link who were originally

coded as nonmovers but the revision coding determined them to be nonresidents.

A couple of important assumptions are:

• If the revision coding determined that a person was a

nonresident, they really are a nonresident. That is,

revision-coded nonresidents are assumed to be a subset

of true nonresidents.

• The rate of inmovers for revision-coded nonresidents is

the same as that for true nonresidents.

M ̃

nm, j D   W
, t P pt ht PRm
, t PRres
, t

t 	 j

t inmover

production

is the number of duplicate persons determined to have

been Census Day residents who matched to the

census in post−stratum j.

Pnm, j ND   W
, t P 1  pt

 PRres
, t

t 	 j

t inmover

production

is the number of nonmovers without links outside the

search area in post-stratum j.

f 6, j ́  Pnm, j ́ ND*

P nm, j ́ ND 

 WRR, t P 1 pt

 PRresR, t

t 	 j ́

t nonmover

revision

 WR
, t P 1  pt

 PRres
, t

t 	 j ́

t nonmover

production

is the double-sampling adjustment for nonmovers in poststratum j ́.

6–6 Section II—Chapter 6 A.C.E. Revision II Estimation

U.S. Census Bureau, Census 2000
P

 ̃

nm, j D  W 
, t P pt ht PRres
, t

t 	 j

t nonmover

production

is the estimated number of nonmover persons with duplicate links who were residents after unduplication.

P nm, j D   W
, t P Pt PRres
, t

t 	 j

t nonmover

production

is the number of P-sample persons with duplicate links,

regardless of whether they were determined to be residents by the unduplication process.

THE A.C.E. REVISION II DSE FORMULA

The A.C.E. Revision II DSE formula, using procedure C for

movers, separate E- and P-sample post-strata, measurement error corrections from the E- and P- Revision

Samples, and duplicate study results is:

DSEij

C 

Cenij  rDD, ij 

[CEi

ND f 1, i ́  CE ̃

i

D

Ei

]

[

M nm, j

ND f 2, j ́ M ̃ nm, jD  [

M om, j f 3, j ́

P om,j f 4, j ́

]P im, j f 5, j ́  g P nm, j

D  P

 ̃ nm, j

D 

P nm, j

ND f 6, j ́  P

 ̃

nm,j

D + Pim, j f 5, j ́  g Pnm, jD  P

 ̃ nm, j

D 

]

Notation

Terms CE Correct enumerations

E E-sample total

M Matches

P P-sample total

f Adjusts for measurement error

g Adjusts nonmovers to movers due to

duplication

Subscripts i,j Full E and P post-strata

i ́, j ́ Revision E and P measurement error

correction post-strata

nm, om, im nonmover, outmover, inmover

Superscripts C DSE procedure C for movers

ND Not a duplicate to census enumeration

outside search area

D Duplicate to census enumeration outside search

area

∼ Includes probability adjustment for residency

given duplication

In some small post-strata, the number of inmovers was

substantially larger than the number of outmovers. If there

were only a few outmovers, the outmover match rate was

subject to high sampling error. In these post-strata, it was

not considered appropriate to apply a suspect match rate

to what could be a relatively large number of inmovers, so

PES-A was used. PES-A uses only outmovers. PES-A was

applied for post-strata with nine or fewer P-sample outmovers. For these post-strata, it was assumed that some

of the duplicate links determined not to have been residents were really outmovers.

The DSE formula that uses procedure A for movers with

different post-strata for the E- and P-samples is:

DSEij

A  Cenij  rDD, ij 

CEi

Ei

[

Mnm, j  Mom, j

Pnm, j  Pom, j

]

The A.C.E. Revision II DSE formula, using procedure A for

movers, separate E- and P-sample post-strata, measurement error corrections from the E- and P- Revision

Samples, and duplicate study results is written:

DSEij

A 

Cenij  rDD,ij 

[CEi

ND f 1, i ́  CE ̃ iD

Ei

]

[Mnm, j ND f 2, j ́  M ̃

nm, j D  Mom, j f 3, j ́  g Mnm, j D M ̃nm, j D 

Pnm, j ND f6, j ́  P

 ̃

nm, j D  Pom,j f 4, j ́  g Pnm, j D  P

 ̃

nm, j D  ]

This version of the formula is used only when the sample

size for outmovers in the Full P sample is strictly less

than 10. This formula was used 93 times in the A.C.E.

Revision II production process. The new term introduced

in this formula is defined as follows:

Mnm, j D   W
, t p pt PRres
, t PRm
, t

t 	 j

t nonmover

production

is the number of matched P-sample persons with duplicate

links, regardless of whether they were determined to be

residents by the unduplication process.

A.C.E. REVISION II POST-STRATIFICATION DESIGN

The Full E- and P-samples with the original coding results

that were used to produce the March 2001 estimates of

census coverage provided the basis of the A.C.E.

Revision II estimates. The March 2001 A.C.E. estimates

were determined to be unacceptable because of the presence of large amounts of measurement error. These Full

samples were comprised of over 700,000 sample persons

each. Instead of one set of post-stratification variables, the

A.C.E. Revision II estimates include separate post-strata for

the Full E and P samples, indicated by subscripts i and j,

respectively.

Full P Sample

For the Full P sample, the new post-strata were nearly

identical to those used for the March 2001 A.C.E. estimates. The only difference was that the 0-17 age group

A.C.E. Revision II Estimation Section II—Chapter 6 6–7

U.S. Census Bureau, Census 2000
was split into two groups, 0-9 and 10-17, which resulted

in some collapsing differences. The Full P sample, consisting of 480 post-strata, was based on the following characteristics (as opposed to the previous 416 post-strata):

• Race/Hispanic Origin Domain

• Tenure

• Size of Metropolitan Statistical Area

• Type of Census Enumeration Area

• Return Rate Indicator (Low vs. High)

• Region

• Age

• Sex

For the Full P sample, the post-stratum groups either

retained all eight Age/Sex categories or were collapsed to

four Age/Sex categories as shown below:

Figure 6-1. P-Sample Age/Sex Groupings

Age

8 groups 4 groups 1 group*

Male Female Male Female Male Female

0-9

10-17

18-29

30-49

50+

*The 1 group is not used for the Full P-sample post-strata (j), only

the Revision P-sample post-strata (j ́).

Table 6-1 shows the 64 Full P-sample post-stratum groups.

The number in each cell represents the number of

Age/Sex categories in each post-stratum group.

6–8 Section II—Chapter 6 A.C.E. Revision II Estimation

U.S. Census Bureau, Census 2000
Table 6-1. Full P-Sample Post-Stratum Groups and Number of Age and Sex Groupings (j)

Race/Hispanic origin

domain number Tenure MSA/TEA

High return rate Low return rate

NE MW S W NE MW S W

Domain 7

(Non-Hispanic White or

‘‘Some other race’’)

Owner

Large MSA MO/MB 8888848 4

Medium MSA MO/MB 8888488 8

Small MSA & Non-MSA MO/MB 8888488 8

All other TEAs 8888888 8

Nonowner

Large MSA MO/MB 8 8

Medium MSA MO/MB 8 8

Small MSA & Non-MSA MO/MB 8 8

All other TEAs 8 8

Domain 4

(Non-Hispanic Black)

Owner

Large MSA MO/MB

8 8

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

8 8

All other TEAs

Nonowner

Large MSA MO/MB

8 8

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

8 4

All other TEAs

Domain 3

(Hispanic)

Owner

Large MSA MO/MB

8 8

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

8 8

All other TEAs

Nonowner

Large MSA MO/MB

8 8

Medium MSA MO/MB

Small MSA & Non-MSA MO/MB

8 4

All other TEAs

Domain 5

(Native Hawaiian or

Pacific Islander)

Owner 4

Nonowner 4

Domain 6

(Non-Hispanic Asian)

Owner 8

Nonowner 8

American

Indian or

Alaska

Native

Domain 1

(On

Reservation)

Owner 8

Nonowner 8

Domain 2

(Off

Reservation)

Owner 8

Nonowner 8

A.C.E. Revision II Estimation Section II—Chapter 6 6–9

U.S. Census Bureau, Census 2000
Full E Sample

For the A.C.E. Revision II Full E sample, the post-strata

definitions have undergone major revisions. Some of the

original post-stratification variables were omitted and

additional variables were added. Logistic regression models identified several variables, not included in the Full

P-sample post-stratification, that were good indicators of

correct enumeration. The Full E sample, consisting of 525

post-strata, was defined using the following

characteristics:

• Proxy Status

• Race/Hispanic Origin Domain

• Tenure

• Household Relationship

• Household Size

• Type of Census Return (mailback vs. nonmailback)

• Date of Return (early vs. late)

• Age

• Sex

The new variables proxy status, household relationship

and size, and type (mailback/nonmailback) and date

(early/late) of census return are described generally below.

• Proxy Status. Nonproxy includes those housing unit

persons for whom census data were provided by a

household member. Proxy includes those housing unit

persons for whom census data were provided by a nonhousehold member, such as a neighbor or rental agent.

• Household Relationship. The Householder/Nuclear

(HHer/Nuclear) relationship category includes persons

in housing units consisting only of the householder with

spouse or own children (l7 or younger). The ‘‘Other’’

relationship category consists of single-person households and persons in housing units with any other type

of relationship, including unrelated persons.

• Household Size. Household size, or number of persons residing in the housing unit.

• Early/Late Mailback. Persons in mailback housing

units with an earliest form processing date. On or

before March 24 is early and after March 24 is late.

• Early/Late Nonmailback. Persons in nonmailback

housing units with an earliest form processing date. On

or before June 1 is early and after June 1 is late.

For the Full E sample, the post-stratum groups either

retained all eight Age/Sex categories or were collapsed to

four, two, or one Age/Sex groups, based on sample sizes,

as shown below:

Figure 6-2. E- Sample Age/Sex Groupings

Age

8 groups 4 groups 2 groups 1 group

Male Female Male Female Male Female Male Female

0-9

10-17

18-29

30-49

50+

Table 6-2 shows the 93 Full E-sample post-stratum groups.

The number in each cell represents the number of

Age/Sex categories in each post-stratum group.

6–10 Section II—Chapter 6 A.C.E. Revision II Estimation

U.S. Census Bureau, Census 2000
Table 6-2. Full E-Sample Post-Stratum Groups and Number of Age and Sex Groupings

Proxy status & domain Tenure Relationship HH Size Early

mailback

Late

mailback

Early

nonmailback

Late nonmailback

Proxy: Domain 7 (Non-Hispanic White or ‘‘Some Other Race’’) 8

Proxy: Domain 4 (Non-Hispanic Black) 8

Proxy: Domain 3 (Hispanic) 8

Proxy: Domain 5 (Native Hawaiian or Pacific Islander) 1

Proxy: Domain 6 (Non-Hispanic Asian) 4

Proxy: Domain 1 (America Indian or Alaska Native On Reservation) 4

Proxy: Domain 2 (American Indian or Alaska Native Off Reservation) 1

Nonproxy:

Domain 7

(Non-Hispanic White or ‘‘Some Other Race’’)

Owner

HHer/Nuclear

2-3 8 8 8 8

4+ 8 8 4 8

Other

1 221 2

2-3 8 8 2 4

4+ 8 8 4 8

Nonowner

HHer/Nuclear 8 8 8 8

Other 8 8 8 8

Nonproxy:

Domain 4

(Non-Hispanic Black)

Owner

HHer/Nuclear 4 4 2 4

Other 8 8 4 8

Nonowner

HHer/Nuclear 8 8 8 8

Other 8 8 8 8

Nonproxy:

Domain 3

(Hispanic)

Owner

HHer/Nuclear 8 8 4 8

Other 8 8 4 8

Nonowner

HHer/Nuclear 8 8 8 8

Other 8 8 8 8

Nonproxy:

Domain 5

(Native Hawaiian or Pacific Islander)

Owner &

Nonowner

HHer/Nuclear 2 2 2 2

Other 2 2 1 2

Nonproxy:

Domain 6

(Non-Hispanic Asian)

Owner &

Nonowner

HHer/Nuclear 8 8 4 4

Other 4 4 2 4

Nonproxy:

(American Indian or Alaska Native)

Domain 1

On Reservation

Owner &

Nonowner

HHer/Nuclear 8

Other 8

Domain 2

Off Reservation

Owner &

Nonowner

HHer/Nuclear 2 2 2 2

Other 2 2 1 2

A.C.E. Revision II Estimation Section II—Chapter 6 6–11

U.S. Census Bureau, Census 2000
Revision P Sample

The Revision P sample is a subsample of the Full P sample

and is comprised of over 60,000 sample persons. The

Revision P sample has been subjected to an additional

field interview and/or rematching operation as part of the

original A.C.E. evaluation program. In support of the

A.C.E. Revision II program, the Revision P sample has

undergone extensive recoding using all available interview

data and matching results. Missing data adjustments have

also been applied to the Revision P sample. This recoded

data are used to correct for measurement error in the Full

P sample.

The measurement error correction post-stratum definitions

(j ́ ) depend on a person’s mover status. Both inmovers

and outmovers are subdivided into Owner and Nonowner

groups. For nonmovers, the measurement error correction

post-strata are: American Indians on Reservations (AIR)

and, for the Non-AIR cases, a cross of Tenure (Owner versus Nonowner) with eight Age and Sex categories. The

Age/Sex collapsing pattern from the Full P sample is

retained when defining the measurement error correction

post-strata. The Revision P-sample post-strata (j ́ ) are

defined as follows:

Figure 6-3. Revision P-Sample Post-Strata (j ́)

Mover Status & Domain Tenure Age

8 groups

1 group

Male Female

Movers:

Domains 1 thru 7

Owner

Nonowner

Nonmovers:

Domains 2 thru 7

Owner

0-9

N/A

10-17

18-29

30-49

50+

Nonowner

0-9

N/A

10-17

18-29

30-49

50+

Nonmovers:

Domain 1 (American Indian or Alaska Native On Reservation)

N/A means not applicable.

6–12 Section II—Chapter 6 A.C.E. Revision II Estimation

U.S. Census Bureau, Census 2000
Revision E Sample

The Revision E sample is a subsample of the Full E sample

and is comprised of over 75,000 sample persons. The

Revision E sample has been subjected to an additional

field interview and/or rematching operation as part of the

original A.C.E. evaluation program. In support of the

A.C.E. Revision II program, the Revision E sample has

undergone extensive recoding using all available interview

data and matching results. Missing data adjustments have

also been applied to the Revision E sample. These recoded

data are used to correct for measurement error in the Full

E Sample.

For the Revision E sample, the measurement error correction post-strata are: Proxies, American Indians on Reservations (AIR) and, for the Nonproxy/Non-AIR cases, a cross

of a two-level Relationship variable with eight Age/Sex

categories. Note that Household Size is collapsed out of

the Household Relationship/Size variable. The Age/Sex

collapsing pattern from the Full E sample is retained when

defining the measurement error correction post-strata. The

Revision E sample post-strata (i ́ ) are defined as follows:

Figure 6-4. Revision E-Sample Post-Strata (i ́)

Proxy Status

& Domain Relationship Age

8 groups

1 group

Male Female

Proxy:

Domain 7 (Non-Hispanic White or ‘‘Some Other Race’’)

Domain 4 (Non-Hispanic Black)

Domain 3 (Hispanic)

Domain 5 (Native Hawaiian or Pacific Islander)

Domain 6 (Non-Hispanic Asian)

Domain 1 (American Indian or Alaska Native On Reservation)

Domain 2 (American Indian or Alaska Native Off Reservation)

Nonproxy:

Domains 2 thru 7

HHer/Nuclear

0-9

N/A

10-17

18-29

30-49

50+

Other

0-9

N/A

10-17

18-29

30-49

50+

Nonproxy:

Domain 1 (American Indian or Alaska Native On Reservation)

N/A means not applicable.

A.C.E. Revision II Estimation Section II—Chapter 6 6–13

U.S. Census Bureau, Census 2000
ADJUSTMENT FOR CORRELATION BIAS USING

DEMOGRAPHIC ANALYSIS

The dual system estimates are adjusted to correct for correlation bias. Correlation bias exists whenever the probability that an individual is included in the census is not

independent of the probability that the individual is

included in the A.C.E. This form of bias generally has a

downward effect on estimates, because people missed in

the census may be more likely to also be missed in the

A.C.E. Estimates of correlation bias are calculated using

the ‘‘two-group model’’ and sex ratios from Demographic

Analysis (DA). The sex ratio is defined as the number of

males divided by the number of females. This model

assumes no correlation bias for females or for males

under 18 years of age; no correlation bias adjustment for

non-Black males aged 18-29; and that Black males have a

relative correlation bias that is different than the relative

correlation bias for non-Black males. The correlation bias

adjustment is also done by three age categories: 18-29,

30-49, and 50 and over. This model further assumes that

relative correlation bias is constant over male post-strata

within age groups. The Race/Hispanic Origin Domain variable is used to categorize Black and non−Black.

The DA totals are adjusted to make them comparable with

A.C.E. Race/Hispanic Origin Domains. Black Hispanics are

subtracted from the DA total for Blacks and added to the

DA total for non-Blacks. This is done because the A.C.E.

assigns Black Hispanics to the Hispanic domain, not the

Black domain. The second adjustment deletes group quarters people from the DA totals using Census 2000 data.

The reason for making this adjustment is that the group

quarters population is not part of the A.C.E. universe. A

final adjustment that could be made would be to remove

the Remote Alaska population from the DA totals, since it

too is not part of the A.C.E. universe. Since this population

is small, the DA sex ratios would not be affected in any

meaningful way. The resulting DA sex ratios for the three

age groups by Black and non-Black domain are shown in

Attachment 3.

In general the correlation bias adjustment factor, ck, is

defined for k=3 age groups such that:

E [ck DSEk

m]  True male population for age group k,

where

DSEk

m is the sum of DSEs over male post-strata in age

group k.

Since the purpose of this adjustment is to reflect persons

missed in both the census and the A.C.E., the value of ck

was not allowed to be less than one.

Correlation Bias Adjustment for Black and

Non-Black Males 18 Years and Older

The correlation bias adjustment for Black and non-Black

males 18 years and older is done so that the A.C.E Revision II sex ratios will agree with the DA sex ratios for

Blacks and non-Blacks. This correlation bias adjustment is

calculated as:

cR, k  ( 

ij 	 k DSE ij

Rf



ij 	 k DSEij

Rm

)rDAR, k

where

DSEij

Rf = DSE for race, R=Black or non-Black, female

post-strata ij.

DSEij

Rm = DSE for race, R=Black or non-Black, male poststrata ij.

rDAR,k = DA sex ratio for race, R=Black or non-Black, for

age group k as given in Attachment 3.

The sum over the ij post-strata includes only the intersection of those post-strata with age group k.

DSEs Adjusted for Correlation Bias

A correlation bias-adjusted DSE for a male, 18+ poststratum ij in age-race group k is calculated as:

DS ̃Eij

m  ck DSEijm

For all remaining post-strata, which includes female poststrata as well as post-strata for persons under 18 years of

age, no correlation bias adjustment is done. Thus:

DS ̃E ij

f  DSE ijf

The DS ̃Eij’s are then used to form synthetic estimates.

SYNTHETIC ESTIMATION

The coverage correction factors for detailed post-strata ij

are calculated as:

CC ̃ Fij  DS ̃Eij

Cenij

where the DS ̃Eij are the correlation bias-adjusted DSEs for

post-stratum ij.

Cenij’s are the census counts for post-stratum ij. Note that

this Cenij includes late census adds.

A coverage correction factor was assigned to each census

person, except those in group quarters or Remote Alaska.

Effectively, these persons have a coverage correction factor of 1.0. In dealing with duplicate links to group quarters persons, the person in the group quarter was treated

as the correct enumeration, or that this was their correct

residence on Census Day. A synthetic estimate for any

area or population subgroup b is given by:

N

 ̃

b   Cenb, ij CC ̃ Fij

ij 	 b

6–14 Section II—Chapter 6 A.C.E. Revision II Estimation

U.S. Census Bureau, Census 2000
Note that the coverage correction factor can be expressed

as:

CC ̃ Fij  ( DD ij

Cen ij

)(rCE, i

rM, j

) ck

where

rCE, i is the correct enumeration rate component of the

DSE, varying over i post-strata.

rM, j is the match rate component of the DSE, varying

over j post-strata.

ck is the correlation bias adjustment factor, varying

over the Black and non-Black groups and k age

cells.

DDij  Cenij is the data-defined rate, varying over the ij

post-strata.

A.C.E. Revision II Estimation Section II—Chapter 6 6–15

U.S. Census Bureau, Census 2000
Attachment 1.

Rules for Assigning zt & ht for Full P- and E-Sample

Duplicate Links

The Linked Situations and assignment of zt’s and ht’s occur in the order listed below.

Linked situation

(E or P) ⇔ (Census)

Original

E coding zt

Original

P coding ht

1. (Person in a housing unit) ⇔ (Person in a group quarters)

EE 0 NonRes 0

CE/UE 0 Res/UE 0

2a. (Person 18+, child of reference person) ⇔ (Person 18+, not child of reference person)

EE 0 NonRes 0

CE/UE 0 Res/UE 0

2b. (Person 18+, not child of reference person) ⇔ (Person 18+, child of reference person)

EE 0 NonRes 0

CE/UE 1 Res/UE 1

3. (All persons in a housing unit) ⇔ (All persons in another housing unit)

EE 0 NonRes 0

CE/UE z

ˆ

1 Res/UE z

ˆ

1

4. (Child 0-17) ⇔ (Child 0-17)

EE 0 NonRes 0

CE/UE z

ˆ

2 Res/UE z

ˆ

2

5. All remaining linked situations

EE 0 NonRes 0

CE/UE z

ˆ

3 Res/UE z

ˆ

3

EE is erroneous enumeration.

CE is correct enumeration.

UE is unresolved.

Res is resident on Census Day.

NonRes is not a resident on Census Day.

6–16 Section II—Chapter 6 A.C.E. Revision II Estimation

U.S. Census Bureau, Census 2000
Attachment 2.

Control Cells for Linked E Sample

Race/Hispanic Origin Domain Tenure Linked situation Control cell

Domain 4 (Non-Hispanic Black)

Owner

3.

4.

5.

Nonowner

3.

4.

5.

Domain 3 (Hispanic)

Owner

3.

4.

5.

Nonowner

3.

4.

5.

Domain 7 (Non-Hispanic White or ‘‘Some Other Race’’)

Domain 5 (Native Hawaiian or Pacific Islander)

Domain 6 (Non-Hispanic Asian)

Domain 1 (American Indian or Alaska Native On Reservation)

Domain 2 (American Indian or Alaska Native Off Reservation)

Owner

3.

4.

5.

Nonowner

3.

4.

5.

A.C.E. Revision II Estimation Section II—Chapter 6 6–17

U.S. Census Bureau Census 2000
Attachment 3.

Correlation Bias Adjustment Groupings and Factors

Race/Hispanic Origin Domain Age DA sex

ratios

Adjustment

factor

Black:

Domain 4 (Non-Hispanic Black)

18-29 0.90 1.08

30-49 0.89 1.10

50+ 0.76 1.05

Non-Black:

Domain 3 (Hispanic)

Domain 7 (Non-Hispanic White or ‘‘Some Other Race’’)

Domain 5 (Native Hawaiian or Pacific Islander)

Domain 6 (Non-Hispanic Asian)

Domain 1 (American Indian or Alaska Native On Reservation)

Domain 2 (American Indian or Alaska Native Off Reservation)

18-29 1.04 1.00*

30-49 1.01 1.02

50+ 0.86 1.01

*This number set to 1.00 due to the inconsistency between DA and A.C.E. Revision II results.

6–18 Section II—Chapter 6 A.C.E. Revision II Estimation

U.S. Census Bureau Census 2000
Chapter 7.

Assessing the Estimates

INTRODUCTION

The evaluations of the A.C.E. Revision II estimates may be

divided into two categories. One category contains the

evaluations that focus on individual error components.

The other group consists of comparisons of the relative

error between the census and the A.C.E. Revision II estimator.

This chapter provides a brief description of the evaluation

studies. The component errors examined by separate

studies are sampling error, error from imputation model

selection, error due to using inmovers to estimate outmovers in PES-C, synthetic error, error in the identification

of the census duplicates as determined by administrative

records, error in the identification of computer duplicates

as determined by a clerical review, error from inconsistent

post-stratification variables, and potential error arising

from the automated coding of some cases, called the

at-risk coding, in the Revision Sample. The comparisons of

relative error between the census and the A.C.E. Revision

II estimator include a comparison with Demographic

Analysis, the construction of confidence intervals that

account for bias as well as random error, and loss function

analyses. Also in this category is an examination of the

consistency of the estimates of coverage error measured

by the A.C.E. Revision II estimator and the Housing Unit

Coverage Study (HUCS). Although an adjustment for correlation bias is included in the A.C.E. Revision II estimates,

no evaluations address the error in the level of correlation

bias or the model used to distribute it across post-strata.

The reason is that examining alternative models only

accounts for differences in models. Those differences

would reflect the variations in how the several models correct the original DSEs for correlation biases, but would not

reflect the presence or absence of correlation bias in the

corrected DSEs.

SAMPLING ERROR

Sampling error gives rise to random error, which is quantified by sampling variance. The sampling variance is

present in any estimate based on a sample instead of the

whole population. The variance estimation methodology is

a simplified jackknife with the block clusters being the primary sampling unit. The effect of within-cluster subsampling is implicitly captured in the weighting.

The March 2001 A.C.E. data showed that the simplified

jackknife method produces satisfactory variance estimates. Since a correlation bias adjustment was included in

the A.C.E. Revision II estimates, the adjustment for correlation bias was recalculated for each replicate. An alternative variance estimation procedure assumed that the form

of the correlation bias adjustment was a scalar times the

double-sampling estimator. The replication method also

accounts for the A.C.E. block cluster sampling.

SYNTHETIC ERROR EVALUATION

The A.C.E. Revision II has several potential sources of synthetic error. One source involves correcting the individual

post-stratum estimates for error estimates at more aggregate levels, such as corrections for correlation bias and

measurement coding errors. However, the evaluation of

synthetic error focuses on error in small area estimation.

Synthetic estimation bias arises when areas in a poststratum have different coverage error rates, but have the

same census coverage correction factor. To assess synthetic estimation bias for a given area, an estimate based

on data from the area alone, called a direct estimate, must

be developed. Such an estimate is possible for only large

areas. In lieu of direct estimates, synthetic estimation bias

in undercount estimates is estimated from analysis of

‘‘artificial populations’’ or ‘‘surrogate’’ variables whose geographic distributions are known. These surrogate variables

are constructed as best as possible to have patterns similar to coverage error. Sensitivity analyses assess the

impact of synthetic estimation bias for these variables.

The evaluation of synthetic error within post-strata uses

an artificial population analysis similar to those conducted

for ESCAP I and ESCAP II. These studies are documented in

Griffin and Malec (2001, 2001b). This time, however, the

evaluation compares the A.C.E. Revision II estimates and

Census 2000. The study uses loss functions for assessing

the effect of synthetic error. The major products are:

• Estimates of the bias in the difference between census

loss and A.C.E. Revision II estimator loss.

• Indicator of whether the decision to use the A.C.E.

Revision II estimator would have changed due to

synthetic error.

ERROR DUE TO USING INMOVERS TO ESTIMATE

OUTMOVERS IN PES-C

The error due to using inmovers to estimate outmovers is

unique to the PES-C model for dual system estimation

used in the original A.C.E. and the A.C.E. Revision II. For

the PES-C model, the members of the P sample are the

Assessing the Estimates Section II—Chapter 7 7–1

U.S. Census Bureau, Census 2000
residents of the housing units on Census Day. There is

some difficulty in identifying all the residents of all the

housing units on Census Day because some move prior to

the A.C.E. interview. The A.C.E. interview relies on the

respondents to identify those who have moved out, the

outmovers. Since the outmovers are identified by proxies,

many of the outmovers are not recorded. Therefore, the

estimate of outmovers is too low. To avoid a bias caused

by an underestimate of the number of movers, PES-C uses

the number of inmovers to estimate the number of outmovers. The inmovers are those who did not live in the

sample blocks on Census Day, but moved in prior to the

A.C.E. interview. Theoretically, the number of inmovers in

the whole country should equal the number of outmovers.

However, the number of inmovers may not equal the number of outmovers in a post-stratum because of circumstances such as economic conditions causing more people

to move out of an area than to move into an area.

The first step of the methodology consists of raking the

number of outmovers to total inmovers. The distribution

of the raked outmovers may better describe the outmovers than the distribution of the inmovers. The A.C.E. Revision II estimates formed by using the number of inmovers

are compared with the A.C.E. Revision II estimates calculated using the raked number.

ERROR FROM IMPUTATION MODEL SELECTION

This project estimates the uncertainty due to choice of

imputation model by drawing on the analysis of reasonable alternatives to the imputation model conducted in

2001. See Keathley et al. (2001) for details. The ideal

approach would be to repeat the very time-consuming

analysis of reasonable alternatives for the A.C.E. Revision

II estimator. However, this analysis was not conducted due

to limited resources. Instead, an estimate of the additional

variance due to the choice of imputation model is developed using the previous A.C.E. work.

Estimates of the variance component for census coverage

correction factors that account for the missing data error

component due to the imputation of enumeration status,

residency status, match status, and the P-sample noninterview adjustment are formed. The replicates used to

estimate the missing data variance are used in the loss

function analysis to represent the random error due to the

choice of the model’s imputation for missing data.

EXAMINING THE QUALITY OF THE COMPUTER

DUPLICATES WITH ADMINISTRATIVE RECORDS

Administrative records provide an opportunity to examine

the quality of the estimates of duplicate enumerations

used in the A.C.E. Revision II estimates. This study uses

the Statistical Administrative Records System (StARS) 2000

(Leggieri et al., 2002; Judson, 2000) to assess the effectiveness of the automated methodology used in the Further Study of Person Duplication (FSPD) to identify duplicate enumerations. Secondary goals are to provide data

that can be analyzed to determine the nature of the census duplication, so that the information may be used in

reducing census duplication in 2010 and to aid in the

evaluation of the methodology for the construction of

StARS 2000. The study produces a comparison of the estimated amount of census duplication based on administrative records with the estimate from FSPD.

StARS is new methodology that compiles seven administrative records files, including files from IRS, Medicare,

HUD, and Selective Service1. The evaluation uses a previous match between the census and StARS 2000 to assign

an Identification (ID) Number to as many census records

as possible. The process of assigning ID Numbers was

based on name and address. One pass through the census

files used both the address and the name to assign ID

Numbers. A second pass used only the name and birth

date. A census record was assigned an ID Number only if

it was linked with exactly one ID Number.

Census enumerations with the same ID Number are considered duplicates. The method accounts for coincidental

agreement of names by requiring assignment of ID Numbers only when exactly one ID Number was linked to the

enumeration. In most cases, two people with very similar

names and characteristics would have linked to each others’ ID Number and would not have been assigned a

unique ID Number.

CLERICAL REVIEW OF COMPUTER DUPLICATES

The study examines accuracy of the FSPD computer identification of duplication in the census by having clerks

review the enumerations that the computer designates as

duplicates. The clerks determine whether the sets of two

enumerations appear to be the same persons. In addition,

census enumerations identified as duplicates by administrative records, but not by the computer, also have a clerical review. The potential census duplicates identified by

administrative records are a by-product of the evaluation

of the computer duplicates using administrative records.

The review is restricted to duplicates between enumerations in the E sample in the A.C.E. blocks and census enumerations outside the search area. Links between

P-sample nonmatches and enumerations outside the

search area also are reviewed.

The clerical review produces the following:

• Number of E-sample enumerations with false duplicate

links identified by the computer.

1

The Census Bureau obtains administrative data for its StARS

database as authorized by Title 13 U.S.C., section 6 and supported by provisions of the Privacy Act of 1974. Under Title 13,

the Census Bureau is required to protect the confidentiality of all

the information it receives directly from respondents or indirectly

from administrative agencies and is permitted only to use that

information for statistical purposes.

7–2 Section II—Chapter 7 Assessing the Estimates

U.S. Census Bureau, Census 2000
• Number of E-sample enumerations with missed duplicates identified by administrative records that are correct.

• Number of P-sample nonmatches with false duplicate

links identified by the computer.

• Number of P-sample nonmatches with missed duplicates identified by administrative records that are correct.

With these results, the accuracy rate for the computer

identification of duplicates in the census and between the

P-sample nonmatches and the census can be computed.

AT-RISK CODING

The study assesses the amount of error at risk due to not

having each and every case in the Evaluation Follow-up

(EFU) sample reviewed clerically (Adams and Krejsa, 2002).

The data collected in the Evaluation Follow-up of the

A.C.E. found errors in the coding of E-sample census enumeration status and P-Sample residence and match status

that needed to be corrected for the A.C.E. Revision II estimator. Ideally, this would mean recoding the entire A.C.E.

sample, but that was not possible because the Evaluation

Follow-up collected data in only 2,259 out of the 11,303

A.C.E. sample clusters. Even clerically recoding the 70,000

cases in the Evaluation Follow-up sample was not feasible

because of time constraints. A new strategy was devised

to provide the most high quality data in the time allowed

by restricting the clerical review to the more difficult

cases. This strategy reduced the clerical workload to

about 25,000, which could be done, and ensured the largest sample possible for the A.C.E. Revision II estimates.

Since the Person Follow-up (PFU) and the Evaluation

Follow-up (EFU) questionnaires had been keyed and were

available in electronic form, data were combined using an

algorithm based on the keyed data and a clerical coding of

the categories of cases where the computer did not

appear to do a good job.

The method compares the code assigned based on the

PFU questionnaire to the code assigned based on the EFU

questionnaire, and then, determines the best code. The

effectiveness of the computer algorithm is assessed by the

agreement between the two new codes, and a comparison

with recodes assigned in the fall of 2001 to a subsample

of the EFU E sample called the Person Follow-up/

Evaluation Follow-up (PFU/EFU) Review. The PFU/EFU

Review is believed to have been the best A.C.E. coding

operation.

For the P sample in the Evaluation Follow-up, a coding

algorithm for the keyed data from the PFU and EFU questionnaires also was developed. Assessing the quality was

not as easy for the nonmatches and unresolved cases as

for the matches. Although recodes from the PFU/EFU

Review were available for the matches in the P sample,

none of the nonmatches or unresolved cases were

included.

The categories of cases not sent for clerical review had a

high agreement rate between the PFU and EFU codes

assigned by the computer algorithm. For the cases in

these categories where the PFU and EFU disagreed, the

selected code came from the form with more detailed

information. Therefore, there are three types of cases in

the estimation:

1. The PFU and EFU codes assigned by computer agree.

2. The PFU and EFU codes assigned by computer disagree, but are in a category where there is high consistency between the PFU and EFU codes, and either

the PFU form or the EFU form does not have answers

to all the questions. The code for the form with complete data is selected.

3. Clerically assigned codes.

The first group is called the ‘‘at-risk’’ cases. These cases

may have a higher risk of error than the others because

the lack of clerical review, even though the codes assigned

by the computer algorithm agree. However, cases in the

second group may also have error, although they are in a

category with high consistency between the PFU and EFU.

For these cases, there is no way to assess the risk of error

due to the lack of information on one of the forms.

To assess the potential for error, the at-risk cases are

assumed to have the same error rate as cases in their category in the PFU/EFU Review. The potential impact is

assessed by comparing the A.C.E. Revision II doublesampling adjustment factors with the double-sampling

ratios under the assumption that incorporates the error

rates. The double-sampling adjustment factors are

described in Chapter 6.

INCONSISTENCY OF POST-STRATIFICATION

VARIABLES

Inconsistency in the E- and P-sample reporting of the characteristics used in defining the post-strata may create a

bias in the dual system estimate (DSE). This bias affects

the estimation of the P-sample match rate.

The analysis of the post-stratification variables for the

A.C.E. Revision II estimator was similar to the investigation

done for the original A.C.E. The basic approach was to

estimate the inconsistency in the post-stratification variables using the matches, then assume that the rates also

held for the nonmatches. The models used for the inconsistency analysis of the original A.C.E. post-strata,

described in Haberman and Spencer (2001), were fitted in

two steps: (1) models for inconsistency of basic variables,

Assessing the Estimates Section II—Chapter 7 7–3

U.S. Census Bureau, Census 2000
and (2) derivation of inconsistency probabilities for poststratification given the inconsistency probabilities of the

basic variables. The inconsistency probabilities led to an

estimate of the bias in the P-sample match rate that was

used to estimate the bias in the DSE. The approach taken

for the A.C.E. Revision II estimator is to re-calculate the

models in (1) and (2) to reflect revisions in the P-sample

post-stratification and repeat the analysis.

To assess the bias due to inconsistency in the poststratification variables, the A.C.E. Revision II estimates are

calculated with a correction to the match rate for the

inconsistency. Estimates with and without the correction

are then compared.

CONSISTENCY BETWEEN THE A.C.E. REVISION II

ESTIMATOR AND HUCS

The study examines the validity of the A.C.E. Revision II

estimates by assessing the consistency in the results from

the A.C.E. Revision II estimates and the Housing Unit Coverage Study (HUCS) described in Barrett et al. (2001). Since

the A.C.E. Revision II estimates could have been used in

the post-censal estimates program that utilizes the average household size in many calculations, it is important to

consider the consistency between the A.C.E. Revision II

estimates and the HUCS data.

A.C.E. Revision II estimates census coverage for people

and HUCS estimates census coverage for housing units.

Patterns in the differential coverage for demographic and

geographic groups were examined. Similar patterns in the

measures of change in census coverage between 1990

and 2000 for demographic and geographic groups are

expected. If there is a substantial difference in the census

coverage error caused by missing whole households and

by missing people within households, the patterns of differential coverage of people and of housing units may not

have similar patterns.

If there are demographic or geographic groups where the

differential coverage from the A.C.E. Revision II estimator

and HUCS is substantially different, the study attempts to

describe whether the disagreement is a symptom of problems with the A.C.E. Revision II estimator or HUCS, or the

result of legitimate differences in coverage.

RELATIVE ACCURACY OF THE CENSUS AND A.C.E.

REVISION II ESTIMATOR USING DEMOGRAPHIC

ANALYSIS

Demographic Analysis (DA) uses vital records, immigration

statistics, and Medicare data to obtain an estimate of the

population size. Since the methods are somewhat independent of the census, DA provides a method for assessing the relative quality of the census and the A.C.E. Revision II. The consistency of estimates of differential census

coverage from the A.C.E. Revision II estimator and DA are

assessed for demographic groups.

Estimates of differential census coverage are compared by

demographic characteristics, including race, sex, and age.

The estimates of population size based on DA are not

viewed with as much confidence as the estimates of differential coverage. DA does a better job of measuring differences in coverage between groups than population size.

In addition, sex ratios from the A.C.E. Revision II estimates

and DA are compared. The sex ratio is the ratio of males

to females and provides a measure of differential coverage

of males and females, especially when calculated for race

groups.

These comparisons are repeated with 1990 PostEnumeration Survey and DA estimates to provide a context for viewing the comparisons with the 2000 data. An

assessment is conducted to determine whether both methods measure the same change in differential net undercounts from 1990 to 2000.

RELATIVE ACCURACY OF THE CENSUS AND THE

A.C.E. REVISION II ESTIMATOR USING CONFIDENCE

INTERVALS AND LOSS FUNCTION ANALYSIS

Two additional methods of assessing the relative accuracy

of the census and the A.C.E. Revision II estimates are

using confidence intervals for the net undercount rate and

a loss function analysis. Confidence intervals for net

undercount rates are formed using estimates of net bias

and variance. Since most of the data available on the quality of the original A.C.E. is being incorporated in the A.C.E.

Revision II estimates, the estimation of the net bias uses

the data that were not included. In the loss function analysis, the mean squared error weighted by the reciprocal of

the census count is used to estimate loss for levels and

shares for counties and places across the nation and

within state.

Confidence intervals that incorporate the net bias as well

as the variance for the net undercount rate Û provide a

method for comparing the relative accuracy of the census

and the A.C.E. Revision II estimates. The net bias in the

census coverage correction factor is estimated for each

post-stratum. With the estimated bias and variance for

each census coverage correction factor, the bias Bˆ (Uˆ) and

variance Vˆ in the net undercount rate Û are estimated.

Also, 95 percent confidence intervals for the net undercount rate are constructed by

(Uˆ  B

ˆ U

ˆ  2Vˆ , Uˆ  Bˆ Uˆ   2Vˆ ).

Since Û=0 corresponds to no adjustment of the census,

one comparison of the relative accuracy of the census and

the A.C.E. Revision II estimates is based on an assessment

of whether the confidence intervals for the evaluation

post-strata cover 0 and Û.

7–4 Section II—Chapter 7 Assessing the Estimates

U.S. Census Bureau, Census 2000
A loss function analysis for levels and shares compares

the census and the A.C.E. Revision II estimator for counties and places across the nation and within state. The

measure of accuracy used by the loss functions is the

weighted mean squared error with the weights set to the

reciprocal of the census count for levels and the reciprocal

of census share for shares. The motivation for the selected

groupings for the loss functions is their potential use in

the post-censal estimates. These groupings are:

• Levels

• All counties with population of 100,000 or less

• All counties with population greater than 100,000

• All places with population at least 25,000 but less

than 50,000

• All places with population at least 50,000 but less

than 100,000

• All places with population greater than 100,000

• Shares within state

• All counties

• All places

• Shares within U.S.

• All places with population at least 25,000 but less

than 50,000

• All places with population at least 50,000 but less

than 100,000

• All places with population greater than 100,000

• All states

Assessing the Estimates Section II—Chapter 7 7–5

U.S. Census Bureau, Census 2000
Section II.

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