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Statistical Aspects of a Census

Carol C. House

_________________________________________________________________________________

This paper focuses on the statistical aspects of a census. It addresses issues such as the coverage,

classification, sampling, non-sampling error, post collection processing, weighting and disclosure

avoidance. The intent of the paper is to demonstrate that most (if not all) of the statistical issues that

are important in conducting a survey are equally germane to conducting a census. 

KEY WORDS: census, coverage, non-response, error, frames, imputation, disclosure

_________________________________________________________________________________

1 INTRODUCTION1

 In this paper the author will provide a

basic overview of the statistical aspects

of planning, conducting and publishing

data from a census. The intent of the

paper is to demonstrate that most (if not

all) of the statistical issues that are

important in conducting a survey are

equally germane to conducting a census. 

 In order to establish the scope for this

paper, we begin by reviewing some basic

definitions. Webster's New Collegiate

Dictionary defines a “census” to be “a

count of the population and a property

evaluation in early Rome”. Although

particularly appropriate to quote at the

CAESAR conference, we will want to

utilize a broader definition. The

International Statistical Institute (ISI) in

its Dictionary of Statistical Terms defines

a census to be “the complete enumeration

of a population or group at a point in time

with respect to well-defined

characteristics”. This definition is more

useable. We now look at the term

“statistics” to further focus the paper.

Again from ISI we find that statistics is

the “numerical data relating to an

aggregate of individuals; the science of

collecting, analyzing and interpreting

such data.” Together these definitions

render a focus for this paper -- those

issues germane to the science and/or

methodology of collecting, analyzing and

interpreting data through what is intended

to be a complete enumeration of a

population at a point in time with respect

to well-defined characteristics. Further,

because of the nature of the CAESAR

conference, this paper will direct its

discussion to agricultural censuses.

Important issues include the (sampling)

frame, sampling methodology, nonsampling error, processing, weighting,

modeling, disclosure avoidance, and data

dissemination. This paper touches on

each of these issues as appropriate to the

paper’s focus on censuses of agriculture.

2 FRAME

 Whether conducting a sample survey or

a census, a core component of

1This paper was presented at the Conference

on Agricultural and Environmental Statistical

Applications in Rome (CAESAR), June 5-7, 2001. 

Carol House is with the National Agricultural Statistics

Service, Research and Development Division, and is

the Division Director.
2

methodology is the sampling frame. The

frame usually consists of a listing of

population units, but alternatively it

might be a structure from which clusters

of units can be delineated. For

agricultural censuses, the frame is likely

to be a business register or a farm

register. Alternatively it might be a

listing of villages from which individual

farm units can be delineated during data

collection. The use of an area frame is a

third common alternative. Often more

than a single frame is used for a census.

Papers presented at the Agricultural

Statistics 2000 conference highlight the

diversity of sampling frames used for

agricultural censuses (Sward, et. al.;

Kiregyera; David).

There are three basic statistical concerns

associated with sampling frames:

coverage, classification and duplication.

These concerns are equally relevant

whether the frame will be used for a

census or sampled for a survey. 

2.1 Coverage

 Coverage deals with how well the frame

fully delineates all population units. The

statistician’s goal should be to maximize

coverage of the frame and to provide

measures of under-coverage. For

agricultural censuses, coverage often

differs by size of farming operation.

Larger farms are covered more

completely, and smaller farms less so.

Complete coverage of smaller farms is

highly problematic, and statistical

organizations have used different

strategies to deal with this coverage

problem. 

The Australian Bureau of Statistics

(Sward, et. al., 1998) intentionally

excludes smaller farms from their

business register and census of

agriculture. They focus instead on

production agriculture, and maintain that

their business register has good coverage

for that target population. Statistics

Canada (Lim, et. al., 2000) has dropped

the use of an area frame as part of its

census of agriculture, and is conducting

research on using various sources of

administrative data to improve coverage

of its farm register. Kiregyera (1998)

reports that a typical agriculture census in

Africa will completely enumerate larger

operations (identified on some listing),

but does not attempt to enumerate

completely the smaller operations

because of the resources required to do

so. Instead they select a sample from a

frame of villages or land areas, and

delineate small farms within the sampled

areas for enumeration. In the United

States, the farm register used for the 1997

Census of Agriculture covered 86.3% of

all farms, but 96.4% of farms with gross

value of sales over $10,000 and 99.5% of

the total value of agricultural products.

The U.S. uses a separate area sampling

frame to measure under-coverage of its

farm register, and has published global

measures of coverage. They are

investigating methodology to model

under-coverage as part of the 2002

census and potentially publish more

detailed measures of that coverage. 

2.2 Classification

A second basic concern with a sampling

frame is whether frame units are

accurately classified. The primary
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classification is whether the unit is, in

fact, a member of the target population,

and thus should be represented on the

frame. For example, in the U.S. there is

an official definition of a farm:

operations that sold $1,000 or more of

agricultural products during the target

year, or would normally sell that much.

The first part of the definition is fairly

straightforward, but the second causes

consider able difficu lty wit h

classification.

 Classification is further complicated

when a population unit is linked with, or

owned by, another business entity. This

is an ongoing problem for all business

registers. The statistician’s goal is to

employ reasonable, standardized

classification algorithms that are

consistent with potential uses of the

census data. For example, a large

farming operation may be a part of a

larger, vertically integrated enterprise

which may have holdings under semiautonomous management in several

dispersed geographic areas. Should each

geographically dispersed establishment

be considered a farm, or should the

enterprise be considered a single farm

and placed only once on the sampling

frame? Another example is when large

conglomerates contract with small,

independent farmers to raise livestock.

The larger firm (contractor) places

immature animals with the contractee

who raises the animals. The contractor

maintains ownership of the livestock,

supplies feed and other input expenses,

then removes and markets the mature

animals. Which is the farm – the

contractor, the contractee, or both?

2.3 Duplication

 A third basic concern with a sampling

frame is duplication. There needs to be a

one-to-one correspondence between

population units and frame units.

Duplication occurs when a population

unit is represented by more than one

frame unit. Similar to misclassification,

duplication is an ongoing concern with

all business registers. Software is

available to match a list against itself to

search for potential duplication. This

process may eliminate much of the

duplication prior to data collection.

Often it is important in a census or

survey to add questions to the data

collection instrument that will assist in a

post-collection evaluation of duplication.

In its 1997 Census of Agriculture, the

U.S. conducted a separate “classification

error study” in conjunction with the

census. For this study, a sample of

census respondents was re-contacted to

examine potential misclassification and

duplication, and to estimate levels of

both. 

3 SAMPLING

 When one initially thinks of a census or

complete enumeration, statistical

sampling may not seem relevant.

However, in the implementation of

agricultural censuses throughout the

world, a substantial amount of sampling

has been employed. David (1998)

presents a strong rationale for extensive

use of sampling for agricultural censuses,

citing specifically those conducted in

Nepal and the Philippines. The reader is

encouraged to review his paper for more

details. This paper does not attempt an
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intensive discussion of different sampling

techniques, but identifies some of the

major areas where sampling has (or can

be) employed. 

 Reducing costs is a major reason that

statistical organizations have employed

sampling in their census processes. We

have already discussed how agricultural

censuses in Africa, Nepal, and the

Philippines have used sampling

extensively for smaller farms. Sampling

may also be used in quality control and

assessment procedures. Examples

include: conducting a sample survey of

census non-respondents to assist in nonresponse adjustment; or conducting a

specialized follow-up survey of census

respondents to more carefully examine

potential duplication and classification

errors. The U.S. uses a sample survey

based on an area frame to conduct a

coverage evaluation of its farm register

and census. It may be advantageous in a

large collection of data to sub-divide the

population and use somewhat different

questionn aires or colle ctio n

methodologies on each group. Here

again is a role for sampling. For

example, in order to reduce overall

respondent burden some organizations

prepare both aggregated and detailed

versions of a census questionnaire and

use statistical sampling to assign

questionnaire versions to the frame units. 

Alternatively sampling may facilitate

efforts to evaluate the effect of

incentives, to use pre-census letters as

response inducements, or to examine

response rates by different modes of data

collection.

4 NON-SAMPLING ERROR

 Collection of data generates sampling

and non-sampling errors. We have

already discussed situations in which

sampling, and thus sampling error, may

be relevant in census data collection.

Non-sampling errors are always present,

and generally can be expected to increase

as the number of contacts and the

complexity of questions increases. Since

censuses generally have many contacts

and fairly involved data collection

instruments, one can expect them to

generate a fairly high level of nonsampling error. In fact, David (1998)

uses expected higher levels of nonsampling error in his rationale for

avoiding complete enumeration in

censuses of agriculture.

“... [a census produces] higher nonsampling error which is not

necessarily less than the total error in

a sample enumeration. What is not

said often enough is that, on account

of their sizes, complete enumeration

CA’s [censuses of agriculture] use

different, less expensive and less

accurate data collection methods than

those employed in the intercensal

surveys.”

 Two categories of non-sampling error

are response error and error due to nonresponse.

4.1 Response Error

 The literature (Groves; Lyberg, et. al.) is

fairly rich in discussions of various

components of this type of error. Selfenumeration methods can be more
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susceptible to certain kinds of response

errors, which could be mitigated, if

interviewer collection were employed.

Censuses, because of their large size, are

often carried out through selfenumeration procedures. The Office of

National Statistics in Britain (Eldridge,

et. al; 2000) has begun to employ

cognitive interviewing techniques for

establishment surveys much the same as

they have traditionally employed for

household surveys. They conclude that

the “... use of focus groups and in-depth

interviews to explore the meaning of

terms and to gain insight into the

backgrounds and perspectives of

potential respondents can be very

valuable ...” They further conclude

regarding self-administered collection

that “...layout, graphics, instructions,

definitions, routing etc. need testing.”

Kiregyera (1998) additionally focuses

readers’ attention on particular

difficulties that are encountered when

collecting information from farmers in

developing countries. These include the

“failure of holders to provide accurate

estimates of crop area and production ...

attributed to many causes including lack

of knowledge about the size of fields and

standard measurement units, or

unwillingness to report correctly for a

number of reasons (e.g. taboos, fear of

taxation, etc.).” 

 The statistician’s role is fourfold: to

understand the “total error” profile of the

census, to develop data collection

instruments and procedures that

minimize total error, to identify and

correct errors during post collection

processing, and to provide, to the extent

reasonable, measures of the important

components of error.

4.2 Non-Response 

 The statistician’s role in addressing nonresponse is very similar to his/her role in

addressing response error: to understand

the reasons for non-response, to develop

data collection procedures that will

maximize response, to provide measures

of non-response error, and to impute or

otherwise adjust for those errors.

Organizations employ a variety of

strategies to maximize response. These

include publicity, pre-collection contacts,

and incentives. Some switch data

collection modes between waves of

collection to achieve higher response

rates. Others are developing procedures

that allow them to target non-response

follow-up to those establishments which

are most likely to significantly impact the

estimates. (McKenzie, 2000)

 A simple method for adjusting for unit

non-response in sample surveys, is to

modify the sampling weights so that

respondent weights are increased to

account for non-respondents. The

assumption in this process is that the

respondents and non-respondents have

similar characteristics. Most often, the

re-weighting is done within strata to

strengthen the basis for this assumption.

A parallel process can be used for

censuses. Weight groups can be

developed so that population units within

groups are expected to be similar in

relationship to important data items. All

respondents in a weight group may be

given a positive weight, or donor
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respondents may be identified to receive

a positive weight. Weight adjustment for

item non-response, although possible,

quickly becomes complex as it creates a

different weight for each item. 

 Imputation is widely used to address

missing data, particularly that due to item

non-response. Entire record imputation

is also an appropriate method of

addressing unit non-response. Manual

imputation of missing data is a fairly

widespread practice in data collection

activities. Many survey organizations

have been moving toward more

automated imputation methods because

of concerns about consistency and costs

associated with manual imputation, and

to improve the ability to measure the

impact of imputation. Automating

processes like imputation are particularly

important for censuses because of the

volume of records that must be

processed.

 Yost et. al. (2000) identify five

categories of automated imputations: i)

deterministic imputation – where only

one correct value exists (such as the

missing sum at the bottom of a column of

numbers; ii) model-based imputation –

use of averages, medians, ratios,

regression estimates, etc. to impute a

value; iii) deck imputation – a donor

questionnaire is used to supply the

missing value; iv) mixed imputation –

more than one method used; and v) the

use of expert systems. Many systems

make imputations based on a specified

hierarchy of methods. Each item on the

questionnaire is resolved according to its

own hierarchy of approaches, the next

being automatically tried when the

previous method has failed. A nearest

neighbor approach based on spatial

“nearness” may make more sense for a

census, where there is a greater density of

responses, than it would in a more

sparsely distributed sample survey.

5 POST COLLECTION

PROCESSING

 Post collection processing involves a

variety of different activities, several of

which (imputation, weighting, etc.) are

discussed in other sections of this paper.

Here we will briefly address editing and

analysis of data. Because of the volume

of information associated with a census

data collection, it becomes very

important to automate as many of these

edit and analyses processes as possible.

Atkinson and House (2001) address this

issue and provide several guiding

principles that the National Agricultural

Statistical Service is using in building an

edit and analysis system for use on the

2002 Census of Agriculture: a) automate

as much as possible, minimizing required

manual intervention; b) adopt a “less is

more” philosophy to editing, creating a

leaner edit that focuses on critical data

problems; and c) identify problems as

early as possible. 

 Editing and analysis must include the

ability to examine individual records for

consistency and completeness. This is

often referred to as “micro” editing or

“input” editing. Consistent with the

guiding principles discussed above, the

Australian Bureau of Statistics has

implemented the use of significance

criteria in input editing of agricultural

data. (Farwell and Raine, 2000) They
7

contend that “... obtaining a corrected

value through clerical action is expensive

(particularly if respondent re-contact is

involved) and the effort is wasted if the

resulting actions have only a minor effect

on estimates." They have developed a

theoretical framework for this approach. 

 Editing and analysis must also include

the ability to perform macro-level

analysis or output editing. These

processes examine trends for important

subpopulations, compare geographical

regions, look at data distributions and

search for outliers. Desjardins and

Winkler (2000) discuss the importance of

using graphical techniques to explore

data and conduct outlier and inlier

analysis. Atkinson and House concur

with these conclusions and further

discuss the importance of having the

macro-analysis tool integrated effectively

with tools for user-defined ad-hoc

queries.

6 WEIGHTING

When one initially thinks of a census,

one thinks of tallying up numbers from a

complete enumeration, and publishing

that information in a variety of cross

tabulations that add to the total. This

paper has already discussed a variety of

situations in which weighting may be a

part of a census process. In this section

we focus on the interaction between

weighting and the rounding of data

values. 

 Many of the important data items

collected in an agricultural census are

intrinsically “integral” numbers, making

sense only in whole increments (i.e. the

number of farms, number of farmers,

number of hogs, etc.). For these data,

desirable characteristics of the census

tabulation is to have integer values at all

published levels of disaggregation, and to

have those cells sum appropriately to

aggregated totals. 

 The existence of non-integer weights

creates non-integer weighted data items.

Rounding each of the multiple cell totals

creates the situation that they may not

add to rounded aggregate totals. This

issue can be addressed in one of several

ways. In the U.S., the census of

agriculture has traditionally employed the

technique of rounding weights to

integers, and then using these integerized

weights. An alternative would be to

retain the non-integer weights and round

the weighted data to integers. A recent

evaluation of census data in the U.S.

(Scholetsky, 2000) showed that totals

produced using the rounded weighted

data values were more precise than the

total produced using the integerized

weights except for the demographic

characteristics, number of farms, and

ratio per farm estimates. A drawback to

using rounded weighted data values is the

complexity these procedures add to

storing and processing information.

7 MODELING

 Modeling can be effective within a

census process by improving estimates of

small geographic areas and rare

subpopulations. Small area statistics is

perhaps one of the most important

products from a census. However, a

number of factors may impact the

census’ ability to produce high quality
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statistics at fairly disaggregate levels.

The highly skewed distribution of data,

which is intrinsic to the structure of

modern farming, creates estimation

difficulties. For example, many larger

operations have production units which

cross the political or geographic

boundaries used in publication. If data

are collected for the large operation and

published as if the “whole” farm is

contained within a single geographic

area, this result will be an over-estimate

of agricultural production within that area

and a corresponding under-estimate

within surrounding areas. Mathematical

models may be used effectively to

prorate the operation totals to appropriate

geographic areas.

 Census processes for measuring and

adjusting non-response, misclassification,

and coverage may produce acceptable

aggregate estimates while being

inadequate for use at the more

disaggregate publication levels.

Statistical modeling and smoothing

methodology may be used to smooth the

measures so that they produce more

reasonable disaggregate measures. For

example, for the 1997 Census of

Agriculture the U.S. provided measures

of frame coverage at the state level for

farm counts for major subpopulations.

They are evaluating several smoothing

techniques that, if successful, may allow

the 2002 census release to include

coverage estimates at the county level

instead of just state level, and for

production data as well as farm counts.

Although a census may be designed to

collect all information from all

population units, there are many cases in

which circumstances and efficiencies

require that census data not stand alone.

W e have alread y discusse d

methodologies in which a separate survey

may be used to adjust census numbers for

non-response, misclassificaion and/or

coverage. Sometimes sources of

administrative data are mixed with

census data to reduce respondent burden

or data collection costs. Most often the

administrative data must be modeled to

make it more applicable to the census

data elements. Alternatively, some

census collection procedures utilize a

“long” and “short” version of the

questionnaire so that all respondents are

not asked every question. To combine

the data from these questionnaire

versions may also require some type of

modeling.

8 DISCLOSURE AVOIDANCE

The use of disclosure avoidance

methodology is critically important in

preparing census and survey data for

publication. Disclosure avoidance can be

very complex for agricultural census

publications because of the scope,

complexity and size of these

undertakings. Disclosure avoidance is

made more difficult by the highly skewed

nature of the farm population. Data from

large, or highly specialized, farming

operations are hard to disguise, especially

when publishing totals disaggregated to

small geographic areas. 

Disclosure avoidance is typically

accomplished through the suppression of

data cells at publication. A primary

suppression occurs when a cell in a

publication table requires suppressing
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because the data for the cell violates

some rule or rules defined by the

statistical agency. Typical rules include:

 

a) threshold rule: the total number of

respondents is less than some

specified number, i.e. the cell may be

suppressed if it had fewer than 20

positive responses.

b) (n,k) rule: a small number of

respondents constitute a large

percentage of the cell’s value, for

example a (2,60) rule would say to

suppress if 2 or fewer responses made

up 60 percent or more of the cell’s

value.

c) p-percent rule: if a reported value

for any respondent can be estimated

within some specified percentage.

 Secondary suppression occurs when a

cell becomes a disclosure risk from

actions taken during the primary

suppression routines. These additional

cells must be chosen in a way that

provide adequate protection to the

primary cell and at the same time make

the value of the cell mathematically

underivable.

 Zayatz et. al. (2000) have discussed

alternatives to cell suppression. They

propose a methodology that adds “noise”

to record level data. The approach does

not attempt to add noise to each

publication cell, but uses a random

assignment of multipliers to control the

effect of the noise on different types of

cells. This results in the noise having the

greatest impact on sensitive cells, with

little impact on cells that do not require

suppression.

9 DISSEMINATION 

Data products from a census are typically

extensive volumes of interconnected

tables. The Internet, CD-rom, and other

technical tools now provide statistical

agencies with exciting options for

dissemination of dense pools of

information. This paper will discuss

several opportunities to provide high

quality data products.

 The first component of a quality

dissemination system is metadata, or data

about the data. Dippo (2000) expounds

on the importance of providing metadata

to users of statistical products and on the

components of quality metadata.

“Powerful tools like databases and the

Internet have vastly increased

communication and sharing of data

among rapidly growing circles of

users of many different categories. 

This development has highlighted the

importance of metadata, since easily

available data without appropriate

metadata could sometimes be more

harmful than beneficial.” 

“Metadata descriptions go beyond the

pure form and contents of data.

Metadata are also used to describe

administrative facts about data, like

who created them, and when. Such

metadata may facilitate efficient

searching and locating of data. Other

types of metadata describe the

processes behind the data, how the

data were collected and processed,

before they were communicated or

stored in a database. An operational

description of the data collection
10

process behind the data (including e.g.

questions asked to respondents) is

often more useful than an abstract

definition of the “ideal” concept

behind the data.”

 The Internet has become a focal point

for the spread of information. Web users

expect: to have sufficient guidance on

use; to be able to find information

quickly, even if they do not know

precisely what they are looking for; to

understand the database organization and

naming conventions; and to be able to

easily retrieve information once it is

found. This implies the need, at a

minimum, for high quality web design,

searchable databases, and easy to use

print and download mechanisms. The

next step is to provide tools such as

interactive graphical analysis with drilldown capabilities and fully functional

interactive query systems. Graphs, charts

and tables would be linked, and users

could switch between these different

representations of information. Finally,

there would be links between the census

information and databases and websites

containing information on agriculture,

rural development, and economics.

10. SUMMARY 

Conducting a census involves a number

of highly complex statistical processes.

One must begin with a quality sampling

frame, in which errors due to undercoverage, mis-classification and

duplication are minimized. There may be

opportunities in which statistical

sampling will help bring efficiency to the

data collection or facilitate quality

control measurements. Non-sampling

errors will be present, and the design

must deal effectively with both response

and non-response errors. Post collection

processing should allow both micro and

macro analysis. Census processing will

probably involve weighting and some

type of modeling. The dissemination

processes should prevent disclosure of

respondent data while providing useful

access by data users.

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