United States

Department of

Agriculture

National

Agricultural

Statistics

Service

Research Division

SRB Research Report

Number SRB-94-10

October 1994

REDRAWING THE 1993 FARM

COSTS AND RETURNS SURVEY

LIST FRAME SAMPLE TO

REDUCE ITS OVERLAP WITH

THE 1992 FCRS AND THREE

OTHER MAJOR 1993 SURVEYS

Charles R. Perry

Jameson C. Burt

William C. Iwig
REDRAWING THE 1993 FARM COSTS AND RETURNS SURVEY LIST

FRAME SAMPLE TO REDUCE ITS OVERLAP WITH THE 1992 FCRS AND

THREE OTHER MAJOR 1993 SURVEYS, by Charles R. Perry, Jameson C. Burt,

and William C. Iwig, Sampling and Estimation Research Section, Survey Research Branch,

Research Division, National Agricultural Statistics Service, U.S. Department of Agriculture,

Washington, D.C. 20250, October, 1994, Report No. SRB 94-10.

ABSTRACT

This report describes the Two Stage Algorithm used by the National Agricultural Statistics

Service (NASS) to redraw the 1993 Farm Costs and Returns Survey (FCRS) list frame

sample. This algorithm was devised to reduce the number of farm and ranch operators in

the FCRS sample that are also in other major surveys’ samples. It decreased the number of

operators in the 1993 FCRS sample that were also in one or more of the four other major

surveys from 4,561 to 1,966 (a decrease of 57 percent). It decreased the number of operators

in the 1993 FCRS sample that were also in the previous year’s FCRS sample from 469 to 29

(a decrease of 94 percent). It increased the number of operators in the 1993 FCRS sample

that were not in any of the four other major surveys from 6,617 to 9,212 (an increase of 39

percent). It is recommended that a five stage algorithm be used to redraw the 1994 FCRS

sample.

KEYWORDS

Respondent Burden, Multiple Selection, Cross-classification, Sample Coordination.

This report was prepared for distribution to the research community outside the U.S.

Department of Agriculture. The views expressed herein are not necessarily those of NASS

or USDA.

ACKNOWLEDGEMENTS

We would like to thank Jim Davies for suggesting the application discussed in this report

and to express our appreciation once more to Ron Bosecker, George Hanuschak and Jim

Davies for their continued support of our research into sampling methods that reduce burden.

We would like to express our appreciation to Charles Day for a thorough job of technical

editing, which greatly improved the readability of the report. We would also like to thank

Vic Tolomeo, Joe Prusacki, and Wayne Dionne for their assistance in retrieving the large

amount of data required for this application.

i
Table of Contents

SUMMARY iii

INTRODUCTION 1

ALGORITHM 2

First Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Second Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Reasons for Using a Two Stage Algorithm . . . . . . . . . . . . . . . . . . . . . . 10

RESULTS 11

U.S. Level Burden Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

State Level Burden Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

U.S. Level Control Variable Estimates . . . . . . . . . . . . . . . . . . . . . . . . 17

BIAS CONSIDERATIONS 17

For the 1993 FCRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

For the 1994 FCRS, If the Same Algorithm is Used . . . . . . . . . . . . . . . . . 23

For the 1994 FCRS, If a Four Stage Algorithm is Used . . . . . . . . . . . . . . . 24

For the 1994 FCRS, If a Five Stage Algorithm is Used . . . . . . . . . . . . . . . 26

CONCLUSIONS 27

RECOMMENDATIONS 28

For the 1994 FCRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

For the 1996 Sample Select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

REFERENCES 28

APPENDIX A: Burden Reduction for a Single Stage Algorithm 29

APPENDIX B: Burden Reduction, Overlap Reduction, and Bias, for the Four

Stage and Five Stage Algorithms 33

ii
SUMMARY

This report describes a sampling algorithm implemented by the National Agricultural

Statistics Service (NASS) to reduce substantially the number of farmers selected for the

1993 Farm Costs and Returns Survey (FCRS) who were also selected for one or more of

NASS’s three other major 1993 surveys or for the 1992 FCRS. To accomplish this, NASS

employed a two stage process:

1) Redraw the 1993 FCRS sample in order to reduce overlap between the 1993 FCRS sample

and the 1993 Quarterly Agricultural Survey (QAS), Agricultural Labor Survey (ALS),

and Cattle and Sheep Survey (CSS) samples; then,

2) Redraw the sample resulting from the first stage in order to reduce overlap between the

1993 FCRS sample and the 1992 FCRS sample.

The report begins with a description of the two stage algorithm. It proceeds with theoretical

and empirical justification for the algorithm, including tables showing that the estimated

totals for eight control variables are very similar for the original and redrawn samples. Next,

results are given. Tables are presented showing counts for different sample configurations of:

1) Records initially selected for the 1993 FCRS,

2) Records selected at the end of the first stage of the algorithm, and

3) Records selected for the final redrawn sample.

Following the results, conclusions are given. Among other encouraging findings, redrawing

the 1993 FCRS sample:

1) Decreased the number of 1993 FCRS sample units that were in one or more of the other

four surveys from 4,561 to 1,966 (a decrease of 57 percent),

2) Decreased the number of 1993 FCRS sample units that were also in the previous year’s

FCRS sample from 469 to 29 (a decrease of 94 percent), and

3) Increased the number of 1993 FCRS sample units that were not in any of the other four

surveys from 6,617 to 9,212 (an increase of 39 percent).

iii
It should be noted that the redrawn sample was based on stratification and sample select

information from the 1992 and 1993 list frame spring classify and sample select. The analysis

does not reflect reclassification and resampling (after spring classify and sample select) of

some records in 1992 in certain states’ Cost of Production specialty strata (California (rice),

Michigan (sugar beets), Ohio (sugar beets), and Florida (sugar cane)). It should also be

noted that the records selected in Illinois, Iowa, and Minnesota for the 1993 CUFFS were

excluded from the redrawing process and analysis.

The potential for bias resulting from the second stage of the algorithm in 1993 is discussed.

It is concluded that any such bias will be much less than one percent of the 1993 FCRS

estimates, hence undetectable in light of the coefficients of variation associated with the

estimates.

It is recommended that a five stage algorithm, which is an extension of the two stage

algorithm used in 1993, be used to redraw the 1994 FCRS sample. The two stage algorithm

would increase the potential for bias in the 1994 estimates. By using the five stage algorithm,

the potential for bias in the 1994 FCRS estimates will be only slightly greater than in 1993,

while the reduction in burden will remain essentially the same.

iv
Redrawing the 1993 Farm Costs and Returns Survey List Frame

Sample to Reduce its Overlap with the 1992 FCRS and Three

other Major 1993 Surveys

Charles R. Perry, Jameson C. Burt, William C. Iwig

INTRODUCTION

Because of the length of the Farm Costs

and Returns Survey (FCRS) questionnaire,

the detail of the information required

to answer many FCRS questions, and

the intrusive nature of the information

asked for in many FCRS questions, there

exists a general agreement among National

Agricultural Statistics Service (NASS)

statisticians and interviewers that the

FCRS causes more burden on a respondent

than any other NASS survey.

In the last few years, as the number of

public and private surveys has increased,

statisticians and other government officials

have become increasingly concerned about

the burden these surveys place on individual respondents. The widely held belief is

that the burden experienced by individual

respondents tends to increase nonlinearly

as they are asked to participate in multiple surveys over a short time period. This

means that the burden placed on the population can be reduced by minimizing the

number of times any one individual is contacted. For example, burden is reduced by

contacting two individuals for one survey

each instead of contacting one individual

for two surveys.

In addition to reducing burden, there are

two other reasons for spreading the burden

over the population to the extent possible.

First, responding to surveys is one of the

costs of providing agricultural statistics.

To the extent that these statistics benefit

farmers, it is more equitable that their

costs be shared equally among farmers.

Second, at some level of burden, farmers

may refuse to participate in surveys. By

spreading the burden to more farmers, the

number of refusals should be reduced.

The points above lead most NASS

statisticians to conclude that the FCRS

sample should be selected using a method

that minimizes the overlap within survey

cycles between the FCRS sample and

other major survey samples and minimizes

the overlap across survey cycles between

FCRS samples. The general assumption

is that decreasing the number of times

NASS contacts individual farm and ranch

operators (farmers) should decrease the

burden placed on the farm population.

This should not only improve the overall

response rates and quality of NASS

surveys, but it should also improve the

cooperation farmers give to NASS and

other survey organizations.

In “Methods of Selecting Samples In

Multiple Surveys To Reduce Respondent

Burden,” Perry, Burt, and Iwig (1993)

presented two new methods of drawing

samples in multiple surveys that minimize

the burden on the individual population

units sampled. These new methods work

by spreading the burden from multiple

surveys as uniformly as possible over the

1
population without changing the selection

probabilities for any survey.

This report describes how a special case

of the Second-Method presented by Perry,

Burt, and Iwig (1993) was first used to

redraw the 1993 FCRS list frame sample

so that its overlap with the 1993 Quarterly

Agricultural Survey (QAS), Agricultural

Labor Survey (ALS), and Cattle and

Sheep Survey (CSS) is minimized and then

used again to randomly shift the redrawn

sample where necessary so that its overlap

with the 1992 FCRS is minimized.

In the remainder of this report, the

qualifying phrase list frame is dropped

from terms such as list frame sample.

Since this report deals exclusively with the

list frame part of NASS surveys, these

abbreviations should cause no ambiguity.

The first section of this report describes

the two stage algorithm used to redraw

the 1993 FCRS sample. Within groups

of farmers having the same multivariate

stratification for the four major 1993

surveys (that is to say, farmers A and

B are in the same group when farmer A

is in the same stratum as farmer B for

all four surveys), the first stage of the

algorithm randomly shifts the 1993 FCRS

sample, where possible, to another sample

of farmers having lower burden for the four

1993 surveys. Within groups of farmers

having the same multivariate stratification

for the 1992 and 1993 FCRS surveys, the

second stage of the algorithm randomly

shifts the part of first stage sample that

overlaps with the 1992 FCRS sample,

where possible, to another sample of

farmers who were not in the 1992 FCRS

sample.

The second section describes the results of

redrawing the 1993 FCRS sample. Tables

are given that show a detailed breakdown

of the burden associated with the initial,

first stage, and final redrawn samples

along with the burden reduction achieved

by redrawing the sample. Also, tables

are given that show, for eight population

control variables, the estimated totals and

coefficients of variation that are associated

with the initial, first stage, and redrawn

samples.

The third section discusses any possible

bias that may be introduced into the

estimates by the algorithm. Particularly,

the bias that could result from the second

stage of the algorithm is examined. In

addition, the potential for bias that arises

when the algorithm is applied in two

consecutive years is examined. Finally,

four stage and five stage algorithms are

introduced and examined which limit the

potential for bias that arises when the

algorithm is applied in two consecutive

years.

The fourth and fifth sections respectively

give conclusions and recommendations for

redrawing the 1994 FCRS that result from

what has been learned in the course of

redrawing the 1993 FCRS sample.

ALGORITHM

There are three steps to the SecondMethod described by Perry, Burt, and

Iwig (1993) for drawing multiple surveys

samples that minimize the burden on the

individual units sampled:

Step 1. Use an equal probability of selection procedure within each stratum to select independent stratified samples for each survey.

2
Step 2. Cross-classify the population by

the stratifications used in the

individual surveys.

Step 3. Within each substratum, randomly reassign the samples associated with sampling units having

excess burden to population units

having less burden. Repeat the

process until the burden on individual units sampled is minimized.

A two stage algorithm is given below that

first redraws the 1993 FCRS sample to

reduce its overlap with the 1993 QAS,

ALS, and CSS samples and then redraws

the redrawn sample to reduce its overlap

with the 1992 FCRS sample. The first

stage of the algorithm randomly shifts

the 1993 FCRS sample within groups

of farmers having the same multivariate

stratification for the four 1993 surveys,

where possible, to another sample of

farmers having lower burden for the four

1993 surveys. The second stage of

the algorithm randomly shifts the part

of first stage sample that overlaps with

the 1992 FCRS sample within groups

of farmers having the same multivariate

stratification for the 1992 and 1993 FCRS

surveys, where possible, to other farmers

who were not in the 1992 FCRS sample.

It will be shown that the first stage of the

algorithm is a special case of the SecondMethod. Thus, the FCRS estimates that

are based on the first stage sample have

the same expected values as those based

on the original FCRS sample. Under

the assumption that no sample data from

the 1992 FCRS is used to update the

1993 frame, it will be shown that the

second stage of the algorithm is also a

special case of the Second-Method. It then

follows that the FCRS estimates that are

based on the second stage sample have

the same expected values as those based

on the original FCRS sample. It will be

shown that less than four percent of the

sample is redrawn by the second stage of

the algorithm. Consequently, the two stage

algorithm used to redraw the 1993 FCRS

has only a limited potential to introduce

bias into the 1993 FCRS estimates even

if some 1992 sample data were used to

update the 1993 FCRS frame.

First Stage: Redrawing the 1993

FCRS to Reduce “Overlap” with

Three Other Major 1993 Surveys

The sampling procedures used with the

1993 FCRS, QAS, ALS, and CSS satisfy

the condition of Step 1 of the SecondMethod. The cross-classification of the

population required in Step 2 of the

Second-Method is produced by sequentially sorting the population records by

the individual 1993 FCRS, QAS, ALS,

and CSS stratifications.

Throughout the first stage of the algorithm, all of the 1993 samples, except the

1993 FCRS, are assumed to be fixed and

hence cannot be reassigned. Thus, the

reassignment required in Step 3 of the

Second-Method is produced by Steps B

through F of the algorithm below. Steps BF randomly reassign the 1993 FCRS sample so that the total burden from all

four 1993 surveys on the farmers in the

1993 FCRS sample is minimized.

Step A: Merge the stratification and sample selection information from

the 1992 FCRS frame onto the

1993 FCRS frame.

3
Note: The first stage of the algorithm

is totally independent of the 1992 FCRS.

Nevertheless, the 1992 FCRS stratification

and sample information is merged onto the

1993 FCRS frame at this point so that it

can be made clear how the first stage of the

algorithm interacts with the 1992 FCRS

sample. This information will be used

in the second stage of the algorithm to

minimize the overlap of the 1993 FCRS

sample with the 1992 FCRS sample.

Step B: Within each of the 1993 FCRS list

frame strata, sequentially sort the

records by:

1. The 1993 QAS strata,

2. The 1993 ALS strata, and

3. The 1993 CSS strata.

This step puts the 1993 FCRS

list frame records into substrata

such that within each substratum

all records have the same multivariate stratification and selection

probabilities with respect to all

four 1993 surveys.

Step C: For each record on the 1993 FCRS

frame, compute the burden that

comes from its being sampled in

the 1993 QAS, ALS, or CSS.

Step D: Within each substratum, sequentially sort the records:

1. In ascending order of the

total burden from the other

three 1993 surveys (the records

are now ordered by ascending

value of the burden from

all 1993 surveys except the

1993 FCRS),

2. In descending order of a zeroone indicator variable, with

one indicating selection for the

initial 1993 FCRS sample (this

places the records initially

selected for the 1993 FCRS

sample first within the burden

groups formed by step D.1,

thus ensuring that records are

redrawn only when it reduces

burden), and

3. In ascending order of a random

number (this randomly orders

the records within each of the

subgroups formed by steps D.1

and D.2).

Step E: Redraw the 1993 FCRS sample by

reassigning within each substratum the initial 1993 FCRS sample

to the first elements of the substratum.

The next step permits a larger sample

to be drawn initially than will actually

be required. The initial sample can be

reduced later to the required size (which

may not be known initially) by dropping

the larger replicates while still minimizing

the burden on the sample.

Step F: Sort the replicate numbers associated with the substratum sample in ascending order and reassign them to the first elements of

the substratum. This assigns the

smaller replicate numbers to the

records with the smaller total burden for the other three 1993 surveys.

The sequence of implications given in

the next paragraph proves the following

4
three assertions, which in turn imply the

conditions of Step 3 of the Second-Method

are satisfied (see page 3).

1. The redrawn FCRS sample for this year

has exactly the same selection probabilities (and hence same expansion factors)

as the initial sample.

2. Within each substratum, the records

are put in random order by the

sequential sort described in Step D

above, which means that within each

substratum the redrawn FCRS sample

is a simple random sample.

3. Within each substratum the redrawn

FCRS sample minimizes the total

burden on individual farmers.

Since the samples are drawn independently

for each individual survey using an equal

probability of selection mechanism within

each stratum and since within each

substratum all farmers have exactly the

same stratification on individual surveys,

the farmers within each substratum

all have the same set of multivariate

selection probabilities. Since within

each substratum all records have exactly

the same probability of experiencing a

specified burden level, it follows that they

are left in simple random order when they

are sorted by ascending (non-decreasing)

burden in Step D of the algorithm. Since

within each substratum the total burden

on any individual farmer from the other

three 1993 surveys is a non-decreasing

function of the final sort order, shifting the

1993 FCRS sample to the first elements

of the substratum selects a simple random

sample that minimizes the total burden

on the individual farmers from all four

1993 surveys. Since the redrawn FCRS

sample is selected as a simple random

sample within substrata, it has the same

expansion factors as the initial FCRS

sample.

Thus, the first stage of the algorithm can

not bias the sample. That is, the FCRS

estimates based on the first stage sample

have the same expected values as those

based on the original FCRS sample.

Example 1:

Applying The First Stage Of The

Algorithm To Reduce The “Overlap” Of

The 1993 FCRS With Other Major

1993 Surveys

Table 1 displays the relevant sample and

burden information for the records in the

Kansas substratum formed by intersecting

1993 FCRS stratum 92, 1993 QAS

stratum 72, 1993 ALS stratum 95, and

1993 CSS stratum 20. The burdens

assigned in this substratum for the FCRS,

QAS, ALS, and CSS are respectively 60,

45, 40, and 25. (To the extent information

was available, burdens were assigned to

reflect the approximate time required for

all expected survey contacts.)

Columns 1 and 2 of Table 1 contain

the sample configurations for the initial

and redrawn samples respectively. The

configurations indicate whether the record

was sampled (1) or not (0) for the

1993 FCRS, 1992 FCRS, 1993 QAS,

1993 ALS, and 1993 CSS respectively.

For example, the sample configurations

for the tenth record of the table are

respectively 10101 and 00101, which

indicate that initially this record was

selected for the 1993 FCRS, QAS, and CSS

but after the 1993 FCRS was redrawn

the tenth record was selected only for the

1993 QAS and CSS. (We note once again

5
Table 1. Example of the Method Used to Redraw the 1993 FCRS in Substrata to Reduce

the Burden from the Overlap with Other 1993 Surveys.

Burden Uniform Burden Rep Code Burden

Initial Redrawn Other Initial Random Redrawn Initial Redrawn Initial Redrawn Initial Redrawn

Sample Sample 1993 1993 FCRS Number 1993 FCRS 1993 1993 FCRS FCRS All All

Configuration Configuration Surveys Sample Attached Sample Samples Samples Sample Sample Samples Samples

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

01000 11000 0 0 0.46313 1 0 60 0 11 60 120

10001 10001 25 1 0.13284 1 85 85 11 25 85 85

00001 10001 25 0 0.05881 1 25 85 0 72 25 85

00001 00001 25 0 0.28983 0 25 25 0 0 25 25

01001 01001 25 0 0.36130 0 25 25 0 0 85 85

00001 00001 25 0 0.47441 0 25 25 0 0 25 25

00001 00001 25 0 0.93427 0 25 25 0 0 25 25

00100 00100 45 0 0.22914 0 45 45 0 0 45 45

00100 00100 45 0 0.86787 0 45 45 0 0 45 45

10101 00101 70 1 0.07412 0 130 70 25 0 130 70

10101 00101 70 1 0.32697 0 130 70 72 0 130 70

00101 00101 70 0 0.61579 0 70 70 0 0 70 70

00101 00101 70 0 0.69437 0 70 70 0 0 70 70

00101 00101 70 0 0.77151 0 70 70 0 0 70 70

00101 00101 70 0 0.93982 0 70 70 0 0 70 70

that the 1992 FCRS Survey is not involved

in this stage of the algorithm.)

Column 3 of Table 1 shows the total

burden placed on the individual farmers

by the three other 1993 surveys. The

entries of this column are computed from

the individual survey burdens and last

three digits of either the initial or redrawn

sample configurations. For example,

the total burden from the other three

1993 surveys for tenth record is given by

1 ∗ 45 + 0 ∗ 40 + 1 ∗ 25 = 70.

Columns 3, 4, and 5 of Table 1 show that

the records are sorted by the conditions

of Step D above. That is, the records

have been sequentially ordered: first, by

ascending order of the total burden from

three other 1993 surveys (see column 3);

second, by the ones initially selected for

the 1993 FCRS sample followed by those

not initially selected (see column 4); third,

by a uniformly distributed random number

(see column 5).

Column 6 of Table 1 shows the redrawn

1993 FCRS sample, which is obtained by

shifting the 1993 FCRS sample to the first

elements of the table. A comparison of

columns 3, 7, and 8 will confirm that since

the records have been ordered in ascending

order of the burden from the other three

1993 surveys, shifting the 1993 sample to

the first three records yields a sample that

places minimum burden on the sampled

farmers. That is, the total burden placed

on the farmers in the redrawn sample by

the four surveys cannot be reduced, either

individually or collectively, by exchanging

a farmer in the redrawn sample for a farmer

not in the redrawn sample.

Column 10 of Table 1 shows the replicate

numbers attached to the redrawn sample,

which are obtained by sorting the set of

positive replicate numbers from column 9

in ascending order and then attaching

them to the first records of Table 1—the

records in the redrawn sample. Notice

6
that, if any set of records with the

larger replicate numbers are dropped from

the redrawn sample, the remainder of

the redrawn sample is such that no

other sample of the same size in this

substratum places lower burden on the

sampled farmers.

Since this stage of the algorithm is

independent of the 1992 FCRS sample,

some records that are initially in both

1992 and 1993 FCRS samples will end up

being only in the 1992 FCRS sample and

some records that are initially in only the

1992 FCRS sample will end up being in

both the 1992 and 1993 FCRS samples.

The first record of Table 1 demonstrates

the later case. The second stage of

the algorithm reduces the overlap of the

1993 FCRS sample with the 1992 FCRS

sample. To help clarify the situation, the

total burden from the 1992 FCRS and the

four major 1993 surveys is given for the

initial and redrawn samples in columns 11

and 12, respectively.

Second Stage: Redrawing the 1993

FCRS to Reduce “Overlap” with the

1992 FCRS

The sampling procedures used with the

1992 FCRS and 1993 FCRS satisfy the

conditions of Step 1 of the Second-Method,

provided no information from the 1992

FCRS sample is used to update the

1993 FCRS frame. The cross-classification

of the population and sample required in

Step 2 of the Second-Method is produced

by sequentially sorting the population

records by the 1993 FCRS and 1992 FCRS

stratifications.

In this stage of the algorithm, the

1992 FCRS sample is predetermined.

Thus, the reassignment required in Step 3

of the Second-Method is produced by

Steps G through K of the algorithm

below. These steps randomly reassign the

1993 FCRS sample redrawn at the end of

the first stage of the algorithm so that the

total burden from the 1992 and 1993 FCRS

on the farmers in the 1993 FCRS sample

is minimized.

Step G: Within each of the 1993 FCRS

list frame strata, sort the records

by the 1992 FCRS strata. This

step puts the 1993 FCRS list

frame records into substrata such

that within each substratum all

records have the same multivariate stratification and selection

probabilities with respect to the

1992 FCRS and the 1993 FCRS

surveys.

Step H: For each record on the 1993 FCRS

frame, compute the burden that

comes from its being sampled in

the 1992 FCRS.

Step I: Within each substratum, sequentially sort the records:

1. In ascending order of the

burden from the 1992 FCRS

(this puts the record not

sampled in the 1992 FCRS first

followed by those that were

sampled in the 1992 FCRS),

and

2. In descending order of a zeroone indicator variable, with

one indicating selection for the

redrawn 1993 FCRS sample at

the end of the first stage of

the algorithm (this places the

records that were selected at

the end of the first stage of the

7
algorithm first within each of

the two burden groups formed

by step I.1, thus ensuring that

records are redrawn only when

redrawing reduces burden),

and

3. In ascending order of a random

number (this randomly orders

the records within each of the

subgroups formed by steps I.1

and I.2).

Step J: Redraw the 1993 FCRS sample

that was selected at the end of

the first stage of the algorithm

by reassigning it within each

substratum to the first elements

of the substratum.

Step K: Reassign the replicate numbers

associated with the substratum

sample that was redrawn at

the end of first stage of the

algorithm to the first elements of

the substratum in their original

order. Except for those few

records that are also in the

1992 FCRS sample, this leaves

the replicate numbers that were

assigned in the first stage of the

algorithm assigned to exactly the

same sample record. The result

is that the minimal overlap of

the 1993 FCRS sample with three

other major 1993 survey samples

achieved at the end of the first

stage of the algorithm is increased

by less than four percent in the

final redrawn 1993 FCRS U.S.

sample.

If no information from the 1992 FCRS

sample is used to update the 1993 FCRS

frame, then it is clear that the sequence

of logical implications given in the two

paragraphs following Step F applies to the

second stage of the algorithm. It then

follows that within each substratum the

second stage redrawn sample is a simple

random sample with the same expansion

factors as the initial FCRS sample.

Thus, if no information from the 1992

FCRS is used to update the 1993 FCRS

frame, then the second stage of the algorithm can not bias the estimates. This

result, along with the unconditional

unbiasness of the first stage which was

established earlier, shows that the FCRS

estimates based on the second stage

sample have the same expected values

as those based on the original FCRS

sample, provided no information from

the 1992 FCRS is used to update the

1993 FCRS frame (see later discussion of

bias).

Example 2:

Applying The Second Stage Of The

Algorithm To Reduce The “Overlap” Of

The 1993 FCRS With The 1992 FCRS

Table 2 displays the relevant sample

and burden information for the records

in the Iowa substratum formed by

intersecting the 1993 FCRS stratum 92

with 1992 FCRS stratum 92. The burdens

assigned the FCRS and ALS in all strata

are respectively 60 and 40. The burden

assigned the QAS in QAS strata 95

through 98 is 85. In other QAS strata

the QAS is assigned a burden of 45.

The burden assigned the CSS in CSS

strata 35 through 39 is 30. In other

CSS strata the CSS is assigned a burden

of 25. (Higher stratum numbers denote

larger farm operations.)

Columns 1 and 2 of Table 2 contain the

sample configurations for the first stage

8
Table 2. Example of the Method Used to Redraw the 1993 FCRS in Substrata to Reduce

the Burden from Overlap with the 1992 FCRS Sample.

First Final Uniform Burden Rep Code Burden

Stage Redrawn Burden Sampled Random Sampled Stage 1 Redrawn Stage 1 Redrawn Stage 1 Redrawn

Sample Sample 1992 FCRS Stage 1 Number Redrawn 92 & 93 92 & 93 FCRS FCRS All All

Configuration Configuration Survey 1993 FCRS Attached 1993 FCRS FCRS FCRS Sample Sample Samples Samples

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

10001 10001 0 1 0.12824 1 60 60 5 5 90 90

10001 10001 0 1 0.61343 1 60 60 7 7 90 90

10101 10101 0 1 0.89720 1 60 60 13 13 135 135

00001 10001 0 0 0.37579 1 0 60 0 2 30 90

00001 00001 0 0 0.59949 0 0 0 0 0 30 30

11001 01001 60 1 0.06257 0 120 60 2 0 145 85

redrawn and the final redrawn samples

respectively. The configurations indicate

whether the record was sampled (1) or

not (0) for the 1993 FCRS, 1992 FCRS,

1993 QAS, 1993 ALS, and 1993 CSS

respectively. For example, the sample

configurations for the sixth record of the

table are respectively 11001 and 01001,

which indicates that after the first stage

of the algorithm this record was selected

for the 1993 FCRS, 1992 FCRS, and

1993 CSS but after the second stage of the

algorithm the record was selected only for

the 1992 FCRS and 1993 CSS.

In the remainder of this report: (1) the

first stage redrawn sample or simply first

stage sample will refer to the redrawn

sample that is obtained by applying the

first stage of the algorithm to the initial

1993 FCRS sample and (2) the final

redrawn sample or simply final sample

will refer to the redrawn sample that is

obtained by applying the second stage of

the algorithm to the first stage redrawn

1993 FCRS.

Column 3 of Table 2 shows the burden

placed on the individual farmers by the

1992 FCRS. Only the last record in

this substratum was selected for the

1992 FCRS.

Columns 3, 4, and 5 of Table 2 show that

the records are sorted by the conditions

of Step I above. That is, the records

have been sequentially ordered: first, by

whether they were or were not selected

for the 1992 FCRS sample (see column 3);

second, by whether they were or were

not selected for the 1993 FCRS sample

at the end of the first stage of the

algorithm (see column 4); third, by a

uniformly distributed random number (see

column 5).

Column 6 of Table 2 shows the final

redrawn 1993 FCRS sample, which is

obtained by shifting the 1993 FCRS

sample selected at the end of the first stage

of the algorithm to the first elements of

the table. A comparison of columns 3, 7,

and 8 will confirm that since the records

have been ordered in ascending order of the

burden from the 1992 FCRS, shifting the

1993 sample to the first four records yields

a sample that has minimum overlap with

the 1992 FCRS sample.

Column 10 of Table 2 shows the replicate

numbers attached to the final redrawn

9
1993 FCRS sample. They are obtained by

reassigning the positive replicate numbers

in column 9, in their original order, to the

first records of Table 2.

Since the redrawing process in this stage of

the algorithm is independent of the other

three 1993 survey samples, some of the

reduction of overlap between 1993 FCRS

sample and the other three 1993 survey

samples that was achieved in the first stage

of the algorithm will be lost. However,

since only about four percent of the

1993 FCRS sample that was selected at

the end of the first stage of the algorithm

overlaps with the 1992 FCRS, which are

the records being redrawn in this stage of

the algorithm, the loss of overlap reduction

with respect to the other 1993 survey

samples will be small.

Reasons for Using a Two Stage

Algorithm Instead of a Single Stage

Algorithm to Redraw the 1993 FCRS

The first stage of the two stage algorithm

can be converted to a one stage algorithm

that minimizes the “overlap” of the

1993 FCRS sample with the 1993 QAS,

ALS, and CSS samples and the 1992 FCRS

sample by including a sequential sort by

the 1992 FCRS strata in Step B and

adding the burden from the 1992 FCRS

to the burden computed in Step C.

So, why choose a two stage algorithm?

The use of the two stage algorithm

limits the potential for introducing bias

into the FCRS estimates. Also, the

two stage algorithm provides considerably

more burden reduction than the one stage

algorithm.

The primary reason the two stage algorithm was used instead of a single stage

algorithm to redraw the 1993 FCRS was to

minimize the potential for introducing bias

into the FCRS estimates. Since the first

stage of the two stage algorithm is

unconditionally unbiased, bias can only be

introduced in the second stage of the two

stage algorithm. Potential for bias will

exist if the 1992 FCRS data have been used

to update the 1993 FCRS frame. This will

be discussed in the Bias Considerations

section.

In the second stage of the two stage

algorithm, the only part of the sample that

is redrawn is the part that overlaps with

the 1992 FCRS sample. Since this part

of the sample amounts to only about four

percent of the sample, it follows that when

the two stage algorithm is used only about

four percent of the redrawn sample has

any potential for biasing the 1993 FCRS

estimates.

In contrast, when the one stage algorithm

is used every element in the redrawn

sample is drawn conditional on the

1992 FCRS sample. Thus, with the

one stage algorithm, every element of the

redrawn sample has a potential for biasing

the 1993 FCRS estimates.

In summary, unless it can be shown

that no information from the 1992 FCRS

sample is used to update the 1993 FCRS

frame, both the single and two stage

algorithms have potential for biasing the

1993 FCRS estimates. With the single

stage algorithm, every element is redrawn

conditional on the 1992 FCRS sample;

but, with the two stage algorithm only

about four percent of the sample is

redrawn conditional on the 1992 FCRS

sample. Thus it follows that there

is much less potential for biasing the

1993 FCRS estimates with the two stage

10
algorithm than there is with the single

stage algorithm.

In addition to the greatly reduced potential

for biasing the 1993 FCRS estimates, the

two stage algorithm provides considerably

more burden reduction than the single

stage algorithm.

In Appendix A, tables are given that show

the burden reduction that would have been

obtained had the single stage algorithm

been used to redraw the 1993 FCRS

sample. Tables 3A, 3B, and 3C, which

are given in the results section, show the

burden reduction that was obtained by

using the two stage algorithm to redraw

the 1993 FCRS sample. A comparison

of these two sets of tables, which should

be made after reading the first results

section below will show that the two

stage algorithm does a much better job

of reducing the burden that comes from

the overlap of the 1993 FCRS sample with

either the 1992 FCRS sample or the other

1993 samples.

RESULTS

The sample of 11,178 farmers surveyed in

the 1993 FCRS was redrawn with the two

step procedure to reduce the number of

farmers sampled in the 1993 FCRS that

were also contacted in the 1992 FCRS or

the other major 1993 surveys. The redrawing process was based on stratification and sample select information from

the 1992 and 1993 list frame spring classify and sample select. This means that

the analysis does not reflect reclassification

and resampling (after spring classify and

sample select) of some records in 1992 in

certain states’ Cost of Production specialty

strata (California (rice), Michigan (sugar

beets), Ohio (sugar beets), and Florida

(sugar cane)). The records that were selected in Illinois, Iowa, and Minnesota for

the 1993 CUFFS were excluded from the

redrawing process and analysis.

The first section below discusses the

reduction in burden achieved by redrawing

the sample. Tables are given that

show a detailed breakdown of the burden

reduction achieved by redrawing the

sample along with the burden associated

with the initial, first stage, and redrawn

samples.

The second section below discusses the

similarity of the redrawn sample to the

initial sample by examining the associated

population control values. Tables are given

that show for each of eight population

control values the estimated totals and

coefficients of variation that are associated

with the initial, first stage, and redrawn

samples.

U.S. Level Burden Reduction

Recall that the reason for redrawing the

1993 FCRS sample was to reduce the

burden on the individual farmers selected

by replacing the initial FCRS sample of

11,178 farmers with another sample of

11,178 farmers which places less burden

on the individuals selected. Also, recall

that the first stage of the algorithm

used to redraw the sample reduced the

overlap of the 1993 FCRS sample with the

other 1993 surveys’ samples and that the

second stage reduced the overlap of the

1993 FCRS sample with the 1992 FCRS

sample.

11
Consequently, the burden reduction achieved by redrawing the 1993 FCRS

can be summarized by the changes (or

percentage changes) that occurred from

the initial to the redrawn sample in the

number of farmers selected for none, one,

two, three, and four of the other surveys

(1992 FCRS, 1993 QAS, ALS, and CSS).

The next three paragraphs summarize

the burden reduction achieved by the

algorithm for the complete 1993 FCRS

sample, the part of the sample in strata 90

and above, and the part of the sample in

strata 89 and below, respectively.

Redrawing the 1993 FCRS sample of

11,178 farmers:

1. Increased the number of 1993 FCRS

samples that were not selected for any

of the other four surveys from 6,617

to 9,212 (an increase of 39 percent),

2. Decreased the number of 1993 FCRS

samples that were selected for only one

of the other four surveys from 3,603

to 1,598 (a decrease of 56 percent),

3. Decreased the number of 1993 FCRS

samples that were selected for exactly

two of the other four surveys from 843

to 325 (a decrease of 61 percent),

4. Decreased the number of 1993 FCRS

samples that were selected for exactly

three of the other four surveys from 107

to 41 (a decrease of 62 percent),

5. Decreased the number of 1993 FCRS

samples that were selected for all of

the other four surveys from 8 to 2 (a

decrease of 75 percent), and

6. Decreased the number of 1993 FCRS

samples that were also in the previous

year’s FCRS sample from 469 to 29 (a

decrease of 94 percent).

Redrawing the strata 90 and above

FCRS sample of 3,795 farmers (the strata

containing farms with sales of $500,000 or

more):

1. Increased the number of 1993 FCRS

samples that were not selected for any

of the other four surveys from 1,361

to 2,317 (an increase of 70 percent),

2. Decreased the number of 1993 FCRS

samples that were selected for only one

of the other four surveys from 1,760

to 1,177 (a decrease of 33 percent),

3. Decreased the number of 1993 FCRS

samples that were selected for exactly

two of the other four surveys from 586

to 266 (a decrease of 55 percent),

4. Decreased the number of 1993 FCRS

samples that were selected for exactly

three of the other four surveys from 82

to 34 (a decrease of 59 percent),

5. Decreased the number of 1993 FCRS

samples that were selected for all of

the other four surveys from 6 to 1 (a

decrease of 83 percent), and

6. Decreased the number of 1993 FCRS

samples that were also in the previous

year’s FCRS sample from 300 to 13 (a

decrease of 96 percent).

Redrawing the strata 89 and below

FCRS sample of 7,383 farmers (the strata

containing the farms with sales less

than $500,000):

1. Increased the number of 1993 FCRS

samples that were not selected for any

of the other four surveys from 5,256

to 6,895 (an increase of 31 percent),

12
2. Decreased the number of 1993 FCRS

samples that were selected for only one

of the other four surveys from 1,843

to 421 (a decrease of 77 percent),

3. Decreased the number of 1993 FCRS

samples that were selected for exactly

two of the other four surveys from 257

to 59 (a decrease of 77 percent),

4. Decreased the number of 1993 FCRS

samples that were selected for exactly

three of the other four surveys from 25

to 7 (a decrease of 72 percent),

5. Decreased the number of 1993 FCRS

samples that were selected for all of

the other four surveys from 2 to 1 (a

decrease of 50 percent), and

6. Decreased the number of 1993 FCRS

samples that were also in the previous

year’s FCRS sample from 169 to 16 (a

decrease of 91 percent).

In summary, redrawing the 1993 FCRS

sample decreased the number of times the

1993 FCRS sample overlapped with one or

more of the other four survey samples:

1. From 4,561 to 1,966 for the 1993 FCRS

sample of 11,178 farmers (a decrease of

57 percent),

2. From 2,434 to 1,478 for the part of

the sample in strata 90 and above (a

decrease of 39 percent), and

3. From 2,127 to 488 for the part of

the sample in strata 89 and below (a

decrease of 77 percent).

These statistics show the effectiveness of

the two stage algorithm.

Tables 3A, 3B, and 3C provide detailed

summary statistics by sampling stage for

the initial, first stage, and redrawn sample.

In Table 3A, the 11,178 farmers in each

sample are first broken down according to

the number of times they were selected

for other surveys. Then the farmers

in each sample are further broken down

according to the specific combination of

surveys for which they were selected. In

Table 3B, similar breakdowns are given for

the 3,795 farmers of each sample that are

in strata 90 and above. And, in Table 3C,

breakdowns are given for the 7,383 farmers

of each sample that are in strata 89 and

below.

In each table, column 1 shows the number

of other surveys that the 1993 FCRS is

combined with. Column 2 shows the

specific combination of surveys that the

1993 FCRS is combined with. Columns 3,

4, and 5 show the number of records in each

category for the initial, first stage, and

redrawn samples, respectively. Columns 6,

7, and 8 show the percentages of farmers

in each category for the initial, first

stage, and redrawn samples, respectively.

Columns 9 and 10 show the change in the

number of farmers in the category from

the initial sample to the first stage and

redrawn samples, respectively. Columns 11

and 12 show the percentage change in the

number of farmers in the category from

the initial sample to the first stage and

redrawn samples, respectively.

State Level Burden Reduction

Tables 4A, 4B, and 4C show for each

state the number of 1993 FCRS samples

that were in the 1992 FCRS at each

stage of the algorithm. Column two,

13
Table 3A. For All Strata, U.S.: The Number of FCRS Samples and Percent of Total FCRS

Sample by Sampling Configuration for the Initial, First Stage Redrawn, and Final Redrawn

1993 FCRS Samples.

Change

Sampling Count Percent Initial to Stage 1 Stage 1 to Redrawn Initial to Redrawn

Configuration† Initial Stage 1 Redrawn Initial Stage 1 Redrawn Count Percent Count Percent Count Percent

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (#) (%) (%) (%) (#) (%) (#) (%) (#) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

93 FCRS alone 1 0 0 0 0 6617 9095 9212 59.2 81.4 82.4 +2478 +37% +117 +1% +2595 +39%

Total 6617 9095 9212 59.2 81.4 82.4 +2478 +37% +117 +1% +2595 +39%

93 FCRS plus one 1 0 0 0 1 1110 597 662 9.9 5.3 5.9 −513 −46% +65 +11% −448 −40%

other survey 1 0 0 1 0 336 74 93 3.0 0.7 0.8 −262 −78% +19 +26% −243 −72%

1 0 1 0 0 1966 668 836 17.6 6.0 7.5 −1298 −66% +168 +25% −1130 −57%

1 1 0 0 0 191 305 7 1.7 2.7 0.1 +114 +60% −298 −98% −184 −96%

Total 3603 1644 1598 32.2 14.7 14.3 −1959 −54% −46 −3% −2005 −56%

93 FCRS plus two 1 0 0 1 1 74 24 30 0.7 0.2 0.3 −50 −68% +6 +25% −44 −59%

other surveys 1 0 1 0 1 414 189 225 3.7 1.7 2.0 −225 −54% +36 +19% −189 −46%

1 0 1 1 0 147 39 60 1.3 0.3 0.5 −108 −73% +21 +54% −87 −59%

1 1 0 0 1 59 44 4 0.5 0.4 0.0 −15 −25% −40 −91% −55 −93%

1 1 0 1 0 12 6 1 0.1 0.1 0.0 −6 −50% −5 −83% −11 −92%

1 1 1 0 0 137 73 5 1.2 0.7 0.0 −64 −47% −68 −93% −132 −96%

Total 843 375 325 7.5 3.4 2.9 −468 −56% −50 −13% −518 −61%

93 FCRS plus three 1 0 1 1 1 45 26 31 0.4 0.2 0.3 −19 −42% +5 +19% −14 −31%

other surveys 1 1 0 1 1 6 2 0 0.1 0.0 0 −4 −67% −2 −100% −6 −100%

1 1 1 0 1 33 21 6 0.3 0.2 0.1 −12 −36% −15 −71% −27 −82%

1 1 1 1 0 23 9 4 0.2 0.1 0.0 −14 −61% −5 −56% −19 −83%

Total 107 58 41 1.0 0.5 0.4 −49 −46% −17 −29% −66 −62%

93 FCRS plus four 1 1 1 1 1 8 6 2 0.1 0.1 0.0 −2 −25% −4 −67% −6 −75%

other surveys Total 8 6 2 0.1 0.1 0.0 −2 −25% −4 −67% −6 −75%

Total 11,178 11,178 11,178 100.0 100.0 100.0 0 0% 0 0% 0 0%

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

14
Table 3B. For Strata 90 and Above, U.S.: The Number of FCRS Samples and Percent of

Total FCRS Sample by Sampling Configuration for the Initial, First Stage Redrawn, and

Final Redrawn 1993 FCRS Samples.

Change

Sampling Count Percent Initial to Stage 1 Stage 1 to Redrawn Initial to Redrawn

Configuration† Initial Stage 1 Redrawn Initial Stage 1 Redrawn Count Percent Count Percent Count Percent

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (#) (%) (%) (%) (#) (%) (#) (%) (#) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

93 FCRS alone 1 0 0 0 0 1361 2260 2317 35.9 59.5 61.0 +899 +66% +57 +3% +956 +70%

Total 1361 2260 2317 35.9 59.5 61.0 +899 +66% +57 +3% +956 +70%

93 FCRS plus one 1 0 0 0 1 517 459 508 13.6 12.1 13.4 −58 −11% +49 +11% −9 −2%

other survey 1 0 0 1 0 159 42 54 4.2 1.1 1.4 −117 −74% +12 +29% −105 −66%

1 0 1 0 0 986 499 613 26.0 13.2 16.1 −487 −49% +114 +23% −373 −38%

1 1 0 0 0 98 175 2 2.6 4.6 0.1 +77 +79% −173 −99% −96 −98%

Total 1760 1175 1177 46.4 31.0 31.0 −585 −33% +2 +0% −583 −33%

93 FCRS plus two 1 0 0 1 1 52 22 28 1.4 0.6 0.7 −30 −58% +6 +27% −24 −46%

other surveys 1 0 1 0 1 293 158 189 7.7 4.2 5.0 −135 −46% +31 +20% −104 −35%

1 0 1 1 0 91 27 45 2.4 0.7 1.2 −64 −70% +18 +67% −46 −51%

1 1 0 0 1 47 39 2 1.2 1.0 0.1 −8 −17% −37 −95% −45 −96%

1 1 0 1 0 11 5 1 0.3 0.1 0.0 −6 −55% −4 −80% −10 −91%

1 1 1 0 0 92 59 1 2.4 1.6 0.0 −33 −36% −58 −98% −91 −99%

Total 586 310 266 15.4 8.2 7.0 −276 −47% −44 −14% −320 −55%

93 FCRS plus three 1 0 1 1 1 36 23 28 0.9 0.6 0.7 −13 −36% +5 +22% −8 −22%

other surveys 1 1 0 1 1 4 1 0 0.1 0.0 0 −3 −75% −1 −100% −4 −100%

1 1 1 0 1 25 16 5 0.7 0.4 0.1 −9 −36% −11 −69% −20 −80%

1 1 1 1 0 17 6 1 0.5 0.2 0.0 −11 −65% −5 −83% −16 −94%

Total 82 46 34 2.2 1.2 0.9 −36 −44% −12 −26% −48 −59%

93 FCRS plus four 1 1 1 1 1 6 4 1 0.2 0.1 0.0 −2 −33% −3 −75% −5 −83%

other surveys Total 6 4 1 0.2 0.1 0.0 −2 −33% −3 −75% −5 −83%

Total 3795 3795 3795 100.0 100.0 100.0 0 0% 0 0% 0 0%

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

15
Table 3C. For Strata 89 and Below, U.S.: The Number of FCRS Samples and Percent of

Total FCRS Sample by Sampling Configuration for the Initial, First Stage Redrawn, and

Final Redrawn 1993 FCRS Samples.

Change

Sampling Count Percent Initial to Stage 1 Stage 1 to Redrawn Initial to Redrawn

Configuration† Initial Stage 1 Redrawn Initial Stage 1 Redrawn Count Percent Count Percent Count Percent

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (#) (%) (%) (%) (#) (%) (#) (%) (#) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

93 FCRS alone 1 0 0 0 0 5256 6835 6895 71.2 92.6 93.4 +1579 +30% +60 +1% +1639 +31%

Total 5256 6835 6895 71.2 92.6 93.4 +1579 +30% +60 +1% +1639 +31%

93 FCRS plus one 1 0 0 0 1 593 138 154 8.0 1.9 2.1 −455 −77% +16 +12% −439 −74%

other survey 1 0 0 1 0 177 32 39 2.4 0.4 0.5 −145 −82% +7 +22% −138 −78%

1 0 1 0 0 980 169 223 13.3 2.3 3.0 −811 −83% +54 +32% −757 −77%

1 1 0 0 0 93 130 5 1.3 1.8 0.1 +37 +40% −125 −96% −88 −95%

Total 1843 469 421 25.0 6.3 5.7 −1374 −75% −48 −10% −1422 −77%

93 FCRS plus two 1 0 0 1 1 22 2 2 0.3 0.0 0.0 −20 −91% 0 0% −20 −91%

other surveys 1 0 1 0 1 121 31 36 1.6 0.4 0.5 −90 −74% +5 +16% −85 −70%

1 0 1 1 0 56 12 15 0.8 0.2 0.2 −44 −79% +3 +25% −41 −73%

1 1 0 0 1 12 5 2 0.2 0.1 0.0 −7 −58% −3 −60% −10 −83%

1 1 0 1 0 1 1 0 0.0 0.0 0 0 0% −1 −100% −1 −100%

1 1 1 0 0 45 14 4 0.6 0.2 0.1 −31 −69% −10 −71% −41 −91%

Total 257 65 59 3.5 0.9 0.8 −192 −75% −6 −9% −198 −77%

93 FCRS plus three 1 0 1 1 1 9 3 3 0.1 0.0 0.0 −6 −67% 0 0% −6 −67%

other surveys 1 1 0 1 1 2 1 0 0.0 0.0 0 −1 −50% −1 −100% −2 −100%

1 1 1 0 1 8 5 1 0.1 0.1 0.0 −3 −38% −4 −80% −7 −88%

1 1 1 1 0 6 3 3 0.1 0.0 0.0 −3 −50% 0 0% −3 −50%

Total 25 12 7 0.3 0.2 0.1 −13 −52% −5 −42% −18 −72%

93 FCRS plus four 1 1 1 1 1 2 2 1 0.0 0.0 0.0 0 0% −1 −50% −1 −50%

other surveys Total 2 2 1 0.0 0.0 0.0 0 0% −1 −50% −1 −50%

Total 7383 7383 7383 100.0 100.0 100.0 0 0% 0 0% 0 0%

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

16
three, and four of each table, which are

based on the data from the 1992 and

1993 list frame spring classify and sample

select, show respectively the overlap for

the initial, first stage redrawn, and final

redrawn 1993 FCRS samples. Column five

shows the additional overlap that is not

accounted for in columns two, three, and

four. The added overlap resulted from (1)

adjustments made to the 1992 FCRS Cost

of Production Specialty Strata samples in

California, Michigan, Ohio, and Florida

after the spring classify and sample select

and (2) one added overlap that occurred

in Nevada. From Column four of

Table 4A it can be seen that three states—

Arizona (10), New Hampshire (6), and

Rhodes Island (7)—accounted for almost

80 percent of the overlap remaining in the

final redrawn sample.

U.S. Level Control Variable Estimates

This section discusses the similarity of the

redrawn sample to the initial sample by

examining associated population control

values. The tables below show for

each of eight population control values

the estimated totals and coefficients of

variation that are associated with the

initial, first stage, and redrawn samples.

Table 5A gives the U.S. level estimates,

which are derived from the 11,178 farmers

in each of the three samples. Table 5B

gives the U.S. level estimates for strata 90

and above, which are derived from the

3,795 strata 90 and above farmers in each

of the three samples. And, Table 5C gives

the U.S. level estimates for strata 89 and

below, which are derived from the 7,383

strata 89 and below farmers in each of the

three samples.

In each table, column 1 shows the names

of control items. Column 2 shows the

1993 population totals for the control

items. Columns 3 and 4 show, respectively,

the lower and upper bounds for a

90 percent confidence interval centered on

the true total for the estimated totals.

Columns 5, 6, and 7 show the estimated

totals using the initial, first stage, and

redrawn sample, respectively. Column 8

shows the coefficients of variation for the

estimated totals. Columns 9, 10, and 11

show the estimated coefficients of variation

using the initial, first stage, and redrawn

sample, respectively.

These tables show that the three samples

are very similar with respect to the

estimates derived from them. The three

estimates tend to fall at almost the

same place in the respective confidence

intervals. The same is true for the

estimated coefficients of variation. If the

estimated coefficient of variation for an

item is small (large) relative to the true

coefficient of variation for one sample then

it is also small (large) for the other two

samples.

BIAS CONSIDERATIONS

Recall that the first stage of the two stage

algorithm cannot bias the FCRS estimates.

The next section discusses the potential

for bias that arises at the second stage

of the algorithm in 1993. The second

section discusses the potential for bias

that will arise at the second stage of the

algorithm in 1994 and beyond. The third

section presents a four stage algorithm that

should help limit the potential for bias that

results from reapplication of the algorithm

in subsequent years. The fourth section

17
Table 4A. For All Strata: The Number of 1993 FCRS Samples in each State that were

in the 1992 FCRS Sample for the Initial, First Stage Redrawn, and Final Redrawn 1993

FCRS Samples, along with the Added Overlap Caused by Changes Made to the Sample in

the Specialty Strata.

Overlap

State Initial Stage 1 Redrawn Added

01: Alabama 6 4 1

04: Arizona 30 29 10

05: Arkansas 9 14

06: California 26 21 2

08: Colorado 16 17

09: Connecticut 5 1

10: Delaware 3 2

12: Florida 11 10 1 2

13: Georgia 5 4

16: Idaho 15 14

17: Illinois 15 12

18: Indiana 6 13

19: Iowa 23 22

20: Kansas 18 19

21: Kentucky 7 6

22: Louisiana 12 15

23: Maine 3 2

24: Maryland 6 5

25: Massachusetts 2 3

26: Michigan 11 14 3

27: Minnesota 21 18 1

28: Mississippi 13 12 1

29: Missouri 8 7

30: Montana 2 7

31: Nebraska 16 16

32: Nevada 6 4 1

33: New Hampshire 9 7 6

34: New Jersey 2 3

36: New York 2 4

37: North Carolina 12 14

38: North Dakota 17 17

39: Ohio 9 9 1

40: Oklahoma 1 1

41: Oregon 8 7

42: Pennsylvania 9 6

44: Rhode Island 12 11 7

45: South Carolina 9 12

46: South Dakota 18 19

47: Tennessee 4 5

48: Texas 19 17 1

49: Utah 3 4

50: Vermont 8 9

51: Virginia 4 4

53: Washington 7 8

54: West Virginia 4 3

55: Wisconsin 2 3 1

56: Wyoming 15 12

Total 469 466 29 9

Cumulative Percent Reduction 0.6% 93.8%

18
Table 4B. For Stratum 90 and Above: The Number of 1993 FCRS Samples in each State

that were in the 1992 FCRS Sample for the Initial, First Stage Redrawn, and Final Redrawn

1993 FCRS Samples, along with the Added Overlap Caused by Changes Made to the Sample

in the Specialty Strata.

Overlap

State Initial Stage 1 Redrawn Added

01: Alabama 2 2

04: Arizona 17 18 4

05: Arkansas 7 10

06: California 23 18 2

08: Colorado 8 9

09: Connecticut 1 0

10: Delaware 2 1

12: Florida 8 4 1

13: Georgia 4 4

16: Idaho 6 7

17: Illinois 12 10

18: Indiana 3 8

19: Iowa 18 16

20: Kansas 16 18

21: Kentucky 4 4

22: Louisiana 7 8

23: Maine 2 2

24: Maryland 5 4

25: Massachusetts 2 3

26: Michigan 6 6

27: Minnesota 13 13 1

28: Mississippi 8 8

29: Missouri 0 1

30: Montana 0 2

31: Nebraska 13 12

32: Nevada 4 3 1

33: New Hampshire 7 7 6

34: New Jersey 2 3

36: New York 2 4

37: North Carolina 10 11

38: North Dakota 13 12

39: Ohio 5 6

40: Oklahoma 1 1

41: Oregon 4 4

44: Rhode Island

42: Pennsylvania 7 4

45: South Carolina 7 9

46: South Dakota 14 14

47: Tennessee 1 2

48: Texas 17 16 1

49: Utah 0 1

50: Vermont 2 4

51: Virginia 2 3

53: Washington 5 4

54: West Virginia 3 2

55: Wisconsin 0 1

56: Wyoming 7 6

Total 300 305 13 3

Cumulative Percent Reduction -1.7% 95.7%

19
Table 4C. For Stratum 89 and Below: The Number of 1993 FCRS Samples in Each State

that were in the 1992 FCRS Sample for the Initial, First Stage Redrawn, and Final Redrawn

1993 FCRS Samples, along with the Added Overlap Caused by Changes Made to the Sample

in the Specialty Strata.

Overlap

State Initial Stage 1 Redrawn Added

01: Alabama 4 2 1

04: Arizona 13 11 6

05: Arkansas 2 4

06: California 3 3

08: Colorado 8 8

09: Connecticut 4 1

10: Delaware 1 1

12: Florida 3 6 2

13: Georgia 1 0

16: Idaho 9 7

17: Illinois 3 2

18: Indiana 3 5

19: Iowa 5 6

20: Kansas 2 1

21: Kentucky 3 2

22: Louisiana 5 7

23: Maine 1 0

24: Maryland 1 1

26: Michigan 5 8 3

27: Minnesota 8 5

28: Mississippi 5 4 1

29: Missouri 8 6

30: Montana 2 5

31: Nebraska 3 4

32: Nevada 2 1

33: New Hampshire 2

37: North Carolina 2 3

38: North Dakota 4 5

39: Ohio 4 3 1

41: Oregon 4 3

42: Pennsylvania 2 2

44: Rhode Island 12 11 7

45: South Carolina 2 3

46: South Dakota 4 5

47: Tennessee 3 3

48: Texas 2 1

49: Utah 3 3

50: Vermont 6 5

51: Virginia 2 1

53: Washington 2 4

54: West Virginia 1 1

55: Wisconsin 2 2 1

56: Wyoming 8 6

Total 169 161 16 6

Cumulative Percent Reduction 4.7% 90.5%

20
Table 5A. For All Strata, U.S.: The Estimated 1993 Population Control Variable Totals for

the Initial, First Stage Redrawn, and Final Redrawn 1993 FCRS Sample.

90% 90% Estimated Total Exact CV of Estimated CV

Control Population Lower Upper Initial Stage 1 Redrawn Estimated Initial Stage 1 Redrawn

Variable† Total Bound Bound Sample Sample Sample Total Sample Sample Sample

(#) (#) (#) (#) (#) (#) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Total Land in Farm 862.52 47.04 1678.01 791.28 798.17 790.29 57.30 2.31 2.46 2.43

Farm Value of Sales 150.53 148.44 152.62 151.96 151.93 151.76 0.84 0.86 0.85 0.84

Total Cropland 363.62 327.21 400.03 363.54 365.83 364.74 6.07 1.11 1.07 1.06

On-Farm Grain Storage 947.58 902.34 992.81 992.67 990.91 997.68 2.89 2.98 2.88 2.99

All Cattle & Calves 850.13 811.07 889.19 821.80 829.07 840.22 2.78 3.05 3.21 3.61

Total Hogs & Pigs 547.15 457.17 637.12 588.76 576.22 585.09 9.97 5.33 4.08 4.29

All Sheep 114.96 88.60 141.32 106.15 103.90 103.23 13.90 13.02 13.13 13.20

Farm Workers Hired 127.21 58.80 195.61 102.40 102.54 102.05 32.59 5.22 5.31 5.33

† All missing control values were set to zero before any computations were performed. The units of measure for the population

totals and their estimates are:

1, 000, 000 acres for Total Land; $1, 000, 000, 000 for Farm Value Of Sales;

1, 000, 000 acres for Total Cropland; 10, 000, 000 bushels for On-Farm Grain Storage;

100, 000 head for Cattle & Calves, Hogs & Pigs, and Sheep; 10, 000 workers Farm Workers Hired.

Table 5B. For Strata 90 and Above, U.S.: The Estimated 1993 Population Control Variable

Totals for the Initial, First Stage Redrawn, and Final Redrawn 1993 FCRS Sample.

90% 90% Estimated Total Exact CV of Estimated CV

Control Population Lower Upper Initial Stage 1 Redrawn Estimated Initial Stage 1 Redrawn

Variable† Total Bound Bound Sample Sample Sample Total Sample Sample Sample

(#) (#) (#) (#) (#) (#) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Total Land in Farm 200.12 160.57 239.67 196.58 192.54 187.86 11.98 5.19 5.16 5.13

Farm Value of Sales 50.00 48.26 51.73 50.77 50.74 50.52 2.10 2.14 2.13 2.12

Total Cropland 87.84 53.34 122.33 81.81 82.47 81.91 23.80 1.94 1.93 1.90

On-Farm Grain Storage 209.98 198.54 221.41 220.22 221.58 221.84 3.30 3.96 3.93 3.99

All Cattle & Calves 285.97 251.17 320.77 286.42 295.52 307.11 7.38 7.93 8.30 9.29

Total Hogs & Pigs 198.78 113.57 283.98 196.45 177.03 181.23 25.98 12.75 7.47 8.62

All Sheep 32.95 18.40 47.50 32.10 33.26 32.28 26.76 25.68 25.10 25.57

Farm Workers Hired 45.00 25.34 64.64 37.16 36.63 35.48 26.47 8.02 8.04 8.16

† All missing control values were set to zero before any computations were performed. The units of measure for the population

totals and their estimates are:

1, 000, 000 acres for Total Land; $1, 000, 000, 000 for Farm Value Of Sales;

1, 000, 000 acres for Total Cropland; 10, 000, 000 bushels for On-Farm Grain Storage;

100, 000 head for Cattle & Calves, Hogs & Pigs, and Sheep; 10, 000 workers Farm Workers Hired.

21
Table 5C. For Strata 89 and Below, U.S.: The Estimated 1993 Population Control Variable

Totals for the Initial, First Stage Redrawn, and Final Redrawn 1993 FCRS Sample.

90% 90% Estimated Total Exact CV of Estimated CV

Control Population Lower Upper Initial Stage 1 Redrawn Estimated Initial Stage 1 Redrawn

Variable† Total Bound Bound Sample Sample Sample Total Sample Sample Sample

(#) (#) (#) (#) (#) (#) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Total Land in Farm 662.40 -152.13 1476.92 594.70 605.63 602.43 74.52 2.55 2.79 2.76

Value of Sales 100.53 99.36 101.71 101.19 101.19 101.24 0.71 0.70 0.68 0.68

Total Cropland 275.78 264.14 287.43 281.73 283.36 282.83 2.56 1.32 1.26 1.25

On-Farm Grain Storage 737.60 693.84 781.37 772.45 769.32 775.84 3.60 3.66 3.53 3.68

All Cattle & Calves 564.16 546.42 581.89 535.38 533.56 533.11 1.91 1.97 1.93 1.93

Total Hogs & Pigs 348.37 319.46 377.28 392.31 399.19 403.85 5.03 4.82 4.86 4.86

All Sheep 82.01 60.02 103.99 74.05 70.65 70.95 16.25 14.98 15.28 15.29

Farm Workers Hired 82.22 16.70 147.74 65.24 65.91 66.57 48.30 6.80 6.94 6.91

† All missing control values were set to zero before any computations were performed. The units of measure for the population

totals and their estimates are:

1, 000, 000 acres for Total Land; $1, 000, 000, 000 for Farm Value Of Sales;

1, 000, 000 acres for Total Cropland; 10, 000, 000 bushels for On-Farm Grain Storage;

100, 000 head for Cattle & Calves, Hogs & Pigs, and Sheep; 10, 000 workers Farm Workers Hired.

presents a five stage algorithm that should

further limit the potential for bias that

results from reapplication of the algorithm

in subsequent years.

For the 1993 FCRS Estimates

With respect to any bias that might

be caused by redrawing the 1993 FCRS

sample with the two stage algorithm, the

earlier discussions of this report can be

summarized as follows:

1. The first stage of the algorithm has

no potential to introduce bias into the

FCRS estimates;

2. Only when the information from the

1992 FCRS is used to update the

1993 FCRS frame, does the second

stage of the algorithm have a potential

to introduce bias into the FCRS estimates; and

22
3. Only about four percent of the 1993

FCRS sample (444 out of 11,178

sampled records or 3.97 percent) were

redrawn in the second stage of the

two stage algorithm. The expanded

control data associated with the 444

records ranged from 3.4 to 5.9 percent

of respective control data totals.

Thus, only about four percent of the

redrawn 1993 FCRS sample has any

potential to introduce bias into the

1993 FCRS estimates. And, only those

records in the four percent that have

had their control data updated from

1992 FCRS sample data can introduce any

bias into the estimates.

The small impact of any possible bias

that might be introduced by the use of

1992 FCRS sample data to update the

1993 FCRS frame on the 1993 FCRS

estimates can be seen as follows. Assume

that 1992 FCRS sample data are used to

update the 1993 FCRS frame and that

the two stage algorithm discussed in this

report is used to redraw the sample. The

records redrawn in the second stage will

then tend to have older control data than

the ones they replaced. If the difference in

the age of the control data associated with

the records that are redrawn at the second

stage is related to the data collected from

the records then bias will be introduced

into the FCRS estimates.

To show that the effect of this potential

bias on the 1993 FCRS estimates is small,

consider a (highly unlikely) worst-case

example. Suppose that the change in

age of the control data causes the data

collected from the part of the sample

that is redrawn in the second stage to

be consistently 20 percent smaller (or

larger) than the data that would have

been collected had the elements not been

redrawn. Note that this much bias in

the four percent of the sample redrawn

at the second stage seems highly unlikely,

since there is little reason to believe that

any significant amount of information from

the 1992 FCRS sample is used to update

control data prior to the 1993 FCRS frame

stratification. Further, it is unlikely that

slightly older or newer control data would

produce such a large difference in the

relationship between the control data and

observations.

From the discussion above, the expanded

control data of the four percent of the

sample that was redrawn in the second

stage ranged from 3.4 to 5.9 percent of

respective totals. Making a worst case

assumption, assume that the expanded

data of the part of the sample redrawn in

the second stage represents five percent of

the estimate. Even under these extreme

assumptions, redrawing the sample at

the second stage would cause only a

one percent change (0.20 ∗ 0.05 = 0.01)

in the 1993 estimates. This change

would be undetectable in light of the

coefficients of variation associated with the

FCRS estimates. Thus, even though the

second stage of the algorithm cannot be

guaranteed to be unbiased, it is highly

unlikely that any detectable bias will result

from redrawing the 1993 FCRS sample.

For the 1994 FCRS Estimates, If the

Same Two Stage Algorithm is Used

If the same two stage algorithm is used

sequentially in two years, then the second

stage of the algorithm potentially can

introduce bias into the FCRS estimates,

23
even when no information from the

previous year’s FCRS sample is used to

update the current FCRS frame. With

respect to redrawing the 1994 FCRS, the

situation can be summarized as follows:

1. The first stage of the algorithm has

no potential to introduce bias into the

FCRS estimates;

2. The second stage of the algorithm has

a potential to introduce bias into the

FCRS estimates if any sample data

from the 1993 FCRS, QAS, ALS, or

CSS samples is used to update the 1994

FCRS frame; however,

3. In 1994, less than three percent of the

FCRS sample will be redrawn at the

second stage of the two stage algorithm.

This assumes that the 1994 FCRS has

the same sample size as the 1993 FCRS

and that the percentage redrawn in any

year is proportional to the expected

overlap with the previous year’s sample,

which is approximately proportional for

small sampling fractions to the product

of the sample sizes in consecutive years

(3.97% ∗ (11, 178 ∗ 11, 178)/(11, 178 ∗

16, 600) = 2.67% < 3%).

The use of 1993 FCRS sample data to

update the 1994 FCRS frame opens the

1994 FCRS estimates to potential bias just

as it did in 1993. For the same reasons

that were sighted for the 1993 FCRS, it is

unlikely that any detectable bias will result

in 1994 from this source of potential bias.

However, in 1994 the use of 1993 QAS,

ALS, and CSS sample data to update the

1994 FCRS frame opens the 1994 FCRS

estimates to another potential source of

bias. Since the 1993 FCRS sample was

redrawn to reduce its overlap with the

other 1993 survey samples, when the part

of the first stage 1994 FCRS sample

that overlaps with the 1993 FCRS is

redrawn in the second stage to reduce its

overlap with the 1993 FCRS sample, the

resulting sample will be more likely to

contain farmers that were in one of the

other 1993 surveys—hence more likely to

have their control data updated in 1993.

Therefore, the part of the 1994 FCRS

sample that is redrawn at the second stage

is more likely to have updated control data

than the frame population, and hence, may

not be representative of the population.

Thus, in 1994 and subsequent years, even

when no FCRS data from the previous

year’s FCRS sample has been used to

update the FCRS frame, the second

stage of the algorithm has a potential to

introduce bias into the FCRS estimates,

since one cannot guarantee that the

farmers in a substratum do not differ by

the age of their control data. The next

section presents a four stage algorithm that

should help to limit this potential source

of bias by restricting the later stage of

the redrawing process to substrata that

incorporate both the original multivariate

stratifications and two indicators of a

record’s control data age.

For the 1994 FCRS Estimates, If a

Four Stage Algorithm is Used

The four stage algorithm presented in this

section removes at each successive stage

more and more of overlap between the

1993 and 1994 FCRS while maintaining

at each stage, to the extent possible,

the control data age characteristics of

the sample. The four stage algorithm is

24
derived from the components of the two

stage algorithm as follows. First, use the

first stage of the two stage algorithm to

remove, to the extent possible, the overlap

of the 1994 FCRS sample with the other

1994 surveys’ samples. Then, use the

second stage of the two stage algorithm

three times with less and less restrictive

age dependent substrata to reduce the

overlap between the 1993 and 1994 FCRS

samples.

The substrata are made to depend on the

age of the control values of the records

they contain through two age indicators:

the last year Total Land In Farm, Total

Crop Land, or On-Farm Grain Storage

was updated is used as an indicator or

proxy for the age of a record’s field crop

control values; and the last year All

Cattle and Calves, Total Hogs and Pigs,

or All Sheep was updated is used as an

indicator or proxy for the age of a record’s

livestock control values. The second stage

redraws the records of the 1994 FCRS

sample that overlap with the 1993 FCRS

sample within the substrata formed by

cross classifying the records according to

the 1994 FCRS, 1993 FCRS, 1994 QAS,

1994 ALS, 1994 CSS strata and the two

age indicators. The third stage redraws

the records of the 1994 FCRS sample that

overlap with the 1993 FCRS sample within

the substrata formed by cross classifying

the records according to the 1994 FCRS

and 1993 FCRS strata and the two age

indicators. The fourth stage redraws the

records of the 1994 FCRS sample that

overlap with the 1993 FCRS sample within

the substrata formed by cross classifying

the records according to the 1994 FCRS

strata and the two age indicators.

In the last three stages of this four

stage algorithm, each record that is

redrawn has the same age indicator as

the record it replaces, which should limit

the potential for bias that might arise

because of application of the algorithm

in two consecutive years. In addition,

at the second stage, the redrawn records

have the same stratification with respect

to all five surveys, at the third stage

the same stratification with respect to the

1993 and 1994 FCRS surveys, and at the

fourth stage the same stratification with

respect to the 1994 FCRS. The last three

stages are progressively less restrictive.

Hence, each stage provides progressively

more overlap reduction and less protection

against potential bias. Thus, we see that

at each stage the gains in burden reduction

come at the expense of the loss of some

protection against bias.

Had this four stage algorithm been used

to redraw the FCRS sample in 1993, the

overlap between the 1992 and 1993 FCRS

samples would have been reduced at the

second stage from 466 to 273 (a 41 percent

reduction), at the third stage from 273

to 65 (a 44 percent reduction), and at the

fourth stage from 65 to 32 (a 7 percent

reduction). Tables B1, B2, and B3 of

Appendix B show a detailed breakdown of

the burden reduction that would have been

achieved with the four stage algorithm at

each stage of the algorithm.

Tables B4, B5, and B6 of Appendix B

show the number of farmers in each state

that would have been in the redrawn

1993 FCRS sample at each stage with

the four stage algorithm that were also in

the 1992 FCRS sample. Tables B7, B8,

and B9 of Appendix B show the U.S. level

control variable estimates and coefficients

of variation derived from the sample at

each stage with the four stage algorithm

that were also in the 1992 FCRS sample.

25
The next section presents a five stage

algorithm that further restricts the records

of each substrata to one FCRS Farm

Type. This additional restriction will

help ensure that the age indicators are

more comparable with substrata, and

consequently, that the records of each

substratum are more alike with respect to

the expected current FCRS data.

For the 1994 FCRS Estimates, If a

Five Stage Algorithm is Used

The five stage algorithm presented in this

section removes at each successive stage

more and more of overlap between the 1993

and 1994 FCRS while maintaining at each

stage, to the extent possible, the control

data age and farm type characteristics of

the sample.

The first stage of the algorithm is the

same as the first stage of the four stage

algorithm. The second, third, and fourth

stages of the algorithm are obtained

from the corresponding stages of the four

stage algorithm by further restricting the

substrata to one FCRS Farm Type. The

fifth stage is obtained from the fourth stage

by substituting a single age indicator for

the two age indicators. The last year Total

Land In Farm, Total Crop Land, On-Farm

Grain Storage, All Cattle and Calves,

Total Hogs and Pigs, or All Sheep was

updated is used at the fifth stage as a single

age indicator. Restricting the substrata to

one farm type should help make sure that

the age indicators are more comparable

within the substrata. This should further

limit the potential for bias that might arise

because of application of the algorithm in

two consecutive years. A sixth stage is

added to the five stage algorithm solely

for the purpose of making comparisons.

The sixth stage is obtained from the

fifth stage by dropping the age indicators

altogether. The last five stages of the

algorithm are progressively less restrictive.

Hence, each stage provides progressively

more overlap reduction and less protection

against potential bias. Which means that

at each stage the gains in burden reduction

come at the expense of the loss of bias

protection. Note that, the sixth stage

provides no protection against bias arising

from differences in the age of the control

data.

Had this five (six) stage algorithm

been used to redraw the FCRS sample

in 1993, the overlap between the 1992

and 1993 FCRS samples would have been

reduced at the second stage from 466

to 285 (a 39 percent reduction), at the

third stage from 285 to 80 (a 44 percent

reduction), at the fourth stage from 80

to 41 (a 8 percent reduction), at the fifth

stage from 41 to 32 (a 2 percent reduction),

and at the fifth stage from 32 to 23 (a

2 percent reduction). Tables B10, B11,

and B12 of Appendix B show a detailed

breakdown of the burden reduction that

would have been achieved with the five

stage algorithm at each stage of the

algorithm.

Tables B13, B14, and B15 of Appendix B

show the number of farmers in each state

that would have been in the redrawn

1993 FCRS sample at each stage with the

five stage algorithm that were also in the

1992 FCRS sample. Tables B16, B17,

and B18 of Appendix B show the U.S. level

control variable estimates and coefficients

of variation derived from the sample at

each stage with the five stage algorithm

that were also in the 1992 FCRS sample.

26
Theoretically, it would be simple to test

the second and latter stage of these

algorithms for potential bias by either

1) collecting data from the farmers in the

FCRS year-to-year overlap in addition to

the data from redrawn farmers or 2) by

splitting the FCRS year-to-year overlap

and only using half of it. To split the yearto-year FCRS overlap one would divide the

records that were redrawn at the second

and latter stage into pairs based on all

the available information, then randomly

choose one record from each pair to be

redrawn. The other record from each pair

that would be used would be the record

selected at the end of the first stage of

the algorithm. All tests would need to be

based on expanded data, since our interest

is in potential for bias with respect to

the FCRS estimates. Thus, in practice,

neither procedure would likely yield useful

information, since at best one would have

no more than 400 records, which would be

scattered over all strata in all states.

CONCLUSIONS

Redrawing the 1993 FCRS list frame

sample of 11,178 farmers reduced the

burden on the individual farmer sampled

by:

1. Decreasing the number of 1993 FCRS

samples that were in one or more of the

other samples (1993 QAS, ALS, CSS

or 1992 FCRS) from 4,561 to 1,966 (a

decrease of 57 percent),

2. Decreasing the number of 1993 FCRS

samples that were in the 1992 FCRS

sample from 469 to 29 (a decrease of

94 percent), and

3. Increasing the number of 1993 FCRS

samples that are not in any of the other

four surveys from 6,617 to 9,212 (an

increase of 39 percent).

The two stage algorithm used to redraw

the 1993 FCRS has very little potential

to introduce bias into the 1993 FCRS

estimates. In fact, only at the second

stage, which involves less than four percent

of the sample, does it have any potential

of introducing bias. At the second stage,

the potential to introduce bias is limited

to those samples which have had their

1992 FCRS sample information used to

update the 1993 FCRS frame.

The primary reason that a two stage

algorithm was chosen over a single stage

algorithm for redrawing the 1993 FCRS

was to minimize the potential to introduce

bias into the FCRS estimates. A secondary

reason for the choice was that the two stage

algorithm also provides considerably more

burden reduction than the single stage

algorithm.

If the same two step algorithm is used

again next year to redraw the 1994 FCRS,

the potential to introduce bias into the

FCRS estimates will increase. This

increased bias potential results from the

use of 1993 QAS, ALS, and CSS sample

data to update the 1994 FCRS frame which

tends to cause the 1994 FCRS sample to

be placed on records that have had their

control data updated recently.

A four stage algorithm and a five stage

algorithm were discussed that should help

limit the potential bias that may result

from the use of 1993 sample data to

update the 1994 FCRS frame. Since

the five stage algorithm places more age

27
indicator and Farm Type restrictions on

the substrata used in the latter stages

of the algorithm than either the two or

four stage algorithms it should provide the

most protection against potential bias. A

comparison of the two, four, and five stage

algorithms using the 1992 and 1993 frame

and sample data shows that they provide

similar levels of burden reduction.

Since any potential bias is restricted to

the latter stages of the redrawing process

with all algorithms, it will affect less than

three percent of the sample (assuming that

the 1994 FCRS sample is the same size as

in 1993). With only three percent of the

sample being redrawn in the latter stages it

seems that under a worst-case example at

most a one percent bias would be expected

with either the four or five stage algorithm.

Hence, in comparison to the coefficients of

variation associated with FCRS items, any

bias should be undetectable.

RECOMMENDATIONS

The 1993 FCRS was redrawn using a

new two stage algorithm in order to

substantially reduce respondent burden.

The algorithm was performed by the

Research Division in cooperation with

Survey Management Division in a joint

research and operations staff effort.

For The 1994 FCRS

Redraw the 1994 FCRS sample with the

five stage algorithm. The use of the five

stage algorithm will limit to the extent

possible the potential for bias that results

from the use of 1993 sample data to update

the 1994 FCRS frame. Since the potential

for bias in 1994 FCRS estimates is only

slightly more than it was with 1993 FCRS

estimates, the reduction in burden that

will be obtained with the 1994 FCRS

outweighs the increased potential for bias.

For The 1996 Sample Select

Research Division is evaluating the two

methods described by Perry, Burt, and

Iwig (1993) for selecting multiple survey

samples to reduce burden on the individuals selected in all samples. This work will

be completed in 1995 and at that time recommendations will be made for incorporating the results into the 1996 Sample Select.

REFERENCES

Perry, Charles R., Jameson C. Burt, and

William C. Iwig; “Methods Of Selecting

Samples In Multiple Surveys To Reduce

Respondent Burden”; Proceedings of the

International Conference on Establishment

Surveys; ASA; Alexandria, Virginia;

June 1993.

Perry, Charles R., Jameson C. Burt,

and William C. Iwig; “Redrawing the

1993 Farm Cost and Returns Survey List

Sample to Reduce Overlap with Three

Other 1993 Surveys and the 1992 FCRS”;

1994 Proceedings of the Section on Survey

Research Methods; ASA; Alexandria,

Virginia; 1994.

28
APPENDIX A: BURDEN

REDUCTION FOR A SINGLE

STAGE ALGORITHM

The following three tables give a detailed

breakdown of the burden reduction that

would have been obtained had a single

stage algorithm been used to redraw the

1993 FCRS sample. A comparison of

these tables with Table 3A, 3B, and 3C,

respectively, will show that the two step

algorithm does a much better job of

reducing the overlap of the 1993 FCRS

sample with both the 1992 FCRS sample

and the other three 1993 samples. In

particular, had the single stage algorithm

been used to redraw the 1993 FCRS,

there would have been 171 farmers in the

1993 FCRS sample that were also in the

1992 FCRS sample; whereas, with the two

stage algorithm, there were only 29 farmers

in the 1993 FCRS who were also in the

1992 FCRS sample.

29
U.S. Level Burden Reduction

Table A1. For All Strata Using a Single Stage Algorithm, U.S.: The Number of FCRS

Samples and Percent of Total FCRS Sample by Sampling Configuration for the Initial and

Redrawn 1993 FCRS Samples.

Sampling Count Percent Change

Configuration† Initial Redrawn Initial Redrawn Count Percent

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (%) (%) (#) (%)

(1) (2) (3) (4) (5) (6) (7) (8)

93 FCRS alone 1 0 0 0 0 6617 8853 59.2 79.2 +2236 +34%

Total 6617 8853 59.2 79.2 +2236 +34%

93 FCRS plus one 1 0 0 0 1 1110 695 9.9 6.2 −415 −37%

other survey 1 0 0 1 0 336 113 3.0 1.0 −223 −66%

1 0 1 0 0 1966 964 17.6 8.6 −1002 −51%

1 1 0 0 0 191 55 1.7 0.5 −136 −71%

Total 3603 1827 32.2 16.3 −1776 −49%

93 FCRS plus two 1 0 0 1 1 74 38 0.7 0.3 −36 −49%

other surveys 1 0 1 0 1 414 245 3.7 2.2 −169 −41%

1 0 1 1 0 147 69 1.3 0.6 −78 −53%

1 1 0 0 1 59 24 0.5 0.2 −35 −59%

1 1 0 1 0 12 5 0.1 0.0 −7 −58%

1 1 1 0 0 137 43 1.2 0.4 −94 −69%

Total 843 424 7.5 3.8 −419 −50%

93 FCRS plus three 1 0 1 1 1 45 30 0.4 0.3 −15 −33%

other surveys 1 1 0 1 1 6 3 0.1 0.0 −3 −50%

1 1 1 0 1 33 24 0.3 0.2 −9 −27%

1 1 1 1 0 23 11 0.2 0.1 −12 −52%

Total 107 68 1.0 0.6 −39 −36%

93 FCRS plus four 1 1 1 1 1 8 6 0.1 0.1 −2 −25%

other surveys Total 8 6 0.1 0.1 −2 −25%

Total 11,178 11,178 100.0 100.0 0 0%

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

30
Table A2. For Strata 90 and Above Using a Single Stage Algorithm, U.S.: The Number of

FCRS Samples and Percent of Total FCRS Sample by Sampling Configuration for the Initial

and Final Redrawn 1993 FCRS Samples.

Sampling Count Percent Change

Configuration† Initial Redrawn Initial Redrawn Count Percent

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (%) (%) (#) (%)

(1) (2) (3) (4) (5) (6) (7) (8)

93 FCRS alone 1 0 0 0 0 1361 2121 35.9 55.9 +760 +56%

Total 1361 2121 35.9 55.9 +760 +56%

93 FCRS plus one 1 0 0 0 1 517 502 13.6 13.2 −15 −3%

other survey 1 0 0 1 0 159 71 4.2 1.9 −88 −55%

1 0 1 0 0 986 667 26.0 17.6 −319 −32%

1 1 0 0 0 98 39 2.6 1.0 −59 −60%

Total 1760 1279 46.4 33.7 −481 −27%

93 FCRS plus two 1 0 0 1 1 52 31 1.4 0.8 −21 −40%

other surveys 1 0 1 0 1 293 201 7.7 5.3 −92 −31%

1 0 1 1 0 91 52 2.4 1.4 −39 −43%

1 1 0 0 1 47 19 1.2 0.5 −28 −60%

1 1 0 1 0 11 4 0.3 0.1 −7 −64%

1 1 1 0 0 92 29 2.4 0.8 −63 −68%

Total 586 336 15.4 8.8 −250 −43%

93 FCRS plus three 1 0 1 1 1 36 26 0.9 0.7 −10 −28%

other surveys 1 1 0 1 1 4 2 0.1 0.1 −2 −50%

1 1 1 0 1 25 19 0.7 0.5 −6 −24%

1 1 1 1 0 17 8 0.5 0.2 −9 −53%

Total 82 55 2.2 1.4 −27 −33%

93 FCRS plus four 1 1 1 1 1 6 4 0.2 0.1 −2 −33%

other surveys Total 6 4 0.2 0.1 −2 −33%

Total 3795 3795 100.0 100.0 0 0%

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

31
Table A3. For Strata 89 and Below Using a Single Stage Algorithm, U.S.: The Number of

FCRS Samples and Percent of Total FCRS Sample by Sampling Configuration for the Initial

and Final Redrawn 1993 FCRS Samples.

Sampling Count Percent Change

Configuration† Initial Redrawn Initial Redrawn Count Percent

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (%) (%) (#) (%)

(1) (2) (3) (4) (5) (6) (7) (8)

93 FCRS alone 1 0 0 0 0 5256 6732 71.2 91.2 +1476 +28%

Total 5256 6732 71.2 91.2 +1476 +28%

93 FCRS plus one 1 0 0 0 1 593 193 8.0 2.6 −400 −67%

other survey 1 0 0 1 0 177 42 2.4 0.6 −135 −76%

1 0 1 0 0 980 297 13.3 4.0 −683 −70%

1 1 0 0 0 93 16 1.3 0.2 −77 −83%

Total 1843 548 25.0 7.4 −1295 −70%

93 FCRS plus two 1 0 0 1 1 22 7 0.3 0.1 −15 −68%

other surveys 1 0 1 0 1 121 44 1.6 0.6 −77 −64%

1 0 1 1 0 56 17 0.8 0.2 −39 −70%

1 1 0 0 1 12 5 0.2 0.1 −7 −58%

1 1 0 1 0 1 1 0.0 0.0 0 0%

1 1 1 0 0 45 14 0.6 0.2 −31 −69%

Total 257 88 3.5 1.2 −169 −66%

93 FCRS plus three 1 0 1 1 1 9 4 0.1 0.1 −5 −56%

other surveys 1 1 0 1 1 2 1 0.0 0.0 −1 −50%

1 1 1 0 1 8 5 0.1 0.1 −3 −38%

1 1 1 1 0 6 3 0.1 0.0 −3 −50%

Total 25 13 0.3 0.2 −12 −48%

93 FCRS plus four 1 1 1 1 1 2 2 0.0 0.0 0 0%

other surveys Total 2 2 0.0 0.0 0 0%

Total 7383 7383 100.0 100.0 0 0%

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

32
APPENDIX B: BURDEN

REDUCTION, OVERLAP

REDUCTION, AND BIAS FOR

THE FOUR STAGE AND FIVE

STAGE ALGORITHMS

Tables B1, B2, and B3 show a detailed

breakdown of the burden reduction that

would have been achieved had the four

stage algorithm been used to redraw

the 1993 FCRS. The initial 1993 FCRS

sample was redrawn at the first stage

within the substrata formed by crossing

the four 1993 FCRS, QAS, ALS, and

CSS stratifications to reduce to the extent

possible its overlap with the other three

1993 surveys’ samples. The part of the first

stage redrawn sample that overlapped with

the 1992 FCRS sample was redrawn at the

second stage within the substrata formed

by crossing the 1992 FCRS strata; the

1993 FCRS, QAS, ALS, and CSS strata;

and the two age indicators to reduce to

the extent possible its overlap with the

1992 FCRS sample. The part of the second

stage redrawn sample that still overlapped

with the 1992 FCRS sample was redrawn

at the third stage within the substrata

formed by crossing the 1992 FCRS strata,

the 1993 FCRS strata, and the two age

indicators to reduce to the extent possible

its overlap with the 1992 FCRS sample.

The part of the third stage redrawn sample

that still remained overlapped with the

1992 FCRS sample was redrawn at the

fourth stage within the substrata formed

by crossing the 1993 FCRS strata and the

two age indicators to reduce to the extent

possible its overlap with the 1992 FCRS

sample.

Tables B4, B5, and B6 show the overlap in

each state between the 1992 FCRS sample

and the 1993 redrawn FCRS sample that

would have remain at each stage had the

four stage algorithm been used to redraw

the 1993 FCRS. Table B4 shows that the

four stage algorithm reduces the overlap

at the end of the fourth stage to no more

than one in all but three states: Arizona,

New Hampshire, and Rhode Island. The

overlap in these three states account 72

percent of the remaining overlap at the end

of the four stage algorithm.

Tables B7, B8, and B9 show for eight

population control values the estimated

totals and coefficients of variation that

would have been associated with the

sample at each stage had the four

stage algorithm been used to redraw the

1993 FCRS. The U.S. level estimates are

given in Table B7 for all strata; in Table B8

for stratum 90 and above; and in Table B9

for stratum 89 and below. These tables

show that the samples are very similar at

each stage with respect to the estimates

derived from them. The estimates tend

to fall at almost the same place in the

respective confidence intervals; the same

is true for the estimated coefficients of

variation.

Tables B10, B11, and B12 show a detailed

breakdown of the burden reduction that

would have been achieved had the five

stage algorithm been used to redraw

the 1993 FCRS. The initial 1993 FCRS

sample was redrawn at the first stage

within the substrata formed by crossing

the four 1993 FCRS, QAS, ALS, and

CSS stratifications to reduce to the extent

possible its overlap with the other three

1993 surveys’ samples. The part of the first

stage redrawn sample that overlapped with

the 1992 FCRS sample was redrawn at the

second stage within the substrata formed

by crossing the 1992 FCRS strata; the

1993 FCRS, QAS, ALS, and CSS strata;

33
FCRS Farm Type; and the two age

indicators to reduce to the extent possible

its overlap with the 1992 FCRS sample.

The part of the second stage redrawn

sample that still overlapped with the

1992 FCRS sample was redrawn at the

third stage within the substrata formed

by crossing the 1992 FCRS strata, the

1993 FCRS strata, FCRS Farm Type,

and the two age indicators to reduce

to the extent possible its overlap with

the 1992 FCRS sample. The part of

the third stage redrawn sample that still

remained overlapped with the 1992 FCRS

sample was redrawn at the fourth stage

within the substrata formed by crossing

the 1993 FCRS strata, FCRS Farm Type,

and the two age indicators to reduce to

the extent possible its overlap with the

1992 FCRS sample. The part of the

fourth stage redrawn sample that still

remained overlapped with the 1992 FCRS

sample was redrawn at the fifth stage

within the substrata formed by crossing

the 1993 FCRS strata, FCRS Farm Type,

and the single age indicator to reduce

to the extent possible its overlap with

the 1992 FCRS sample. The part of

the fifth stage redrawn sample that still

remained overlapped with the 1992 FCRS

sample was redrawn at the sixth stage

within the substrata formed by crossing

the 1993 FCRS strata and the FCRS Farm

Type to reduce to the extent possible

its overlap with the 1992 FCRS sample.

Note that the sixth stage is not really

a part of the five stage algorithm and

that it provides no protection against bias

arising from differences in the age of the

control data. It is just being carried

along to determine the amount of overlap

reduction that could be obtained with no

age indicator restrictions.

Tables B13, B14, and B15 show the overlap

in each state between the 1992 FCRS

sample and the 1993 redrawn FCRS

sample that would have remained at each

stage (including the extra sixth stage)

had the five stage algorithm been used

to redraw the 1993 FCRS. Table B13

shows that the five stage algorithm reduces

the overlap at the end of the fifth stage

to no more than two in all but three

states: Arizona, New Hampshire, and

Rhode Island. The overlap in these

three states account 66 percent of the

remaining overlap at the end of the five

stage algorithm. Note that, if no age

indicator restrictions had been used the

FCRS to FCRS overlap would have been

reduced only from 32 to 23.

Tables B16, B17, and B18 show for eight

population control values the estimated

totals and coefficients of variation that

would have been associated with the

sample at each stage had the five

stage algorithm been used to redraw the

1993 FCRS. The U.S. level estimates are

given in Table B16 for all strata; in

Table B17 for stratum 90 and above; and

in Table B18 for stratum 89 and below.

These tables show that the samples are

very similar at each stage with respect to

the estimates derived from them. The

estimates tend to fall at almost the

same place in the respective confidence

intervals; the same is true for the estimated

coefficients of variation.

A comparison of Tables B1 through B6 and

Tables B10 through B15 with Tables 3A

through 4C, respectively, shows that the

burden reduction and FCRS to FCRS

overlap reduction achieved with the four

stage and the five stage algorithms is very

similar to that achieved with the two

stage algorithm. With the four stage and

five stage algorithms, there would have

34
been 32 farmers in the 1993 FCRS sample

that were also in the 1992 FCRS sample.

With the two stage algorithm, there were

29 farmers in the 1993 FCRS that were

also in the 1992 FCRS sample. With each

algorithm the larger remaining FCRS to

FCRS overlap tended to be in the same

states.

However, the extra restrictions placed

on the redrawing process in the second,

third, fourth, and fifth stage of the five

stage algorithm should cause it to have a

lower potential for biasing the 1994 FCRS

estimates than the two stage algorithm.

This is indirectly confirmed by observing

that the estimated totals and coefficients

of variations given in Tables B16, B17,

and B18 tend to be almost the same for

the first, second, third, fourth, and fifth

stage from the five stage algorithm.

35
U.S. Level Burden Reduction Using the Four Stage Algorithm

Table B1. For All Strata, U.S.: The Number of FCRS Samples and Percent of Total FCRS

Samples by Sampling Configuration for the Initial, First Stage, Second Stage, Third Stage,

Fourth Stage 1993 FCRS Sample.

Sampling Count Percent

Configuration† Initial Stage 1 Stage 2 Stage 3 Stage 4 Initial Stage 1 Stage 2 Stage 3 Stage 4

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (#) (#) (#) (%) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

93 FCRS alone 1 0 0 0 0 6617 9095 9172 9240 9250 59.2 81.4 82.0 82.7 82.8

Total 6617 9095 9172 9240 9250 59.2 81.4 82.0 82.7 82.8

93 FCRS plus one 1 0 0 0 1 1110 597 607 636 643 9.9 5.3 5.4 5.7 5.8

other survey 1 0 0 1 0 336 74 79 87 89 3.0 0.7 0.7 0.8 0.8

1 0 1 0 0 1966 668 737 801 813 17.6 6.0 6.6 7.2 7.3

1 1 0 0 0 191 305 148 33 11 1.7 2.7 1.3 0.3 0.1

Total 3603 1644 1571 1557 1556 32.2 14.7 14.1 13.9 13.9

93 FCRS plus two 1 0 0 1 1 74 24 28 33 34 0.7 0.2 0.2 0.3 0.3

other surveys 1 0 1 0 1 414 189 206 224 225 3.7 1.7 1.8 2.0 2.0

1 0 1 1 0 147 39 50 59 59 1.3 0.3 0.5 0.5 0.5

1 1 0 0 1 59 44 32 7 4 0.5 0.4 0.3 0.1 0.0

1 1 0 1 0 12 6 5 1 1 0.1 0.1 0.0 0.0 0.0

1 1 1 0 0 137 73 51 10 4 1.2 0.7 0.5 0.1 0.0

Total 843 375 372 334 327 7.5 3.4 3.3 3.0 2.9

93 FCRS plus three 1 0 1 1 1 45 26 26 33 33 0.4 0.2 0.2 0.3 0.3

other surveys 1 1 0 1 1 6 2 2 0 0 0.1 0.0 0.0 0 0

1 1 1 0 1 33 21 20 8 7 0.3 0.2 0.2 0.1 0.1

1 1 1 1 0 23 9 9 3 2 0.2 0.1 0.1 0.0 0.0

Total 107 58 57 44 42 1.0 0.5 0.5 0.4 0.4

93 FCRS plus four 1 1 1 1 1 8 6 6 3 3 0.1 0.1 0.1 0.0 0.0

other surveys Total 8 6 6 3 3 0.1 0.1 0.1 0.0 0.0

Total 11,178 11,178 11,178 11,178 11,178 100.0 100.0 100.0 100.0 100.0

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

36
Table B2. For Stratum 90 and Above, U.S.: The Number of FCRS Samples and Percent of

Total FCRS Samples by Sampling Configuration for the Initial, First Stage, Second Stage,

Third Stage, Fourth Stage 1993 FCRS Samples.

Sampling Count Percent

Configuration† Initial Stage 1 Stage 2 Stage 3 Stage 4 Initial Stage 1 Stage 2 Stage 3 Stage 4

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (#) (#) (#) (%) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

93 FCRS alone 1 0 0 0 0 1361 2260 2293 2332 2339 35.9 59.5 60.4 61.5 61.6

Total 1361 2260 2293 2332 2339 35.9 59.5 60.4 61.5 61.6

93 FCRS plus one 1 0 0 0 1 517 459 465 489 495 13.6 12.1 12.2 12.9 13.0

other survey 1 0 0 1 0 159 42 46 52 54 4.2 1.1 1.2 1.4 1.4

1 0 1 0 0 986 499 545 589 598 26.0 13.2 14.4 15.5 15.8

1 1 0 0 0 98 175 92 22 6 2.6 4.6 2.4 0.6 0.2

Total 1760 1175 1148 1152 1153 46.4 31.0 30.2 30.4 30.4

93 FCRS plus two 1 0 0 1 1 52 22 25 29 30 1.4 0.6 0.7 0.8 0.8

other surveys 1 0 1 0 1 293 158 173 187 188 7.7 4.2 4.6 4.9 5.0

1 0 1 1 0 91 27 36 44 44 2.4 0.7 0.9 1.2 1.2

1 1 0 0 1 47 39 27 6 3 1.2 1.0 0.7 0.2 0.1

1 1 0 1 0 11 5 4 1 1 0.3 0.1 0.1 0.0 0.0

1 1 1 0 0 92 59 40 7 2 2.4 1.6 1.1 0.2 0.1

Total 586 310 305 274 268 15.4 8.2 8.0 7.2 7.1

93 FCRS plus three 1 0 1 1 1 36 23 23 29 29 0.9 0.6 0.6 0.8 0.8

other surveys 1 1 0 1 1 4 1 1 0 0 0.1 0.0 0.0 0 0

1 1 1 0 1 25 16 15 6 5 0.7 0.4 0.4 0.2 0.1

1 1 1 1 0 17 6 6 1 0 0.5 0.2 0.2 0.0 0

Total 82 46 45 36 34 2.2 1.2 1.2 0.9 0.9

93 FCRS plus four 1 1 1 1 1 6 4 4 1 1 0.2 0.1 0.1 0.0 0.0

other surveys Total 6 4 4 1 1 0.2 0.1 0.1 0.0 0.0

Total 3795 3795 3795 3795 3795 100.0 100.0 100.0 100.0 100.0

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

37
Table B3. For Stratum 89 and Below, U.S.: The Number of FCRS Samples and Percent of

Total FCRS Samples by Sampling Configuration for the Initial, First Stage, Second Stage,

Third Stage, Fourth Stage 1993 FCRS Samples.

Sampling Count Percent

Configuration† Initial Stage 1 Stage 2 Stage 3 Stage 4 Initial Stage 1 Stage 2 Stage 3 Stage 4

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (#) (#) (#) (%) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

93 FCRS alone 1 0 0 0 0 5256 6835 6879 6908 6911 71.2 92.6 93.2 93.6 93.6

Total 5256 6835 6879 6908 6911 71.2 92.6 93.2 93.6 93.6

93 FCRS plus one 1 0 0 0 1 593 138 142 147 148 8.0 1.9 1.9 2.0 2.0

other survey 1 0 0 1 0 177 32 33 35 35 2.4 0.4 0.5 0.5 0.5

1 0 1 0 0 980 169 192 212 215 13.3 2.3 2.6 2.9 2.9

1 1 0 0 0 93 130 56 11 5 1.3 1.8 0.8 0.1 0.1

Total 1843 469 423 405 403 25.0 6.3 5.7 5.5 5.5

93 FCRS plus two 1 0 0 1 1 22 2 3 4 4 0.3 0.0 0.0 0.1 0.1

other surveys 1 0 1 0 1 121 31 33 37 37 1.6 0.4 0.5 0.5 0.5

1 0 1 1 0 56 12 14 15 15 0.8 0.2 0.2 0.2 0.2

1 1 0 0 1 12 5 5 1 1 0.2 0.1 0.1 0.0 0.0

1 1 0 1 0 1 1 1 0 0 0.0 0.0 0.0 0 0

1 1 1 0 0 45 14 11 3 2 0.6 0.2 0.1 0.0 0.0

Total 257 65 67 60 59 3.5 0.9 0.9 0.8 0.8

93 FCRS plus three 1 0 1 1 1 9 3 3 4 4 0.1 0.0 0.0 0.1 0.1

other surveys 1 1 0 1 1 2 1 1 0 0 0.0 0.0 0.0 0 0

1 1 1 0 1 8 5 5 2 2 0.1 0.1 0.1 0.0 0.0

1 1 1 1 0 6 3 3 2 2 0.1 0.0 0.0 0.0 0.0

Total 25 12 12 8 8 0.3 0.2 0.2 0.1 0.1

93 FCRS plus four 1 1 1 1 1 2 2 2 2 2 0.0 0.0 0.0 0.0 0.0

other surveys Total 2 2 2 2 2 0.0 0.0 0.0 0.0 0.0

Total 7383 7383 7383 7383 7383 100.0 100.0 100.0 100.0 100.0

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

38
Reduction in Overlap between 1992 and 1993 FCRS Using the Four Stage Algorithm

Table B4. For All Strata: The Number of 1993 FCRS Samples by State that were in the

1992 FCRS Sample at Each Stage of the Redrawing Process.

Overlap

State Initial Stage 1 Stage 2 Stage 3 Stage 4

01: Alabama 6 4 4 2

04: Arizona 30 29 22 14 11

05: Arkansas 9 14 5 2

06: California 26 21 13 2

08: Colorado 16 17 13 4 1

09: Connecticut 5 1 1

10: Delaware 3 2 1

12: Florida 11 10 5 2 2

13: Georgia 5 4 4 1

16: Idaho 15 14 10 1

17: Illinois 15 12 4 1

18: Indiana 6 13 4

19: Iowa 23 22 13 1

20: Kansas 18 19 11

21: Kentucky 7 6 5

22: Louisiana 12 15 7 2 1

23: Maine 3 2

24: Maryland 6 5 4 1

25: Massachusetts 2 3 2

26: Michigan 11 14 4 1

27: Minnesota 21 18 13 2

28: Mississippi 13 12 4 1

29: Missouri 8 7 2 1 1

30: Montana 2 7 5

31: Nebraska 16 16 10 2

32: Nevada 6 4 1

33: New Hampshire 9 7 7 6 6

34: New Jersey 2 3 3

36: New York 2 4 2

37: North Carolina 12 14 10 1

38: North Dakota 17 17 7

39: Ohio 9 9 1 1 1

40: Oklahoma 1 1

41: Oregon 8 7 4 1 1

42: Pennsylvania 9 6 3

44: Rhode Island 12 11 9 6 6

45: South Carolina 9 12 7

46: South Dakota 18 19 13 2

47: Tennessee 4 5 2

48: Texas 19 17 10 2

49: Utah 3 4 2

50: Vermont 8 9 4 1 1

51: Virginia 4 4 3 2

53: Washington 7 8 4 1 1

54: West Virginia 4 3 3

55: Wisconsin 2 3 1 1

56: Wyoming 15 12 11 1

Total 469 466 273 65 32

Cumulative Percent Reduction 0.6% 41.8% 86.1% 93.2%

39
Table B5. For Stratum 90 and Above: The Number of 1993 FCRS Samples by State that

were in the 1992 FCRS Sample at each Stage of the Redrawing Process.

Overlap

State Initial Stage 1 Stage 2 Stage 3 Stage 4

01: Alabama 2 2 2 1

04: Arizona 17 18 14 7 5

05: Arkansas 7 10 5 2

06: California 23 18 11 2

08: Colorado 8 9 8 2 1

09: Connecticut 1

10: Delaware 2 1 1

12: Florida 8 4 2 1 1

13: Georgia 4 4 4 1

16: Idaho 6 7 6 1

17: Illinois 12 10 4 1

18: Indiana 3 8 1

19: Iowa 18 16 11 1

20: Kansas 16 18 11

21: Kentucky 4 4 3

22: Louisiana 7 8 4 2 1

23: Maine 2 2

24: Maryland 5 4 4 1

25: Massachusetts 2 3 2

26: Michigan 6 6 3 1

27: Minnesota 13 13 10 2

28: Mississippi 8 8 1

29: Missouri 1

30: Montana 2 1

31: Nebraska 13 12 9 2

32: Nevada 4 3 1

33: New Hampshire 7 7 7 6 6

34: New Jersey 2 3 3

36: New York 2 4 2

37: North Carolina 10 11 8 1

38: North Dakota 13 12 5

39: Ohio 5 6 1 1 1

40: Oklahoma 1 1

41: Oregon 4 4 2 1 1

42: Pennsylvania 7 4 2

45: South Carolina 7 9 6

46: South Dakota 14 14 9 2

47: Tennessee 1 2 1

48: Texas 17 16 9 2

49: Utah 1 1

50: Vermont 2 4 2 1 1

51: Virginia 2 3 2 1

53: Washington 5 4 3 1 1

54: West Virginia 3 2 2

55: Wisconsin 1

56: Wyoming 7 6 6 1

Total 300 305 189 44 18

Cumulative Percent Reduction 1.7% 37.0% 85.3% 94.0%

40
Table B6. For Stratum 89 and Below: The Number of 1993 FCRS Samples by State that

were in the 1992 FCRS Sample at each Stage of the Redrawing Process.

Overlap

State Initial Stage 1 Stage 2 Stage 3 Stage 4

01: Alabama 4 2 2 1

04: Arizona 13 11 8 7 6

05: Arkansas 2 4

06: California 3 3 2

08: Colorado 8 8 5 2

09: Connecticut 4 1 1

10: Delaware 1 1

12: Florida 3 6 3 1 1

13: Georgia 1

16: Idaho 9 7 4

17: Illinois 3 2

18: Indiana 3 5 3

19: Iowa 5 6 2

20: Kansas 2 1

21: Kentucky 3 2 2

22: Louisiana 5 7 3

23: Maine 1

24: Maryland 1 1

26: Michigan 5 8 1

27: Minnesota 8 5 3

28: Mississippi 5 4 3 1

29: Missouri 8 6 2 1 1

30: Montana 2 5 4

31: Nebraska 3 4 1

32: Nevada 2 1

33: New Hampshire 2

37: North Carolina 2 3 2

38: North Dakota 4 5 2

39: Ohio 4 3

41: Oregon 4 3 2

42: Pennsylvania 2 2 1

44: Rhode Island 12 11 9 6 6

45: South Carolina 2 3 1

46: South Dakota 4 5 4

47: Tennessee 3 3 1

48: Texas 2 1 1

49: Utah 3 3 1

50: Vermont 6 5 2

51: Virginia 2 1 1 1

53: Washington 2 4 1

54: West Virginia 1 1 1

55: Wisconsin 2 2 1 1

56: Wyoming 8 6 5

Total 169 161 84 21 14

Cumulative Percent Reduction 4.7% 50.3% 87.6% 91.7%

41
U.S. Level Control Value Estimates Using the Four Stage Algorithm

Table B7. For All Strata, U.S.: The Estimated 1993 Population Control Variable Totals for

the Initial, First Stage, Second Stage, Third Stage, and Fourth Stage 1993 FCRS Samples.

90% 90% Estimated Total Exact CV of Estimated CV

Control Pop. Lower Upper Initial Stage 1 Stage 2 Stage 3 Stage 4 Estimated Initial Stage 1 Stage 2 Stage 3 Stage 4

Variable† Total Bound Bound Sample Sample Sample Sample Sample Total Sample Sample Sample Sample Sample

(#) (#) (#) (#) (#) (#) (#) (#) (%) (%) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)

Total Land in Farm 862.52 47.04 1678.01 791.28 798.17 794.39 789.44 788.83 57.30 2.31 2.46 2.45 2.43 2.44

Farm Value of Sales 150.53 148.44 152.62 151.96 151.93 152.07 152.28 152.13 0.84 0.86 0.85 0.88 0.88 0.88

Total Cropland 363.62 327.21 400.03 363.54 365.83 365.65 365.74 365.34 6.07 1.11 1.07 1.07 1.06 1.06

On-Farm Grain Storage 947.58 902.34 992.81 992.67 990.91 990.02 987.42 985.70 2.89 2.98 2.88 2.88 2.88 2.88

All Cattle & Calves 850.13 811.07 889.19 821.80 829.07 828.11 825.19 824.34 2.78 3.05 3.21 3.21 3.19 3.18

Total Hogs & Pigs 547.15 457.17 637.12 588.76 576.22 572.97 573.24 571.79 9.97 5.33 4.08 4.08 4.08 4.09

All Sheep 114.96 88.60 141.32 106.15 103.90 104.12 102.14 102.14 13.90 13.02 13.13 13.11 13.30 13.30

Farm Workers Hired 127.21 58.80 195.61 102.40 102.54 103.66 105.11 104.65 32.59 5.22 5.31 5.43 5.41 5.43

† All missing control values were set to zero before any computations were performed. The units of measure for the population

totals and their estimates are:

1, 000, 000 acres for Total Land; $1, 000, 000, 000 for Farm Value Of Sales;

1, 000, 000 acres for Total Cropland; 10, 000, 000 bushels for On-Farm Grain Storage;

100, 000 head for Cattle & Calves, Hogs & Pigs, and Sheep; 10, 000 workers Farm Workers Hired.

Table B8. For Stratum 90 and Above, U.S.: The Estimated 1993 Population Control

Variable Totals for the Initial, First Stage, Second Stage, Third Stage, and Fourth Stage

1993 FCRS Samples.

90% 90% Estimated Total Exact CV of Estimated CV

Control Pop. Lower Upper Initial Stage 1 Stage 2 Stage 3 Stage 4 Estimated Initial Stage 1 Stage 2 Stage 3 Stage 4

Variable† Total Bound Bound Sample Sample Sample Sample Sample Total Sample Sample Sample Sample Sample

(#) (#) (#) (#) (#) (#) (#) (#) (%) (%) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)

Total Land in Farm 200.12 160.57 239.67 196.58 192.54 191.38 186.91 186.52 11.98 5.19 5.16 5.14 5.13 5.14

Farm Value of Sales 50.00 48.26 51.73 50.77 50.74 50.95 51.05 50.90 2.10 2.14 2.13 2.26 2.26 2.26

Total Cropland 87.84 53.34 122.33 81.81 82.47 82.35 82.37 82.12 23.80 1.94 1.93 1.92 1.92 1.91

On-Farm Grain Storage 209.98 198.54 221.41 220.22 221.58 222.99 222.68 222.82 3.30 3.96 3.93 3.93 3.98 3.98

All Cattle & Calves 285.97 251.17 320.77 286.42 295.52 295.02 291.71 290.60 7.38 7.93 8.30 8.31 8.30 8.30

Total Hogs & Pigs 198.78 113.57 283.98 196.45 177.03 175.51 174.99 173.93 25.98 12.75 7.47 7.48 7.49 7.53

All Sheep 32.95 18.40 47.50 32.10 33.26 33.26 33.49 33.49 26.76 25.68 25.10 25.10 24.83 24.83

Farm Workers Hired 45.00 25.34 64.64 37.16 36.63 37.78 38.29 37.99 26.47 8.02 8.04 8.69 8.73 8.76

† All missing control values were set to zero before any computations were performed. The units of measure for the population

totals and their estimates are:

1, 000, 000 acres for Total Land; $1, 000, 000, 000 for Farm Value Of Sales;

1, 000, 000 acres for Total Cropland; 10, 000, 000 bushels for On-Farm Grain Storage;

100, 000 head for Cattle & Calves, Hogs & Pigs, and Sheep; 10, 000 workers Farm Workers Hired.

42
Table B9. For Stratum 89 and Below, U.S.: The Estimated 1993 Population Control

Variable Totals for the Initial, First Stage, Second Stage, Third Stage, and Fourth Stage

1993 FCRS Samples.

90% 90% Estimated Total Exact CV of Estimated CV

Control Pop. Lower Upper Initial Stage 1 Stage 2 Stage 3 Stage 4 Estimated Initial Stage 1 Stage 2 Stage 3 Stage 4

Variable† Total Bound Bound Sample Sample Sample Sample Sample Total Sample Sample Sample Sample Sample

(#) (#) (#) (#) (#) (#) (#) (#) (%) (%) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)

Total Land in Farm 662.40 -152.13 1476.92 594.70 605.63 603.01 602.53 602.31 74.52 2.55 2.79 2.78 2.76 2.76

Value of Sales 100.53 99.36 101.71 101.19 101.19 101.12 101.23 101.23 0.71 0.70 0.68 0.68 0.68 0.68

Total Cropland 275.78 264.14 287.43 281.73 283.36 283.30 283.37 283.22 2.56 1.32 1.26 1.26 1.25 1.25

On-Farm Grain Storage 737.60 693.84 781.37 772.45 769.32 767.03 764.74 762.89 3.60 3.66 3.53 3.54 3.54 3.54

All Cattle & Calves 564.16 546.42 581.89 535.38 533.56 533.08 533.48 533.75 1.91 1.97 1.93 1.93 1.93 1.93

Total Hogs & Pigs 348.37 319.46 377.28 392.31 399.19 397.47 398.24 397.86 5.03 4.82 4.86 4.86 4.86 4.86

All Sheep 82.01 60.02 103.99 74.05 70.65 70.86 68.65 68.65 16.25 14.98 15.28 15.24 15.65 15.65

Farm Workers Hired 82.22 16.70 147.74 65.24 65.91 65.89 66.81 66.67 48.30 6.80 6.94 6.95 6.90 6.91

† All missing control values were set to zero before any computations were performed. The units of measure for the population

totals and their estimates are:

1, 000, 000 acres for Total Land; $1, 000, 000, 000 for Farm Value Of Sales;

1, 000, 000 acres for Total Cropland; 10, 000, 000 bushels for On-Farm Grain Storage;

100, 000 head for Cattle & Calves, Hogs & Pigs, and Sheep; 10, 000 workers Farm Workers Hired.

43
U.S. Level Burden Reduction Using the Five Stage Algorithm

Table B10. For All Strata, U.S.: The Number of FCRS Samples and Percent of Total FCRS

Samples by Sampling Configuration for the Initial, First Stage, Second Stage, Third Stage,

Fourth Stage, Fifth Stage, Sixth Stage 1993 FCRS Samples.

Sampling Count Percent

Configuration† Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (#) (#) (#) (#) (#) (%) (%) (%) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)

93 FCRS alone 1 0 0 0 0 6617 9095 9158 9227 9240 9245 9249 59.2 81.4 81.9 82.5 82.7 82.7 82.7

Total 6617 9095 9158 9227 9240 9245 9249 59.2 81.4 81.9 82.5 82.7 82.7 82.7

93 FCRS plus one 1 0 0 0 1 1110 597 607 631 635 637 638 9.9 5.3 5.4 5.7 5.7 5.7 5.7

other survey 1 0 0 1 0 336 74 80 87 88 88 89 3.0 0.7 0.7 0.8 0.8 0.8 0.8

1 0 1 0 0 1966 668 738 800 813 814 816 17.6 6.0 6.6 7.2 7.3 7.3 7.3

1 1 0 0 0 191 305 160 41 19 10 4 1.7 2.7 1.4 0.4 0.2 0.1 0.0

Total 3603 1644 1585 1559 1555 1549 1547 32.2 14.7 14.2 13.9 13.9 13.9 13.8

93 FCRS plus two 1 0 0 1 1 74 24 29 35 36 36 36 0.7 0.2 0.3 0.3 0.3 0.3 0.3

other surveys 1 0 1 0 1 414 189 206 231 234 235 235 3.7 1.7 1.8 2.1 2.1 2.1 2.1

1 0 1 1 0 147 39 49 55 57 57 57 1.3 0.3 0.4 0.5 0.5 0.5 0.5

1 1 0 0 1 59 44 31 7 4 4 4 0.5 0.4 0.3 0.1 0.0 0.0 0.0

1 1 0 1 0 12 6 5 1 1 1 1 0.1 0.1 0.0 0.0 0.0 0.0 0.0

1 1 1 0 0 137 73 52 16 5 5 3 1.2 0.7 0.5 0.1 0.0 0.0 0.0

Total 843 375 372 345 337 338 336 7.5 3.4 3.3 3.1 3.0 3.0 3.0

93 FCRS plus three 1 0 1 1 1 45 26 26 32 34 34 35 0.4 0.2 0.2 0.3 0.3 0.3 0.3

other surveys 1 1 0 1 1 6 2 2 0 0 0 0 0.1 0.0 0.0 0 0 0 0

1 1 1 0 1 33 21 20 9 7 7 6 0.3 0.2 0.2 0.1 0.1 0.1 0.1

1 1 1 1 0 23 9 9 3 2 2 2 0.2 0.1 0.1 0.0 0.0 0.0 0.0

Total 107 58 57 44 43 43 43 1.0 0.5 0.5 0.4 0.4 0.4 0.4

93 FCRS plus four 1 1 1 1 1 8 6 6 3 3 3 3 0.1 0.1 0.1 0.0 0.0 0.0 0.0

other surveys Total 8 6 6 3 3 3 3 0.1 0.1 0.1 0.0 0.0 0.0 0.0

Total 11,178 11,178 11,178 11,178 11,178 11,178 11,178 100.0 100.0 100.0 100.0 100.0 100.0 100.0

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

44
Table B11. For Stratum 90 and Above, U.S.: The Number of FCRS Samples and Percent of

Total FCRS Samples by Sampling Configuration for the Initial, First Stage, Second Stage,

Third Stage, Fourth Stage, Fifth Stage, Sixth Stage 1993 FCRS Samples.

Sampling Count Percent

Configuration† Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (#) (#) (#) (#) (#) (%) (%) (%) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)

93 FCRS alone 1 0 0 0 0 1361 2260 2284 2323 2334 2337 2339 35.9 59.5 60.2 61.2 61.5 61.6 61.6

Total 1361 2260 2284 2323 2334 2337 2339 35.9 59.5 60.2 61.2 61.5 61.6 61.6

93 FCRS plus one 1 0 0 0 1 517 459 465 484 488 490 491 13.6 12.1 12.2 12.8 12.9 12.9 12.9

other survey 1 0 0 1 0 159 42 46 51 52 52 52 4.2 1.1 1.2 1.3 1.4 1.4 1.4

1 0 1 0 0 986 499 548 593 601 602 603 26.0 13.2 14.4 15.6 15.8 15.9 15.9

1 1 0 0 0 98 175 99 26 11 4 1 2.6 4.6 2.6 0.7 0.3 0.1 0.0

Total 1760 1175 1158 1154 1152 1148 1147 46.4 31.0 30.5 30.4 30.4 30.2 30.2

93 FCRS plus two 1 0 0 1 1 52 22 26 31 32 32 32 1.4 0.6 0.7 0.8 0.8 0.8 0.8

other surveys 1 0 1 0 1 293 158 173 193 196 197 197 7.7 4.2 4.6 5.1 5.2 5.2 5.2

1 0 1 1 0 91 27 35 39 40 40 40 2.4 0.7 0.9 1.0 1.1 1.1 1.1

1 1 0 0 1 47 39 26 6 3 3 3 1.2 1.0 0.7 0.2 0.1 0.1 0.1

1 1 0 1 0 11 5 4 1 1 1 1 0.3 0.1 0.1 0.0 0.0 0.0 0.0

1 1 1 0 0 92 59 40 13 3 3 1 2.4 1.6 1.1 0.3 0.1 0.1 0.0

Total 586 310 304 283 275 276 274 15.4 8.2 8.0 7.5 7.2 7.3 7.2

93 FCRS plus three 1 0 1 1 1 36 23 23 27 29 29 30 0.9 0.6 0.6 0.7 0.8 0.8 0.8

other surveys 1 1 0 1 1 4 1 1 0 0 0 0 0.1 0.0 0.0 0 0 0 0

1 1 1 0 1 25 16 15 6 4 4 4 0.7 0.4 0.4 0.2 0.1 0.1 0.1

1 1 1 1 0 17 6 6 1 0 0 0 0.5 0.2 0.2 0.0 0 0 0

Total 82 46 45 34 33 33 34 2.2 1.2 1.2 0.9 0.9 0.9 0.9

93 FCRS plus four 1 1 1 1 1 6 4 4 1 1 1 1 0.2 0.1 0.1 0.0 0.0 0.0 0.0

other surveys Total 6 4 4 1 1 1 1 0.2 0.1 0.1 0.0 0.0 0.0 0.0

Total 3795 3795 3795 3795 3795 3795 3795 100.0 100.0 100.0 100.0 100.0 100.0 100.0

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

45
Table B12. For all Stratum 89 and Below, U.S.: The Number of FCRS Samples and Percent

of Total FCRS Samples by Sampling Configuration for the Initial, First Stage, Second Stage,

Third Stage, Fourth Stage, Fifth Stage, Sixth Stage 1993 FCRS Samples.

Sampling Count Percent

Configuration† Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

Combination

of Surveys

9

3

F

C

R

S

9

2

F

C

R

S

9

3

Q

A

S

9

3

A

L

S

9

3

C

S

S (#) (#) (#) (#) (#) (#) (#) (%) (%) (%) (%) (%) (%) (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)

93 FCRS alone 1 0 0 0 0 5256 6835 6874 6904 6906 6908 6910 71.2 92.6 93.1 93.5 93.5 93.6 93.6

Total 5256 6835 6874 6904 6906 6908 6910 71.2 92.6 93.1 93.5 93.5 93.6 93.6

93 FCRS plus one 1 0 0 0 1 593 138 142 147 147 147 147 8.0 1.9 1.9 2.0 2.0 2.0 2.0

other survey 1 0 0 1 0 177 32 34 36 36 36 37 2.4 0.4 0.5 0.5 0.5 0.5 0.5

1 0 1 0 0 980 169 190 207 212 212 213 13.3 2.3 2.6 2.8 2.9 2.9 2.9

1 1 0 0 0 93 130 61 15 8 6 3 1.3 1.8 0.8 0.2 0.1 0.1 0.0

Total 1843 469 427 405 403 401 400 25.0 6.3 5.8 5.5 5.5 5.4 5.4

93 FCRS plus two 1 0 0 1 1 22 2 3 4 4 4 4 0.3 0.0 0.0 0.1 0.1 0.1 0.1

other surveys 1 0 1 0 1 121 31 33 38 38 38 38 1.6 0.4 0.5 0.5 0.5 0.5 0.5

1 0 1 1 0 56 12 14 16 17 17 17 0.8 0.2 0.2 0.2 0.2 0.2 0.2

1 1 0 0 1 12 5 5 1 1 1 1 0.2 0.1 0.1 0.0 0.0 0.0 0.0

1 1 0 1 0 1 1 1 0 0 0 0 0.0 0.0 0.0 0 0 0 0

1 1 1 0 0 45 14 12 3 2 2 2 0.6 0.2 0.2 0.0 0.0 0.0 0.0

Total 257 65 68 62 62 62 62 3.5 0.9 0.9 0.8 0.8 0.8 0.8

93 FCRS plus three 1 0 1 1 1 9 3 3 5 5 5 5 0.1 0.0 0.0 0.1 0.1 0.1 0.1

other surveys 1 1 0 1 1 2 1 1 0 0 0 0 0.0 0.0 0.0 0 0 0 0

1 1 1 0 1 8 5 5 3 3 3 2 0.1 0.1 0.1 0.0 0.0 0.0 0.0

1 1 1 1 0 6 3 3 2 2 2 2 0.1 0.0 0.0 0.0 0.0 0.0 0.0

Total 25 12 12 10 10 10 9 0.3 0.2 0.2 0.1 0.1 0.1 0.1

93 FCRS plus four 1 1 1 1 1 2 2 2 2 2 2 2 0.0 0.0 0.0 0.0 0.0 0.0 0.0

other surveys Total 2 2 2 2 2 2 2 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Total 7383 7383 7383 7383 7383 7383 7383 100.0 100.0 100.0 100.0 100.0 100.0 100.0

† Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,

93ALS and 93CSS (Cattle and Sheep). For example, a 10001 indicates sample units selected for only the

93FCRS and 93CSS.

46
Table B13. For All Strata: The Number of 1993 FCRS Samples by State that were in the

1992 FCRS Sample at each Stage of the Redrawing Process.

Overlap

State Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

01: Alabama 6 4 4 1

04: Arizona 30 29 22 12 9 9 9

05: Arkansas 9 14 5 2

06: California 26 21 13 2

08: Colorado 16 17 13 4

09: Connecticut 5 1 1 1 1 1

10: Delaware 3 2 1

12: Florida 11 10 5 2 2 1

13: Georgia 5 4 4 1

16: Idaho 15 14 10 2 1

17: Illinois 15 12 5 1 1 1

18: Indiana 6 13 5 1 1

19: Iowa 23 22 13 2

20: Kansas 18 19 11 1

21: Kentucky 7 6 5 1

22: Louisiana 12 15 8 2 2

23: Maine 3 2

24: Maryland 6 5 4 1 1 1

25: Massachusetts 2 3 2

26: Michigan 11 14 4 1 1

27: Minnesota 21 18 16 4

28: Mississippi 13 12 4 1

29: Missouri 8 7 2 1 1 1

30: Montana 2 7 5

31: Nebraska 16 16 9 3

32: Nevada 6 4 1 1

33: New Hampshire 9 7 7 6 6 6 6

34: New Jersey 2 3 3

36: New York 2 4 2

37: North Carolina 12 14 10 1

38: North Dakota 17 17 8 1

39: Ohio 9 9 1 1 1

40: Oklahoma 1 1

41: Oregon 8 7 4

42: Pennsylvania 9 6 3

44: Rhode Island 12 11 11 6 6 6 6

45: South Carolina 9 12 8 2 2 2 1

46: South Dakota 18 19 13 2

47: Tennessee 4 5 2 1

48: Texas 19 17 12 4

49: Utah 3 4 2 1

50: Vermont 8 9 5 2 2 2 1

51: Virginia 4 4 2 2 1

53: Washington 7 8 4 1 1

54: West Virginia 4 3 3

55: Wisconsin 2 3 2 1

56: Wyoming 15 12 11 2 2 2

Total 469 466 285 80 41 32 23

Cumulative Percent Reduction 0.6% 39.2% 82.9% 91.3% 93.2% 95.1%

47
Table B14. For Stratum 90 and above: The Number of 1993 FCRS Samples by State that

were in the 1992 FCRS Sample at each Stage of the Redrawing Process.

Overlap

State Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

01: Alabama 2 2 2

04: Arizona 17 18 14 5 3 3 3

05: Arkansas 7 10 5 2

06: California 23 18 11 2

08: Colorado 8 9 7 2

09: Connecticut 1

10: Delaware 2 1 1

12: Florida 8 4 2 1 1

13: Georgia 4 4 4 1

16: Idaho 6 7 6 1

17: Illinois 12 10 5 1 1 1

18: Indiana 3 8 1

19: Iowa 18 16 11 2

20: Kansas 16 18 11 1

21: Kentucky 4 4 3 1

22: Louisiana 7 8 4 2 2

23: Maine 2 2

24: Maryland 5 4 4 1 1 1

25: Massachusetts 2 3 2

26: Michigan 6 6 3 1 1

27: Minnesota 13 13 13 4

28: Mississippi 8 8 1

29: Missouri 1

30: Montana 2 1

31: Nebraska 13 12 8 3

32: Nevada 4 3 1 1

33: New Hampshire 7 7 7 6 6 6 6

34: New Jersey 2 3 3

36: New York 2 4 2

37: North Carolina 10 11 8 1

38: North Dakota 13 12 6 1

39: Ohio 5 6 1 1 1

40: Oklahoma 1 1

41: Oregon 4 4 2

42: Pennsylvania 7 4 2

45: South Carolina 7 9 7 2 2 2 1

46: South Dakota 14 14 9 2

47: Tennessee 1 2 1

48: Texas 17 16 11 4

49: Utah 1 1 1

50: Vermont 2 4 2 2 2 2 1

51: Virginia 2 3 1 1 1

53: Washington 5 4 3 1 1

54: West Virginia 3 2 2

55: Wisconsin 1 1

56: Wyoming 7 6 6 1 1 1

Total 300 305 195 54 23 16 11

Cumulative Percent Reduction -1.7% 35.0% 82.0% 92.3% 94.7% 95.1%

48
Table B15. For Stratum 89 and below: The Number of 1993 FCRS Samples by State that

were in the 1992 FCRS Sample at each Stage of the Redrawing Process.

Overlap

State Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

01: Alabama 4 2 2 1

04: Arizona 13 11 8 7 6 6 6

05: Arkansas 2 4

06: California 3 3 2

08: Colorado 8 8 6 2

09: Connecticut 4 1 1 1 1 1

10: Delaware 1 1

12: Florida 3 6 3 1 1 1

13: Georgia 1

16: Idaho 9 7 4 1 1

17: Illinois 3 2

18: Indiana 3 5 4 1 1

19: Iowa 5 6 2

20: Kansas 2 1

21: Kentucky 3 2 2

22: Louisiana 5 7 4

23: Maine 1

24: Maryland 1 1

26: Michigan 5 8 1

27: Minnesota 8 5 3

28: Mississippi 5 4 3 1

29: Missouri 8 6 2 1 1 1

30: Montana 2 5 4

31: Nebraska 3 4 1

32: Nevada 2 1

33: New Hampshire 2

37: North Carolina 2 3 2

38: North Dakota 4 5 2

39: Ohio 4 3

41: Oregon 4 3 2

42: Pennsylvania 2 2 1

44: Rhode Island 12 11 11 6 6 6 6

45: South Carolina 2 3 1

46: South Dakota 4 5 4

47: Tennessee 3 3 1 1

48: Texas 2 1 1

49: Utah 3 3 1

50: Vermont 6 5 3

51: Virginia 2 1 1 1

53: Washington 2 4 1

54: West Virginia 1 1 1

55: Wisconsin 2 2 1 1

56: Wyoming 8 6 5 1 1 1

Total 169 161 90 26 18 16 12

Cumulative Percent Reduction 4.7% 46.7% 84.6% 89.3% 90.5% 92.9%

49
U.S. Level Control Value Estimates Using the Five Stage Algorit

Table B16. For All Strata, U.S.: The Estimated 1993 Population Control Vari

Initial, First Stage, Second Stage, Third Stage, Fourth Stage, Fifth Stage, and 

FCRS Samples.

90% 90% Estimated Total Exact CV of E

Control Pop. Lower Upper Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Estimated Initial Stage 1 Stage 

Variable† Total Bound Bound Sample Sample Sample Sample Sample Sample Sample Total Sample Sample Samp

(#) (#) (#) (#) (#) (#) (#) (#) (#) (#) (%) (%) (%) (%) 

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) 

Total Land in Farm 862.52 47.04 1678.01 791.28 798.17 792.91 790.77 790.81 790.67 790.89 57.30 2.31 2.46 2.4

Farm Value of Sales 150.53 148.44 152.62 151.96 151.93 151.91 151.91 151.92 151.90 151.90 0.84 0.86 0.85 0.8

Total Cropland 363.62 327.21 400.03 363.54 365.83 365.45 364.63 364.57 364.50 364.48 6.07 1.11 1.07 1.0

On-Farm Grain Storage 947.58 902.34 992.81 992.67 990.91 989.17 992.07 990.66 990.48 990.49 2.89 2.98 2.88 2.8

All Cattle & Calves 850.13 811.07 889.19 821.80 829.07 825.44 830.78 831.88 832.10 832.38 2.78 3.05 3.21 3.2

Total Hogs & Pigs 547.15 457.17 637.12 588.76 576.22 573.72 573.26 571.33 571.33 571.31 9.97 5.33 4.08 4.0

All Sheep 114.96 88.60 141.32 106.15 103.90 104.15 100.09 101.15 101.15 101.39 13.90 13.02 13.13 13.1

Farm Workers Hired 127.21 58.80 195.61 102.40 102.54 103.75 104.50 104.45 104.47 104.58 32.59 5.22 5.31 5.4

† All missing control values were set to zero before any computations were performed. The units of measure 

and their estimates are:

1, 000, 000 acres for Total Land; $1, 000, 000, 000 for Farm Value Of Sales;

1, 000, 000 acres for Total Cropland; 10, 000, 000 bushels for On-Farm Grain Stora

100, 000 head for Cattle & Calves, Hogs & Pigs, and Sheep; 10, 000 workers Farm Workers Hired.

Table B17. For Stratum 90 and Above, U.S.: The Estimated 1993 Population 

Totals for the Initial, First Stage, Second Stage, Third Stage, Fourth Stage, Fift

Stage 1993 FCRS Samples.

90% 90% Estimated Total Exact CV of E

Control Pop. Lower Upper Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Estimated Initial Stage 1 Stage 

Variable† Total Bound Bound Sample Sample Sample Sample Sample Sample Sample Total Sample Sample Samp

(#) (#) (#) (#) (#) (#) (#) (#) (#) (#) (%) (%) (%) (%) 

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) 

Total Land in Farm 200.12 160.57 239.67 196.58 192.54 191.11 188.35 188.56 188.42 188.71 11.98 5.19 5.16 5.1

5000 4826 5173 5077 5074 5078 5064 5065 5064 5065 210 214 213 22
Table B18. For Stratum 89 and Below, U.S.: The Estimated 1993 Population 

Totals for the Initial, First Stage, Second Stage, Third Stage, Fourth Stage, Fift

Stage 1993 FCRS Samples.

90% 90% Estimated Total Exact CV of E

Control Pop. Lower Upper Initial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Estimated Initial Stage 1 Stage 

Variable† Total Bound Bound Sample Sample Sample Sample Sample Sample Sample Total Sample Sample Samp

(#) (#) (#) (#) (#) (#) (#) (#) (#) (#) (%) (%) (%) (%) 

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) 

Total Land in Farm 662.40 -152.13 1476.92 594.70 605.63 601.80 602.42 602.25 602.25 602.18 74.52 2.55 2.79 2.7

Value of Sales 100.53 99.36 101.71 101.19 101.19 101.13 101.27 101.27 101.27 101.25 0.71 0.70 0.68 0.6

Total Cropland 275.78 264.14 287.43 281.73 283.36 283.35 283.31 283.23 283.23 283.20 2.56 1.32 1.26 1.2

On-Farm Grain Storage 737.60 693.84 781.37 772.45 769.32 767.24 769.20 767.75 767.72 767.75 3.60 3.66 3.53 3.5

All Cattle & Calves 564.16 546.42 581.89 535.38 533.56 533.52 536.26 536.46 536.49 536.64 1.91 1.97 1.93 1.9

Total Hogs & Pigs 348.37 319.46 377.28 392.31 399.19 397.44 397.54 396.78 396.78 396.78 5.03 4.82 4.86 4.8

All Sheep 82.01 60.02 103.99 74.05 70.65 70.90 68.41 68.41 68.41 68.43 16.25 14.98 15.28 15.2

Farm Workers Hired 82.22 16.70 147.74 65.24 65.91 66.02 66.80 66.66 66.66 66.80 48.30 6.80 6.94 6.9

† All missing control values were set to zero before any computations were performed. The units of measure 

and their estimates are:

1, 000, 000 acres for Total Land; $1, 000, 000, 000 for Farm Value Of Sales;

1, 000, 000 acres for Total Cropland; 10, 000, 000 bushels for On-Farm Grain Stora

100, 000 head for Cattle & Calves, Hogs & Pigs, and Sheep; 10, 000 workers Farm Workers Hired.