REDRAWING THE 1993 FARM COSTS AND RETURNS SURVEY LISTFRAME SAMPLE TO REDUCE ITS OVERLAP WITH THE 1992 FCRS ANDTHREE 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 StatisticsService (NASS) to redraw the 1993 Farm Costs and Returns Survey (FCRS) list framesample. This algorithm was devised to reduce the number of farm and ranch operators inthe FCRS sample that are also in other major surveys' samples. It decreased the number ofoperators in the 1993 FCRS sample that were also in one or more of the four other majorsurveys from 4,561 to 1,966 (a decrease of 57 percent). It decreased the number of operatorsin 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 samplethat were not in any of the four other major surveys from 6,617 to 9,212 (an increase of 39percent). It is recommended that a five stage algorithm be used to redraw the 1994 FCRSsample.

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 NASSor USDA.

ACKNOWLEDGEMENTS

We would like to thank Jim Davies for suggesting the application discussed in this reportand to express our appreciation once more to Ron Bosecker, George Hanuschak and JimDavies 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 technicalediting, which greatly improved the readability of the report. We would also like to thankVic Tolomeo, Joe Prusacki, and Wayne Dionne for their assistance in retrieving the largeamount of data required for this application.

Table of Contents

SUMMARY

INTRODUCTION

ALGORITHMFirst Stage .

Second Stage

Reasons for Using a Two Stage Algorithm

RESULTSu.S. Level Burden Reduction

State Level Burden Reduction

U.S. Level Control Variable Estimates

HI

1

2

3,..,I

10

11

11

13

17

For the 1994 FCRS, If the Same Algorithm is Used

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

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

BIAS CONSIDERATIONSFor the 1993 FCRS ..... •••• 4 ••• 4 ••••

17

22

23

2425

CONCLUSIONS

RECOMMENDATIONS

For the 1994 FCllS

For the 1996 Sample Select .

REFERENCES

APPENDIX A: Burden Reduction for a Single Stage Algorithm

27

27

2828

28

29

APPENDIX B: Burden Reduction, Overlap Reduction, and Bias, for the FourStage and Five Stage Algorithms 33

11

SUMMARY

This report describes a sampling algorithm implemented by the National AgriculturalStatistics Service (NASS) to reduce substantially the number of farmers selected for the1993 Farm Costs and Returns Survey (FCRS) who were also selected for one or more ofNASS's three other major 1993 surveys or for the 1992 FCRS. To accomplish this, NASSemployed a two stage process:

1) Redraw the 1993 FCRS sample in order to reduce overlap between the 1993 FCRS sampleand 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 the1993 FCRS sample and the 1992 FCRS sample.

The report begins with a description of the two stage algorithm. It proceeds with theoreticaland empirical justification for the algorithm, including tables showing that the estimatedtotals 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, redrawingthe 1993 FCRS sample:

1) Decreased the number of 1993 FCRS sample units that were in one or more of the otherfour 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'sFCRS 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 foursurveys from 6,617 to 9,212 (an increase of 39 percent).

1ll

It should be noted that the redrawn sample was based on stratification and sample selectinformation from the 1992 and 1993 list frame spring classify and sample select. The analysisdoes not reflect reclassification and resampling (after spring classify and sample select) ofsome 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 benoted that the records selected in Illinois, Iowa, and Minnesota for the 1993 CUFFS wereexcluded 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 FCRSestimates, hence undetectable in light of the coefficients of variation associated with theestimates.

It is recommended that a five stage algorithm, which is an extension of the two stagealgorithm used in 1993, be used to redraw the 1994 FCRS sample. The two stage algorithmwould 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 FrameSample 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 Costsand Returns Survey (FCRS) questionnaire,the detail of the information requiredto answer many FCRS questions, andthe intrusive nature of the informationasked for in many FCRS questions, thereexists a general agreement among NationalAgricultural Statistics Service (NASS)statisticians and interviewers that theFCRS causes more burden on a respondentthan any other NASS survey.

In the last few years, as the number ofpublic and private surveys has increased,statisticians and other government officialshave become increasingly concerned aboutthe burden these surveys place on individ-ual respondents. The widely held belief isthat the burden experienced by individualrespondents tends to increase nonlinearlyas they are asked to participate in multi-ple surveys over a short time period. Thismeans that the burden placed on the pop-ulation can be reduced by minimizing thenumber of times anyone individual is con-tacted. For example, burden is reduced bycontacting two individuals for one surveyeach instead of contacting one individualfor two surveys.

In addition to reducing burden, there aretwo other reasons for spreading the burdenover the population to the extent possible.First, responding to surveys is one of the

1

costs of providing agricultural statistics.To the extent that these statistics benefitfarmers, it is more equitable that theircosts be shared equally among farmers.Second, at some level of burden, farmersmay refuse to participate in surveys. Byspreading the burden to more farmers, thenumber of refusals should be reduced.

The points above lead most NASSstatisticians to conclude that the FCRSsample should be selected using a methodthat minimizes the overlap within surveycycles between the FCRS sample andother major survey samples and minimizesthe overlap across survey cycles betweenFCRS samples. The general assumptionis that decreasing the number of timesNASS contacts individual farm and ranchoperators (farmers) should decrease theburden placed on the farm population.This should not only improve the overallresponse rates and quality of NASSsurveys, but it should also improve thecooperation farmers give to NASS andother survey organizations.

In "Methods of Selecting Samples InMultiple Surveys To Reduce RespondentBurden," Perry, Burt, and Iwig (1993)presented two new methods of drawingsamples in multiple surveys that minimizethe burden on the individual populationunits sampled. These new methods workby spreading the burden from multiplesurveys as uniformly as possible over the

population without changing the selectionprobabilities for any survey.

This report describes ho\v a special caseof the Second- Method presented by Perry,Burt, and Iwig (1993) '\-vas first used toredraw the 1993 FCRS list frame sampleso that its overlap with the 1993 QuarterlyAgricultural Survey (QAS), AgriculturalLabor Survey (ALS), and Cattle andSheep Survey (CSS) is minimized and thenused again to randomly shift the redrawnsample where necessary so that its overlapwith the 1992 FCRS is minimized.

In the remainder of this report, thequalifying phrase list frame is droppedfrom terms such as list frame sample.Since this report deals exclusively with thelis t fr ame part of NASS surveys, theseabbreviations should cause no ambiguity.

The first section of this report describesthe two stage algorithm used to redrawthe 1993 FCRS sample. Within groupsof farmers having the same multivariatestratification for the four major 1993surveys (that is to say, farmers A andB are in the same group when farmer Ais in the same stratum as farmer B forall four surveys), the first stage of thealgorithm randomly shifts the 1993 FCRSsample, where possible, to another sampleof farmers having lower burden for the four1993 surveys. 'Within groups of farmershaving the same multivariate stratificationfor the 1992 and 1993 FCRS surveys, thesecond stage of the algorithm randomlyshifts the part of first stage sample thatoverlaps with the 1992 FCRS sample,where possible, to another sample offarmers who were not in the 1992 FCRSsample.

The second section describes the results ofredrawing the 1993 FCRS sample. Tables

2

are given that show a detailed breakdownof the burden associated with the initial,first stage, and final redrawn samplesalong 'with the burden reduction achievedby redrawing the sample. Also, tablesare given that show, for eight populationcontrol variables, the estimated totals andcoefficients of variation that are associatedwith the initial, first stage, and redrawnsamples.

The third section discusses any possiblebias that may be introduced into theestimates by the algorithm. Particularly,the bias that could result from the secondstage of the algorithm is examined. Inaddition, the potential for bias that ariseswhen the algorithm is applied in twoconsecutive years is examined. Finally,four stage and five stage algorithms areintroduced and examined which limit thepotent ial for bias that arises when thealgorithm is applied in two consecutiveyears.

The fc,urth and fifth sections respectivelygive conclusions and recommendations forredrawing the 1994 FCRS that result fromvvhat has been learned in the course ofredrawing the 1993 FCRS sample.

ALGORITHM

There are three steps to the Second-Method described by Perry, Burt, andhvig (1993) for drawing multiple surveyssamples that minimize the burden on theindividual units sampled:

Step l. Use an equal probability of selec-tion procedure within each stra-tum to select independent strati-fied samples for each survey.

Step 2. Cross-classify the population bythe stratifications used in theindividual surveys.

Step 3. Within each substratum, ran-domly reassign the samples asso-ciated with sampling units havingexcess burden to population unitshaving less burden. Repeat theprocess until the burden on indi-vidual units sampled is minimized.

A two stage algorithm is given below thatfirst redraws the 1993 FCRS sample toreduce its overlap with the 1993 QAS,ALS, and CSS samples and then redrawsthe redrawn sample to reduce its overlapwith the 1992 FCRS sample. The firststage of the algorithm randomly shiftsthe 1993 FCRS sample within groupsof farmers having the same multivariatestratification for the four 1993 surveys,where possible, to another sample offarmers having lower burden for the four1993 surveys. The second stage ofthe algorithm randomly shifts the partof first stage sample that overlaps withthe 1992 FCRS sample within groupsof farmers having the same multivariatestratification for the 1992 and 1993 FCRSsurveys, where possible, to other farmerswho were not in the 1992 FCRS sample.

It will be shown that the first stage of thealgorithm is a special case of the Second-Method. Thus, the FCRS estimates thatare based on the first stage sample havethe same expected values as those basedon the original FCRS sample. Underthe assumption that no sample data fromthe 1992 FCRS is used to update the1993 frame, it will be shown that thesecond stage of the algorithm is also aspecial case of the Second-Method. It thenfollows that the FCRS estimates that are

3

based on the second stage sample havethe same expected values as those basedon the original FCRS sample. It will beshown that less than four percent of thesample is redrawn by the second stage ofthe algorithm. Consequently, the two stagealgorithm used to redraw the 1993 FCRShas only a limited potential to introducebias into the 1993 FCRS estimates evenif some 1992 sample data were used toupdate the 1993 FCRS frame.

First Stage: Redrawing the 1993FCRS to Reduce "Overlap" withThree Other Major 1993 Surveys

The sampling procedures used with the1993 FCRS, QAS, ALS, and CSS satisfythe condition of Step 1 of the Second-Method. The cross-classification of thepopulation required in Step 2 of theSecond-Method is produced by sequen-tially sorting the population records bythe individual 1993 FCRS, QAS, ALS,and CSS stratifications.

Throughout the first stage of the algo-rithm, all of the 1993 samples, except the1993 FCRS, are assumed to be fixed andhence cannot be reassigned. Thus, thereassignment required in Step 3 of theSecond-Method is produced by Steps Bthrough F ofthe algorithm below. Steps B-F randomly reassign the 1993 FCRS sam-ple so that the total burden from allfour 1993 surveys on the farmers in the1993 FCRS sample is minimized.

Step A: Merge the stratification and sam-ple selection information fromthe 1992 FCRS frame onto the1993 FCRS frame.

Note: The first stage of the algorithmis totally independent of the 1992 FCRS.Nevertheless, the 1992 FCRS stratificationand sample information is merged onto the1993 FCRS frame at this point so that itcan be made clear how the first stage of thealgorithm interacts with the 1992 FCRSsample. This information will be usedin the second stage of the algorithm tominimize the overlap of the 1993 FCRSsample with the 1992 FCRS sample.

Step B: Within each of the 1993 FCRS listframe strata, sequentially sort therecords by:

1. The 1993 QAS strata,

2. The 1993 ALS strata, and

3. The 1993 CSS strata.

This step puts the 1993 FCRSlist frame records into substratasuch that within each substratumall records have the same multi-variate stratification and selectionprobabilities with respect to allfour 1993 surveys.

Step C: For each record on the 1993 FCRSframe, compute the burden thatcomes from its being sampled inthe 1993 QAS, ALS, or CSS.

Step D: vVithin each substratum, sequen-tially sort t he records:

1. In ascending order of thetotal burden from the otherthree 199:3surveys (the recordsare now ordered by ascendingvalue of the burden fromall 199:3 surveys except the1993 FCRS),

4

2. In descending order of a zero-one indicator variable, withone indicating selection for theinitial 1993 FCRS sample (thisplaces the records initiallyselected for the 1993 FCRSsample first within the burdengroups formed by step D.1,thus ensuring that records areredrawn only when it reducesburden), and

3. In ascending order of a randomnumber (this randomly ordersthe records within each of thesubgroups formed by steps D.land D.2).

Step E: Redraw the 1993 FCRS sample byreassigning within each substra-tum the initial 1993 FCRS sampleto the first elements of the sub-stratum.

The next step permits a larger sampleto be drawn initially than will actuallybe required. The initial sample can bereduced later to the required size (whichmay not be known initially) by droppingthe larger replicates while still minimizingthe burden on the sample.

Step F: Sort the replicate numbers asso-ciated with the substratum sam-ple in ascending order and reas-sign them to the first elements ofthe substratum. This assigns thesmaller replicate numbers to therecords with the smaller total bur-den for the other three 1993 sur-veys.

The sequence of implications gIVen IIIthe next paragraph proves the following

three assertions, which in turn imply theconditions of Step 3 of the Second-Methodare satisfied (see page 3).

1. The redrawn FCRS sample for this yearhas exactly the same selection probabil-ities (and hence same expansion factors)as the initial sample.

2. Within each substratum, the recordsare put in random order by thesequential sort described in Step Dabove, which means that within eachsubstratum the redrawn FCRS sampleis a simple random sample.

3. Within each substratum the redrawnFCRS sample minimizes the totalburden on individual farmers.

Since the samples are drawn independentlyfor each individual survey using an equalprobability of selection mechanism withineach stratum and since within eachsubstratum all farmers have exactly thesame stratification on individual surveys,the farmers within each substratumall have the same set of multivariateselection probabilities. Since withineach substratum all records have exactlythe same probability of experiencing aspecified burden level, it follows that theyare left in simple random order when theyare sorted by ascending (non-decreasing)burden in Step D of the algorithm. Sincewithin each substratum the total burdenon any individual farmer from the otherthree 1993 surveys is a non-decreasingfunction of the final sort order, shifting the1993 FCRS sample to the first elementsof the substratum selects a simple randomsample that minimizes the total burdenon the individual farmers from all four1993 surveys. Since the redrawn FCRS

5

sample is selected as a simple randomsample within substrata, it has the sameexpansion factors as the initial FCRSsample.

Thus, the first stage of the algorithm cannot bias the sample. That is, the FCRSestimates based on the first stage samplehave the same expected values as thosebased on the original FCRS sample.

Example 1:Applying The First Stage Of The

Algorithm To Reduce The "Overlap" OfThe 1993 FCRS With Other Major

1993 Surveys

Table 1 displays the relevant sample andburden information for the records in theKansas substratum formed by intersecting1993 FCRS stratum 92, 1993 QASstratum 72, 1993 ALS stratum 95, and1993 CSS stratum 20. The burdensassigned in this substratum for the FCRS,QAS, ALS, and CSS are respectively 60,45, 40, and 25. (To the extent informationwas available, burdens were assigned toreflect the approximate time required forall expected survey contacts.)

Columns 1 and 2 of Table 1 containthe sample configurations for the initialand redrawn samples respectively. Theconfigurations indicate whether the recordwas sampled (1) or not (0) for the1993 FCRS, 1992 FCRS, 1993 QAS,1993 ALS, and 1993 CSS respectively.For example, the sample configurationsfor the tenth record of the table arerespectively 10101 and 00101, whichindicate that initially this record wasselected for the 1993 FCRS, QAS, and CSSbut after the 1993 FCRS was redrawnthe tenth record was selected only for the1993 QAS and CSS. (We note once again

Table 1. Example of the Method Used to Redraw the 1993 FCRS in Substrata to Reducethe Burden from the Overlap with Other 1993 Surveys.

: Uniform i-~ -.

Burden Burden Rep Code BurdenInitial

--.-I Redrawn IInitial I Redrawn Other Random I Redrawn Imtla.1 Redra.wn Initial Redra.wn Inihal

Sample I Sample 1~1l3 111113 FCRS Number l1111S FCRS 1~193 1993 FCRS FCRS All All ~i Conflguration I Configuration Surveys Sample Attached I Sample Sa.mple.:; Sa.mples Sample Sample Samples Sa.mple:;. II (1) (2) ( 3) ( 4) (5) (6) : 7) (8) (9) (10) (11) (12) II

01000 11 000 0 0 0.46313 1 0 60 0 11 60 i 120. f---- - -- ---------r--

i10001 10001 25 1 0.13284 1 il5 85 11 25 85 85

i__ u

I00001 I 10001 2S 0 0.05881 1 :IS 8S 0 72 2S 85

00001 I 00001 25 0 0.28983 0

:l

5=H 0 0 25 25 ,

If----

01001 01001 25 0 0.36130 0 __ :_~ 25 0 0 85 85f--

1I 00001 I 00001 25 0 0.47441 i 0 "25 , 25 0 0 25 25f-- .. -

I!

00001 00001 ;,5 0 0.93427 0 15 25 0 0 25 25, f-

!.....--

! !00100 I 00100 45 0 o 22914 0 is 45 0 0 45 4S

If- .- ! ---~-- ~_ ..

00100 00100 45 0 o 86787 0 1S I 45 0 0 45 45

If-

10101 00101 ~O 1 0.07412 0 130 L 70 25 0 130 70--- ---

10101 i 00101 ,'0 1 o 32697 I 0 130 70 72 I 0 130 70 II

,

00101 00101 ·,0 0I

0.61579 0 ;0 70 0 0 70 70 I-- I-

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

1

--- --00101 00101 70 0 0.77151 I 0 70 70 0 I 0 70 70

~~~-- .I 0.93982

-- -~_._ ..

00101 70 0 0 70 70 0 ! 0 70 70- ------ - -

that the 1992 FCRS Survey is not involvedin this stage of the algori thm.)

Column 3 of Table 1 shows the totalburden placed on the individual farmersby the three other 199:3 surveys. Theentries of this column are computed fromthe individual survey burdens and lastthree digits of either the initial or redrawnsample configurations. For example,the total burden from the other three1993 surveys for tenth record is given by1 * 45 + 0 * 40 + 1 * 25 = 70.

Columns 3, 4, and S of Table 1 show thatthe records are sorted by the conditionsof Step D above. That is, the recordshave been sequentially ordered: first, byascending order of the total burden fromthree other 1993 surveys (see column 3);second, by the ones initially selected forthe 1993 FCRS sample followed by thosenot initially selected (see column 4); third,by a uniformly distributed random number(see column 5).

6

Column 6 of Table 1 shows the redrawn199:3 FCRS sample, which is obtained byshifting the 1993 FCRS sample to the firstelements of the table. A comparison ofcolumns 3, 7, and 8 will confirm that sincethe records have been ordered in ascendingorder of the burden from the other three199:3 surveys, shifting the 1993 sample tothe fir~t three records yields a sample thatplaces minimum burden on the sampledfarmers. That is, the total burden placedon the farmers in the redrawn sample bythe four surveys cannot be reduced, eitherindividually or collectively, by exchanginga farmer in the redrawn sample for a farmernot in the redrawn sample.

Column 10 of Table 1 shows the replicatenumbers attached to the redrawn sample,which are obtained by sorting the set ofpositi\e replicate numbers from column 9in ascending order and then attachingthem to the first records of Table I-therecord 3 in the redrawn sample. Notice

- ------~-++------ ~~- -----_._----_._----~-~. -~-.-..• -.. _,

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in u. s. federal government statistical data collection programs andfor specific contributions in the introduction of new methods intofederal statistical data collection programs, data analysis, orstatistical program management. Describe below the unique andunusual characteristics of the contribution or the approach to theproblem upon which your nomination is based. Explain thesignificance of this work in relation to the Guidelines for theAward. Attach a copy of relevant documentation such as apublication, report, or other material.

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that, if any set of records with thelarger replicate numbers are dropped fromthe redrawn sample, the remainder ofthe redrawn sample is such that noother sample of the same size in thissubstratum places lower burden on thesampled farmers.

Since this stage of the algorithm isindependent of the 1992 FCRS sample,some records that are initially in both1992 and 1993 FCRS samples will end upbeing only in the 1992 FCRS sample andsome records that are initially in only the1992 FCRS sample will end up being inboth the 1992 and 1993 FCRS samples.The first record of Table 1 demonstratesthe later case. The second stage ofthe algorithm reduces the overlap of the1993 FCRS sample with the 1992 FCRSsample. To help clarify the situation, thetotal burden from the 1992 FCRS and thefour major 1993 surveys is given for theinitial and redrawn samples in columns 11and 12, respectively.

Second Stage: Redrawing the 1993FCRS to Reduce "Overlap" with the1992 FCRS

The sampling procedures used with the1992 FCRS and 1993 FCRS satisfy theconditions of Step 1 of the Second-Method,provided no information from the 1992FCRS sample is used to update the1993 FCRS frame. The cross-classificationof the population and sample required inStep 2 of the Second-Method is producedby sequentially sorting the populationrecords by the 1993 FCRS and 1992 FCRSstratifications.

In this stage of the algorithm, the1992 FCRS sample is predetermined.

7

Thus, the reassignment required in Step 3of the Second-Method is produced bySteps G through K of the algorithmbelow. These steps randomly reassign the1993 FCRS sample redrawn at the end ofthe first stage of the algorithm so that thetotal burden from the 1992 and 1993 FCRSon the farmers in the 1993 FCRS sampleis minimized.

Step G: Within each of the 1993 FCRSlist frame strata, sort the recordsby the 1992 FCRS strata. Thisstep puts the 1993 FCRS listframe records into substrata suchthat within each substratum allrecords have the same multivari-ate stratification and selectionprobabilities with respect to the1992 FCRS and the 1993 FCRSsurveys.

Step H: For each record on the 1993 FCRSframe, compute the burden thatcomes from its being sampled inthe 1992 FCRS.

Step I: Within each substratum, sequen-tially sort the records:

1. In ascending order of theburden from the 1992 FCRS(this puts the record notsampled in the 1992 FCRS firstfollowed by those that weresampled in the 1992 FCRS),and

2. In descending order of a zero-one indicator variable, withone indicating selection for theredrawn 1993 FCRS sample atthe end of the first stage ofthe algorithm (this places therecords that were selected atthe end of the first stage of the

algorithm first within each ofthe two burden groups formedby step 1.L thus ensuring thatrecords are redrawn only whenredrawing reduces burden),and

3. In ascending order of a randomnumber (this randomly ordersthe records \vithin each of thesubgroups formed by steps 1.1and 1.2).

Step J: Redraw the 1993 FCRS samplethat was selected at the end ofthe first stage of the algorithmby reassigning it within eachsubstratum to the first elementsof the substrat urn.

Step K: Reassign the replicate numbersassociated with the substratumsample that was redrawn atthe end of first stage of thealgorithm to the first elements ofthe substratum in their originalorder. Except for those fewrecords that are also in the1992 FCRS sample, this leavesthe replicate numbers that wereassigned in the first stage of thealgorithm assigned to exactly thesame sample record. The resultis that the minimal overlap ofthe 1993 FCRS sample with threeother major 1993 survey samplesachieved at the end of the firststage of the algorithm is increasedby less than four percent in thefinal redravm 1993 FCRS U.S.sample.

If no information from the 1992 FCRSsample is used to update the 1993 FCRSframe, then it is clear that the sequenceof logical implications given in the two

8

paragraphs following Step F applies to thesecond stage of the algorithm. It thenfollows that within each substratum thesecond stage redrawn sample is a simplerandom sample with the same expansionfactors as the initial FCRS sample.

Thus, if no information from the 1992FCRS is used to update the 1993 FCRSframe, then the second stage of the algo-rithm can not bias the estimates. Thisresult, along with the unconditionalunbiasness of the first stage which wasestablished earlier, shows that the FCRSestimates based on the second stagesample have the same expected valuesas those based on the original FCRSsample, provided no information fromthe 1992 FCRS is used to update the1993 FCRS frame (see later discussion ofbias).

Example 2:Applying The Second Stage Of The

Algorithm To Reduce The "Overlap" OfThe 1993 FCRS With The 1992 FCRS

Table 2 displays the relevant sampleand burden information for the recordsm the Iowa substratum formed byintersecting the 1993 FCRS stratum 92with 1992 FCRS stratum 92. The burdensassigned the FCRS and ALS in all strataare respectively 60 and 40. The burdenassigned the QAS in QAS strata 9.5through 98 is 85. In other QAS stratathe QAS is assigned a burden of 45.The burden assigned the CSS in CSSstrata 3.5 through 39 is 30. In otherCSS strata the CSS is assigned a burdenof :2.5. (Higher stratum numbers denotelarger farm operations.)

Columns 1 and 2 of Table 2 contain thesample configurations for the first stage

Table 2. Example of the Method Used to Redraw the 1993 FCRS in Substrata to Reducethe Burden from Overlap with the 1992 FCRS Sample.

I First I Final I Uniform I Burden Rep Code Burden IStage I Redrawn Burden Sampled Random Sampled Slage ] I Redrawn Slage 1 Redrawn Slage 1 Redrawn I

'Sample Sample 1992 FCRS Stage 1 : Number Redrawn 92 &c 93 I 92 &c 93 FCRS FCRS All AllI Configuration Configuration Survey 1993 FCRS'r Attached 11993 FCRS FCRS FCRS Sample Sample Samples Samples I

(]) I (2) (3) (4) I (5) (6) (7) (8) (9) (]O) (11) ( ]2)

I i O.]2824I

]000] 1000] a ] i ] 60 60 5 5 90 90 I

I 1000] 10001 a ] I 0.6]343 1 60 60 7 7 90 i 90I

I]0101 10]01 a 1 i 0.89720 ] 60 60 13 13 ]35 135

!,

I 0.37579I

0000] ]000] a a ] a 60 a 2 30 90

I 00001 00001 a a i 0.59949 a a a a a 30 30I

\ 1100]I

01001 60 ] I 0.06257 a 120 60 2 a 145 85 !

redrawn and the final redrawn samplesrespectively. The configurations indicatewhether the record was sampled (1) ornot (0) for the 1993 FCRS, 1992 FCRS,1993 QAS, 1993 ALS, and 1993 CSSrespectively. For example, the sampleconfigurations for the sixth record of thetable are respectively 11001 and 01001,which indicates that after the first stageof the algorithm this record was selectedfor the 1993 FCRS, 1992 FCRS, and1993 CSS but after the second stage of thealgorithm the record was selected only forthe 1992 FCRS and 1993 CSS.

In the remainder of this report: (1) thefirst stage redrawn sample or simply firststage sample will refer to the redrawnsample that is obtained by applying thefirst stage of the algorithm to the initial1993 FCRS sample and (2) the finalredrawn sample or simply final samplewill refer to the redrawn sample that isobtained by applying the second stage ofthe algorithm to the first stage redrawn1993 FCRS.

Column 3 of Table 2 shows the burdenplaced on the individual farmers by the1992 FCRS. Only the last record in

9

this substratum was selected for the1992 FCRS.

Columns 3, 4, and 5 of Table 2 show thatthe records are sorted by the conditionsof Step I above. That is, the recordshave been sequentially ordered: first, bywhether they were or were not selectedfor the 1992 FCRS sample (see column 3);second, by whether they were or werenot selected for the 1993 FCRS sampleat the end of the first stage of thealgorithm (see column 4); third, by auniformly distributed random number (seecolumn 5).

Column 6 of Table 2 shows the finalredrawn 1993 FCRS sample, which isobtained by shifting the 1993 FCRSsample selected at the end of the first stageof the algorithm to the first elements ofthe table. A comparison of columns 3, 7,and 8 will confirm that since the recordshave been ordered in ascending order of theburden from the 1992 FCRS, shifting the1993 sample to the first four records yieldsa sample that has minimum overlap withthe 1992 FCRS sample.

Column 10 of Table 2 shows the replicatenumbers attached to the final redrawn

1993 FCRS sample. They are obtained byreassigning the positive replicate numbersin column 9, in their original order, to thefirst records of Table 2.

Since the redrawing process in this stage ofthe algorithm is independent of the otherthree 1993 survey samples, some of thereduction of overlap between 1993 FCRSsample and the other three 1993 surveysamples that was achieved in the first stageof the algorithm will be lost. However,since only about four percent of the1993 FCRS sample that was selected atthe end of the first stage of the algorithmoverlaps with the 1992 FCRS, which arethe records being redrawn in this stage ofthe algorithm, the loss of overlap reductionwith respect to the other 1993 surveysamples will be small.

Reasons for Using a Two StageAlgorithm Instead of a Single StageAlgorithm to Redraw the 1993 FCRS

The first stage of the tViOstage algorithmcan be converted to a one stage algorithmthat minimizes the "overlap" of the1993 FCRS sample with the 1993 QAS,ALS, and CSS samples and the 1992 FCRSsample by including a sequential sort bythe 1992 FCRS strata in Step Bandadding the burden from the 1992 FCRSto the burden computed in Step C.So, why choose a two stage algorithm?The use of the two stage algorithmlimits the potential for introducing biasinto the FCRS estimates. Also, thetwo stage algorithm provides considerablymore burden reduction than the one stagealgorithm.

The primary reason the two stage algo-rithm was used instead of a single stage

10

algorithm to redraw the 1993 FCRS was tominimize the potential for introducing biasinto the FCRS estimates. Since the firststage of the two stage algorithm isunconc.itionally unbiased, bias can only beintroduced in the second stage of the twostage algorithm. Potential for bias willexist if the 1992 FCRS data have been usedto update the 1993 FCRS frame. This willbe discussed in the Bias Considerationssection.

In the second stage of the two stagealgorithm, the only part of the sample thatis redrawn is the part that overlaps withthe 1992 FCRS sample. Since this partof the sample amounts to only about fourpercent of the sample, it follows that whenthe two stage algorithm is used only aboutfour percent of the redrawn sample hasany potential for biasing the 1993 FCRSestimates.

In contrast, when the one stage algorithmis used every element in the redrawnsample is drawn conditional on the1992 FCRS sample. Thus, with theone stage algorithm, every element of theredrawn sample has a potential for biasingthe 1993 FCRS estimates.

In summary, unless it can be shownthat no information from the 1992 FCRSsample is used to update the 1993 FCRSframe, both the single and two stagealgorithms have potential for biasing the1993 FCRS estimates. With the singlestage algorithm, every element is redrawnconditional on the 1992 FCRS sample;but. with the two stage algorithm onlyabout four percent of the sample isredrawn conditional on the 1992 FCRSsample. Thus it follows that thereis much less potential for biasing the1993 FCRS estimates with the two stage

algorithm than there IS with the singlestage algorithm.

In addition to the greatly reduced potentialfor biasing the 1993 FCRS estimates, thetwo stage algorithm provides considerablymore burden reduction than the singlestage algorithm.

In Appendix A, tables are given that showthe burden reduction that would have beenobtained had the single stage algorithmbeen used to redraw the 1993 FCRSsample. Tables 3A, 3B, and 3C, whichare given in the results section, show theburden reduction that was obtained byusing the two stage algorithm to redrawthe 1993 FCRS sample. A comparisonof these two sets of tables, which shouldbe made after reading the first resultssection below will show that the twostage algorithm does a much better jobof reducing the burden that comes fromthe overlap of the 1993 FCRS sample witheither the 1992 FCRS sample or the other1993 samples.

RESULTS

The sample of 11,178 farmers surveyed inthe 1993 FCRS was redrawn with the twostep procedure to reduce the number offarmers sampled in the 1993 FCRS thatwere also contacted in the 1992 FCRS orthe other major 1993 surveys. The re-drawing process was based on stratifica-tion and sample select information fromthe 1992 and 1993 list frame spring clas-sify and sample select. This means thatthe analysis does not reflect reclassificationand resampling (after spring classify andsample select) of some records in 1992 incertain states' Cost of Production specialty

11

strata (California (rice), Michigan (sugarbeets), Ohio (sugar beets), and Florida(sugar cane)). The records that were se-lected in Illinois, Iowa, and Minnesota forthe 1993 CUFFS were excluded from theredrawing process and analysis.

The first section below discusses thereduction in burden achieved by redrawingthe sample. Tables are given thatshow a detailed breakdown of the burdenreduction achieved by redrawing thesample along with the burden associatedwith the initial, first stage, and redrawnsamples.

The second section below discusses thesimilarity of the redrawn sample to theinitial sample by examining the associatedpopulation control values. Tables are giventhat show for each of eight populationcontrol values the estimated totals andcoefficients of variation that are associatedwith the initial, first stage, and redrawnsamples.

U.S. Level Burden Reduction

Recall that the reason for redrawing the1993 FCRS sample was to reduce theburden on the individual farmers selectedby replacing the initial FCRS sample of11 178 farmers with another sample of,11,178 farmers which places less burdenon the individuals selected. Also, recallthat the first stage of the algorithmused to redraw the sample reduced theoverlap of the 1993 FCRS sample with theother 1993 surveys' samples and that thesecond stage reduced the overlap of the1993 FCRS sample with the 1992 FCRSsample.

Consequently, the burden reduction a-chieved by redrawing the 1993 FCRS

can be summarized by the changes (orpercentage changes) that occurred fromthe initial to the redrawn sample in thenumber 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 summarizethe burden reduction achieved by thealgorithm for the complete 1993 FCRSsample, the part of the sample in strata 90and above, and the part of the sample instrata 89 and below. respectively.

Redrawing the 1993 FCRS sample of11,178 farmers:

1. Increased the number of 1993 FCRSsamples that were not selected for anyof the other four surveys from 6,617to 9,212 (an increase of 39 percent),

2. Decreased the number of 1993 FCRSsamples that were selected for only oneof the other four surveys from 3,603to 1,598 (a decrease of .56 percent),

3. Decreased the number of 1993 FCRSsamples that were selected for exactlytwo of the other four surveys from 843to 325 (a decrease of 61 percent),

4. Decreased the number of 1993 FCRSsamples that were selected for exactlythree of the other four surveys from 107to 41 (a decrease of 62 percent),

5. Decreased the number of 1993 FCRSsamples that were selected for all ofthe other four surveys from 8 to 2 (adecrease of 75 percent), and

6. Decreased the number of 1993 FCRSsamples that were also in the previousyear's FCRS sample from 469 to 29 (adecrease of 94 percent).

12

Redrawing the strata 90 and aboveFCRS sample of 3,795 farmers (the stratacontaining farms with sales of $500,000 ormore) :

1. Increased the number of 1993 FCRSsamples that were not selected for anyof the other four surveys from 1,361to 2,317 (an increase of 70 percent),

2. Decreased the number of 1993 FCRSsamples that were selected for only oneof the other four surveys from 1,760to '.,177 (a decrease of 33 percent),

3. Decreased the number of 1993 FCRSsamples that were selected for exactlyt \VO of the other four surveys from 586to :266 (a decrease of 55 percent),

4. Decreased the number of 1993 FCRSsamples that were selected for exactlyt luee of the other four surveys from 82to :)4 (a decrease of 59 percent),

oJ. Decreased the number of 1993 FCRSsamples that were selected for all ofthe other four surveys from 6 to 1 (adecrease of 83 percent), and

6. Decreased the number of 1993 FCRSsamples that were also in the previousyear's FCRS sample from 300 to 13 (adecrease of 96 percent).

Redrawing the strata 89 and belowFCRS sample of 7,383 farmers (the stratacontaining the farms with sales lessthan $500,000):

1. Increased the number of 1993 FCRSsamples that were not selected for anyof the other four surveys from 5,256to 6,895 (an increase of .31 percent),

2. Decreased the number of 1993 FCRSsamples that were selected for only oneof the other four surveys from 1,843to 421 (a decrease of 77 percent),

3. Decreased the number of 1993 FCRSsamples that were selected for exactlytwo of the other four surveys from 257to 59 (a decrease of 77 percent),

4. Decreased the number of 1993 FCRSsamples that were selected for exactlythree of the other four surveys from 25to 7 (a decrease of 72 percent),

5. Decreased the number of 1993 FCRSsamples that were selected for all ofthe other four surveys from 2 to 1 (adecrease of 50 percent), and

6. Decreased the number of 1993 FCRSsamples that were also in the previousyear's FCRS sample from 169 to 16 (adecrease of 91 percent).

In summary, redrawing the 1993 FCRSsample decreased the number of times the1993 FCRS sample overlapped with one ormore of the other four survey samples:

1. From 4,561 to 1,966 for the 1993 FCRSsample of 11,178 farmers (a decrease of57 percent),

2. From 2,434 to 1,478 for the part ofthe sample in strata 90 and above (adecrease of 39 percent), and

3. From 2,127 to 488 for the part ofthe sample in strata 89 and below (adecrease of 77 percent).

These statistics show the effectiveness ofthe two stage algorithm.

13

Tables 3A, 3B, and 3C provide detailedsummary statistics by sampling stage forthe initial, first stage, and redrawn sample.In Table 3A, the 11,178 farmers in eachsample are first broken down according tothe number of times they were selectedfor other surveys. Then the farmersin each sample are further broken downaccording to the specific combination ofsurveys for which they were selected. InTable 3B, similar breakdowns are given forthe 3,795 farmers of each sample that arein strata 90 and above. And, in Table 3C,breakdowns are given for the 7,383 farmersof each sample that are in strata 89 andbelow.

In each table, column 1 shows the numberof other surveys that the 1993 FCRS iscombined with. Column 2 shows thespecific combination of surveys that the1993 FCRS is combined with. Columns 3,4, and 5 show the number of records in eachcategory for the initial, first stage, andredrawn samples, respectively. Columns 6,7, and 8 show the percentages of farmersin each category for the initial, firststage, and redrawn samples, respectively.Columns 9 and 10 show the change in thenumber of farmers in the category fromthe initial sample to the first stage andredrawn samples, respectively. Columns 11and 12 show the percentage change in thenumber of farmers in the category fromthe initial sample to the first stage andredrawn samples, respectively.

State Level Burden Reduction

Tables 4A, 4B, and 4C show for eachstate the number of 1993 FCRS samplesthat were in the 1992 FCRS at eachstage of the algorithm. Column two,

Table 3A. For All Strata, U.S.: The Number of FCRS Samples and Percent of Total FCRSSample by Sampling Configuration for the Initial, First Stage Redrawn, and Final Redrawn1993 FCRS Samples.

---._------ . --Change

I Sampling Count Percent Initia.l to Sh,s:e 1 Sta.sc 1 to Redra.wu Initi •.) to Redu.wn I

I Configuration t Initl •.l I Sta.se 11 Redr""'11 Initia.ll Stage 1 i Redra.wu Count I Per<:ent Count Percent CouPt Percent i

,99 iI 3 2 9 9 9 i

F F 3 3 3 I

C C Q A C:Combination RRA L S,

(%) ::of Surveys S S S S s (#) (#)

I

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

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

I1 0 0 0 0 6617, 9095 9212 59.21

81.41 82.4 +2478 +37% +117 +1% +2595 +39%93 FCRS aloDei

Total 6617 9095; 9212 59.2 81.41 82.4 +2478 +37% +117, +1% + 2595 +39%

93 FCRS pl •• one I 1 0 0 0 1 1110 597! 662 9.9 5.31 5.9 -513 -46% +65: +11% -448 -40%1I ----"

-78% +26% -72%'lot her ••• rvey 1 0 0 1 0 336 74 93 3.0: 0.7: 0.8 -262 +19: -243, -

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

I1 1 0 0 0 191 305 7 1.7 2.7 0.1 +114 +60% -298 -98% -184, -96%

----2005. -56%1I Total 3603 1644 1598 32.2 14.7 14.3 -1959 -54% -46 -3%

93 FCRS phu two I 1 0 0 1 1 74 24 30 0.7 0.21 0.3 -50 -68% +6 +25% -44 -59%i

10. h or ••• vey.I 1 0 1 0 1 414, 189 225 3.71 3--20 -225 -54% +361 +19% -189 -46%I

1 0 1 1 0 147 39' 60 1.3 0.31 0.5 -108 -73% +21i +54% -87 -59%-- ----

I 1 0 0 1 59 44 4 0.51 0.4 0.0 -15 -25% -40) -91% -55 -93%------- - ..

1 1 0 1 a 121 61 1 0.1 0.1 00 -6 -50% -5 -83% -11 -92%--

1 1 1 a 0 137' 73 5 1.2 0.7 00 -64 -47% -68 -93% -132, -96%,.--

-50', Total 843 375 325 7.5 3.4 29 -468; -56% -13% -518 -61%

'93 FCR.S phu three I 1 0 1 1 1 45 26, 31 0.4 0.2' 03 -191 -42% +5' +19% -14 -31%..- ---~_._.-

lother ••• rvey. 1 1 0 1 1 6 2' 0 0.11 0.0 I) -41 -67% -2: -100% -6 -100%.-331 0.31

--~------82%11 1 1 0 1 21 6 0.2 o 1 -12 -36% -15 -71% -27

------~ ~---14 -61% -56% -19' -83%

I

1 1 1 1 0 23 9 4 0.2 0.1 0.0 -5

I

.---------- "---661Total 107

1

58 41 1.0 0.5 04 -49; -46% -17, -29% -62%,

193 FCRS pi •• fou. I 1 1 1 1 1 8'

6 2 O.li 0.1 i 0.0 -2 -25% -4 -67% -6 -75%i- .~--2

'-25%lather .ur-vey. Total 8 6 2 0.11 0.1 0.0 -4 -67% -6 -75%

Total 11,178 11,178 11,178 100.01 100.0 100.0 oi 0% a 0% a 0%1- _. I

t Note: The Sampling Configuration indicates the sampling f'attem 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 ofTotal FCRS Sample by Sampling Configuration for the Initial, First Stage Redrawn, andF' 1R d 1993 FCRS S 1ma e rawn amPJes.!

I Change,

Ii Sampling Count Percent Initi..I to Sh·sc 1 St..le 1 1.0 Redra.wn Initia.l 1.0 Redra.WD I

I Configuration t hl.iti.J Sta.ge 1 Redn.wD Initia.l Sta·se 11 Redra.wD. Count Percent Count Percent COUDt Percenti

I I 9 9

I

III 3 2 9 9 9

I\

iF F 3 3 3

ICCQAC

I Combination RRAL Sfof Surveys

IS S S S s (#) (#) (#) (%) I (%) (%) (#) (%) (#) (%) (#) (%)

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

I

je" FCRS .10 ••I I

59.51 +70%1II 0 0 0 0 1361 2260 2317 35.9 61.0 +899 +66% +57 +3% +956

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

[9:3 FCRS ph. o.e I 0 0 0 1 517 459 508 13.6 12.1 13.4 -58 -11% +49 +11% -9 -2%

lot her .u rvey I 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 26.01 13.2 16.1 -487 -49% +114 +23% -373 -38%:i

i I 1 0 0 0 98 175 2 2.6 4.6 0.1 +77 +79% -173 -99% -96 -98%

I Total 1760 1175 1177 46.4 31.0 31.0 -585 -33% +2 +0% -583 -33%:I

1 0 0 1 1 52! 22 28 1.4 0.6 0.7 -30 -58% +61 +27% -24 -46%193 FCRS pi •• twoother .urvey. I 0 1 0 1 293 158 189 7.7 4.2 5.0 -135 -46% +31 +20% -104 -35%

I

1 0 1 1 0 91 27 45 2.4 0.7 1.2 -64 -70% +181 +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%

I 1 1 0 0 92 59 1 2.4 1.6 0.0 -33 -36% -58 -98% -91 -99%I Total 586 310 266 15.4 8.2 7.0 -276 -47% -44 -14% -320 -55%

93 FCRS ph•• three I 0 1 1 1 36 23 28 0.9 0.6 0.7 -13 -36% +5 +22% -8 -22%

[O'her .urvey. 1 1 0 1 1 4 1 0 0.1 0.0 0 -3 -75% -1' -100% -4-100%

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

I 1 1 1 0 17 6 1 0.5 0.2 0.0 -11. -65% -5 -83% -16 -94%~

I Total 82 46 34 2.2 1.2 0.9 -36 -44% -12 -26% -481 -59%

93 FCRS pia. fou r I 1 1 1 1 61 41 1 0.2' 0.1 0.0 -2 -33% -3 -75% -5 -83%

other aurvey. Total 6 4! 1 0.2 0.1 0.0 -2, -33% -3 -75% -51 -83%

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

t 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 the93FCRS and 93CSS.

15

Table 3C. For Strata 89 and Below, U.S.: The Number of FCRS Samples and Percent ofTotal FCRS Sample by Sampling Configuration for the Initial, First Stage Redrawn, andFinal Redrawn 1993 FCRS Samples.

-- . --- -- --

ChangeSampling Count Percent I nih&l to Sh."e 1 st. •..s:~1 to Redrawn Iniha.l to Redra.wnj

1 Configuration t.---

lnitia.l Sta.S'e 1 I R~dn.wn IDitia.11 Sta.ge 1 I R~d[a.wD. Count P-er<:ent Count P~rcent Count I Percent, c--------.-

I I ,--I

II

19 9

! 3 2 9 9 9 I 1 1F F 3 3 3

,

I

I! ,

C C Q A CI,Combination RRA L S 1 1 1

lof Surveys S S S S s (#) , (#) (#) (%) I (%) I (91,) (#) 1 (%) (#) (%) (#) (%) I(3) I (4) i I I

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

193 FCRS aloat!

,

+15791 +30% +16391 +31%!

I1 0 0 0 0 5256 68351 6895 71.2j 92.6 93.4 +60 +1%

----Total 5256 6835 6895 71.21 92.61 93.4 +1579, +30% +60 +1% +1639 +31%1

i 93 FCRS p •••• one 1 0 0 0 1 593 1381 154 8.0 1.9 2.1 -455 -77% +16! +12% -439i -74% 11 - ----

,other a.rvey 1 0 0 1 0 177 32 39 2.4 i 0.4 0.5 -1451 -82% +71 +22% -138 -78%1!

---.- -- --<, 1 0 1 0 0 980 169, 223 13.3, 2.3 :3.0 -811' -83% +54 +32% -757j -77%I lila-a ,--I

93)0 130 5 1.31 1.8 0.1 +37! +40% -125 ' -96% -88 -95%1-" .-------

I Total 18431 469 421 25.0 6.3 5.7 -1374 -75% -48 -10% -14221 -77% I

)93 FCRS phu two 1 0 0 1 1 22 2 ! 2 0.31 0.0 0.0 -201 -91% a 0% -20 -91%--- --~--~otber •• rvey. ~.:_~_ 1 121 31, 36 1.6 0.4 0.5 -90 -74% +5 +16% -85 -70%

i 1 0 1 1 0 56 12 15 0.8 0.2 0.2 -44 -79% +3 +25% -41 -73% I----.- --I 1 0 0 1 12 5 2 0.21 0.1 0.0 -7 -58% -3 -60% -wi -83%------- -+--- -

, 1 1 0 1 0 Ij 1: 0 0.0 0.0 0 0 0% -1 -100% -1 -100%1 ---- . .--

~~ __ O 0 451 14 4 0.6, 0.21 0.1 -31 -69% -10, -71% -411 -91%.----- -

-77%1I Total 257 65· 59 3.5 0.9 0.8 -192 -75% -6 -9% -198

,93 FCRS plue three ~ 1 1 1 9, 3 3 0.1, 0.0, 0.0 -6 i -67% 01 0% -6 -67%1 ,- -

211--""';'" .- ..-

-50% -100% -100%ot ber eu rvey. 1 1 () 1 1 1 a 0.0" 0.0 0 -1 -1 -2111-1--0 0.11

-.---411 8, 5 1 0.1 : 0.0 -3 -38% -80% -7, -880/0--- ------

61..-~--~-..•...... --- ..

-31 -50% -3 -500/01 1 I 1 0 3 3 0.1 0.0 0.0 OJ 0%r-~----- 0.31-r - --

! Total 25 12 7 0.21 0.1 -131 -52% -5 -42% -18 -72%

i 93 FCRS pI•• r" •• L~ __~__l __1 2 21 1 0.01 o~_. 0.0 01 0% -11 -50% -Ii -50%1

lot her •• rve,.. j Total 2, 2) 1 0.01, O.Oi 0.0 oj 0% -1 -50% - 1 I - 50% I,

7383 7383. 7383 100.01 100.01 100.0 0, 0% 01

0% 01 00/0I1Total ,--- - -

t 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 arebased on the data from the 1992 and1993 list frame spring classify and sampleselect, show respectively the overlap forthe initial, first stage redrawn, and finalredrawn 1993 FCRS samples. Column fiveshows the additional overlap that is notaccounted for in columns two, three, andfour. The added overlap resulted from (1)adjustments made to the 1992 FCRS Costof Production Specialty Strata samples inCalifornia, Michigan, Ohio, and Floridaafter the spring classify and sample selectand (2) one added overlap that occurredin Nevada. From Column four ofTable 4A it can be seen that three states-Arizona (10), New Hampshire (6), andRhodes Island (7)-accounted for almost80 percent of the overlap remaining in thefinal redrawn sample.

U.S. Level Control Variable Esti-mates

This section discusses the similarity of theredrawn sample to the initial sample byexamining associated population controlvalues. The tables below show foreach of eight population control valuesthe estimated totals and coefficients ofvariation that are associated with theinitial, first stage, and redrawn samples.

Table 5A gives the U.S. level estimates,which are derived from the 11,178 farmersin each of the three samples. Table 5Bgives the U.S. level estimates for strata 90and above, which are derived from the3,795 strata 90 and above farmers in eachof the three samples. And, Table 5C givesthe U.S. level estimates for strata 89 andbelow, which are derived from the 7,383strata 89 and below farmers in each of thethree samples.

17

In each table, column 1 shows the namesof control items. Column 2 shows the1993 population totals for the controlitems. Columns 3 and 4 show, respectively,the lower and upper bounds for a90 percent confidence interval centered onthe true total for the estimated totals.Columns 5, 6, and 7 show the estimatedtotals using the initial, first stage, andredrawn sample, respectively. Column 8shows the coefficients of variation for theestimated totals. Columns 9, 10, and 11show the estimated coefficients of variationusing the initial, first stage, and redrawnsample, respectively.

These tables show that the three samplesare very similar with respect to theestimates derived from them. The threeestimates tend to fall at almost thesame place in the respective confidenceintervals. The same is true for theestimated coefficients of variation. If theestimated coefficient of variation for anitem is small (large) relative to the truecoefficient of variation for one sample thenit is also small (large) for the other twosamples.

BIAS CONSIDERATIONS

Recall that the first stage of the two stagealgorithm cannot bias the FCRS estimates.The next section discusses the potentialfor bias that arises at the second stageof the algorithm in 1993. The secondsection discusses the potential for biasthat will arise at the second stage of thealgorithm in 1994 and beyond. The thirdsection presents a four stage algorithm thatshould help limit the potential for bias thatresults from reapplication of the algorithmin subsequent years. The fourth section

Table 4A. For All Strata: The Number of 1993 FCRS Samples in each State that werein the 1992 FCRS Sample for the Initial, First Stage Redrawn, and Final Redrawn 1993FCRS Samples, along with the Added Overlap Caused by Changes Made to the Sample inthe Specialty Strata.

----,------IOverlap I

State Initial Stage 1 Hedrawn Added

I

01: Alabama 6 4 1 I

. 04 :-Arizona 30 29 10 I•.--+------.

05: Arkansas 9 14 iCalifornia 26

------

I06: 21

I2

Colorado 16.-----

08: 17 I_ .. _._--~--09: Connecticut 5 1 i

,

Delaware-~-

I10: 3 2 ,12: Florida 11 10

-- :'-~8 I213: Georgia 5 , 4

..

Idaho16: 15 14illinois 15 12

I17:ru: Indiana 6 13

-~--'- i----~----- I

19: Iowa 23 22Kansas 18 I 19

-- --20:

Kentucky 7 6_..._H.

I21:1- __ .0-

II 22: Louisiana 12 I 15r- 23: Maine 3 I

---_.-.2

I- , .24: Maryland 6 5

~I..

Massachusetts 2------

25: 3-

Michigan------"-- .

26: 11 14 327: Minnesota 21 18 1 , i

~: t I

Mississippi 13 12 1 i

Missouri 8 7- --

I 29:- Montana 2 I ';"- ..~-

30:Nebraska

------. ru

I31: 16 16- 3'2: Nevada 6

-----.--4 , 1- New Hampshire 9 ~u,t I

33: 6 i

134: New Jersey 2 ,I

36: New York 2 I 4North Carolina 12

------ ----I37: 14 I i."-- .....- I

~ 38: North Dakota 17 17I

I

39: Ohio 9 I 9 1Oklahoma 1 I

-_..

40: 1c

Oregon' - ------

41: 8 7 I i-- , ,----42: Pennsylvania 9 , 6

-- - - -.I 44: Rhode Island 12 11 7r4S: South Carolina 9

", --

II

12-- r- --- --

46: South Dakota 18 19Tennessee

- ___ u_ -. --

47: 4 S..

48: Texas 19 17 'II 1

------- I

49: Utah 3 4,

Vermont.. - ~-

C. SO: 8 9 I I.• - ----51: Virginia 4 4

-----,53: Washington 7 I 8

West Virginia-------~-_.

I,

54: 4 3,. --- ------- ---- ..

55: Wisconsin 2 3 156: W yorning 15 12 -:

Cumulative Percent Reduction

Total 469 466

0.6%

29

93.8%

9

18

Table 4B. For Stratum 90 and Above: The Number of 1993 FCRS Samples in each Statethat were in the 1992 FCRS Sample for the Initial, First Stage Redrawn, and Final Redrawn1993 FCRS Samples, along with the Added Overlap Caused by Changes Made to the Samplein the Specialty Strata.

IOverlap

I

I State Initial Stage 1 Redrawn I Added

I

01: Alabama 2 2 I

iI 04: Arizona 17 18 4

05: Arkansas 7 I 1006: California 23 18 208: Colorado 8 9

, 09: Connecticut 1 010: Delaware 2 1

I 12: Florida 8 4 1, 13: Georgia 4 4I I

16: Idaho 6 7 I!, 17: Dlinois 12 10

18: Indiana 3 819: Iowa 18 16 I

20: Kansas 16 : 1821: Kentucky 4 4 I22: Louisiana 7 823: Maine 2 2 j

24: Maryland 5 425: Massachusetts 2 326: Michigan 6 627: Minnesota 13 13 128: Mississippi 8 829: Missouri 0 130: Montana 0 I 2 I

31: Nebraska 13 1232: Nevada 4 3 1 I33: New Hampshire 7 I 7 634: New Jersey 2 3

I 36: New York 2 437: North Carolina 10 I 11I

38: North Dakota 13 I 1239: Ohio 5 640: Oklahoma 1 141: Oregon 4 I 444: Rhode Island I

I 42: Pennsylvania 7 445: South Carolina 7 946: South Dakota 14 1447: Tennessee 1 248: Texas 17 16 1

i 49: Utah 0 150: Vermont 2 451: Virginia 2 3 I53: Washington 5 4 ,

54: West Virginia 3 255: Wisconsin 0 156: Wyoming 7 6

Total 300 305 13 3I

Cwnulative Percent Reduction I -1.7% 95.7%

19

Table 4C. For Stratum 89 and Below: The Number of 1993 FCRS Samples in Each Statethat were in the 1992 FCRS Sample for the Initial, First Stage Redrawn, and Final Redrawn1993 FCRS Samples, a10ng with the Added Overlap Caused by Changes Made to the Samplein the Specialty Strata.

State

413

2384131933523511585823 42 12+~ ~.t4 3 _.J..4 3

...----- --"--2 2-----~._,12 11

,------"2 3

---- ---r-4 53 --;--3---1-"

-- .------r-2 l'

-'3 36 52 1----.2 41 128

01: Alabama04: Arizona

,-

os: Arkansas06: California08: Colorado09: Connecticut10: Delaware12: Florida13: Georgia

.. 16: Idaho

17: lllinois18: Indiana

~'

19: Iowa20: Kansas21: Kentucky

-22: Louisiana23: Maine

-24: Maryland26: Michigan27: Minnesota

I 28: Mississippi29: Missouri

I 30: Montanar 31: Nebraska-'32: Nevada

33: New Hampshire37: North Carolina38: North Dakotai39: Ohio, 41: Oregon142: Pennsylvaniar 44: Rhode Island, 45: South Carolina

46: South Dakota-

47: TennesseeI" 48: Texas

49: Utah50: Vermont51: Virginia53: Washington54: West Virginia55: Wisconsin56: Wyoming

!

II

I

2

11

4-~-----

3-- ---

8--_.11

6o

2

6

16

7

1

I

I

I

·1

2

1

III

I

Total ~ __~__~. __ 16 6

Cumulative Percent Reduction 4,7% 90.5%

20

$1,000,000,000 for Farm Value Of Sales;10, 000, 000 bushels for On-Farm Grain Storage;10, 000 workers Farm Workers Hired.

$1,000,000,000 for Farm Value Of Sales;10,000, 000 bushels for On-Farm Grain Storage;10,000 workers Farm Workers Hired.

Table 5A. For All Strata, U.S.: The Estimated 1993 Population Control Variable Totals forthe Initial, First Stage Redrawn, and Final Redrawn 1993 FCRS Sample.

I90% 90% Estimated Total Exact CV of Estimated CV

Control Population Lower Upper Inicia.l ' Slage 1 Redrawn Estimated Initia.l Slage 1 Redrawn

IVariablet Total Bound Bound Sample Sample Sample Total Sample Sample Sample

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

Total Land in Farm 862.52 1 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 0.861 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

IOn-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 I 811.07 889.19 821.80 829.07 840.22 2.78 3.051 3.21 3.611

Total Hogs &; Pigs 547.15 457.17 637.12 588.76 576.22 585.09 9.97 5.33 4.081 4.29.I

13.131lI All Sheep 114.96

I88.60 I 141.32 106.15 103.90 103.23 13.90 13.02 13.20 I

j Farm Workers Hired 127.21 58.80 195.61 102.40 102.541 102.05 32.59 5.22 ! 5.311 5.331

t All missing control values were set to zero before any computations were performed. The units of measure for the populationtotals and their estimates are:1,000,000 acres for Total Land;1, 000, 000 acres for Total Cropland;100, 000 head for Cattle & Calves, Hogs & Pigs, and Sheep;

Table 5B. For Strata 90 and Above, U.S.: The Estimated 1993 Population Control VariableTotals for the Initial, First Stage Redrawn, and Final Redrawn 1993 FCRS Sample.

I,

1 90% I 90% Estimated Total Exact CV of Estimated CVI

Initial T Slage 1 IRedrawn fSlage 1[Redrawn

IControl Population' Lower' Upper Estimated Initia.l

Variablet Total Bound Bound Sample Sample, Sample Total Sample Sample, SampleI

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

iI

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

j Total Land in Farm 200.12 160.57 239.67 196.58 192.541 187.86 11.98 5.19 5.16 5.13

48.26 iI

2.1211Farm Value of Sales 50.00 51.73 50.77 50.74 i 50.52 2.10 2.14 2.13

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

I209.98 198.54 221.41 220.22 I 221.58 221.84 3.30 3.96 3.93, 3.99:On.-Farm Grain Storage

295.521I

i All Cattle &; Calves 285.97 251.17 320.77 286.42 307.11 7.38 7.93 8.30 I 9.29

I Total Hogs &; Pigs 198.78 113.57 283.98 196.451177.03 181.23 25.98 12.75 7.47 8.621

I 47.50I

32.28 26.76 25.68 25.10 25.57:All Sheep 32.95 18.40 32.10 i 33.26

I Farm Workers Hired 45.00 25.34 64.64 37.16 36.63 35 .48 26.4 7 8.02 8.04 8.16

t All missing control values were set to zero before any computations were performed. The units of measure for the populationtotals and their estimates are:1, 000, 000 acres for Total Land;1, 000, 000 acres for Total Cropland;100,000 head for Cattle & Calves, Hogs & Pigs, and Sheep;

21

Table 5C. For Strata 89 and Below, U.S.: The Estimated 1993 Population Control VariableTotals for the Initial, First Stage Redrawn, and Final Redrawn 1993 FCRS Sample.

90% : 90% Estimated Total Exact CV of,

Control Population Lower Upper Initial I Stage 1 R~dra.wn Estimated Initial

Variablet Total Bound Bound I TotalSample : Sample Sample Sample' Sample Sa.mple

I(#) (#) (#) (#) (#) (#) (%) (%) (%) i (%)

I

I

(1 ) (21 (3) (4) (5) (6) (7) (8) (9)I

(10) ! (11) II

Total Land in Farm 662.40 • -152.1311476.92 594.70,605.63 602.43 74.52 2.55 2.76

! Value of" Sales 10053 101.71 101.19 ' 101.19 101.24 0.71 0.70 0.68

,Total Cropland 27578 287.43 281.73 283.36 282.83 2.56 1.32 1.25~--_ ..

On-Farm Gra.in Storage 737.60 781.37 772.45 ! 769.32 775.84 3.60 3.66 ' 3.531 3.68

All Cattle &£ Calve ••. 564.16 581.89 535.38 , 533.56 ,533.11 1.91 1.97 I 1.93, 1.931

I Total Hogs &£ Pigs 348.37 377.28 392.31 5.03 4.82 4.86

All Sheep 82.01 60.02 103.99 74.05 70.95 16.25 15.29

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

t All missing control values were set to zero before any computations were p.erformed. The units of measure for the populationtotals and their estimates are:1,000,000 acres for Total Land,1,000,000 acres for Total Cropland;100.000 head for Cattle & Calv~, Hogs & Pigs, and Sheep;

presents a five stage algorithm that shouldfurther limit the potential for bias thatresults from reapplication of the algorithmin subsequent years.

For the 1993 FCRS Estimates

With respect to any bias that mightbe caused by redrawing the 1993 FCRSsample with the tvm stage algorithm, theearlier discussions of this report can besummarized as follows:

1. The first stage of the algorithm hasno potential to introduce bias into theFCRS estimates:

2. Only when the information from the1992 FCRS is used to update the1993 FCRS frame. does the secondstage of the algorithm have a potentialto introduce bias into the FCRS esti-mates; and

$1,000, 000, 000 for Farm Value Of Sales;la, 000, 000 bushels for On-Farm Grain Storage;10,000 workers Farm Workers Hired.

3. Only about four percent of the 1993FCRS sample (444 out of 11,178sampled records or 3.97 percent) wereredrawn in the second stage of thetwo stage algorithm. The expandedcontrol data associated with the 444records ranged from 3.4 to 5.9 percentof respective control data totals.

Thus. only about four percent of theredrawn 1993 FCRS sample has anypotential to introduce bias into the1993 FCRS estimates. And, only thoserecords in the four percent that havehad their control data updated from1992 FCRS sample data can introduce anybiac: into the estimates.

The small impact of any possible biasthat might be introduced by the use of1992 FCRS sample data to update the1993 FCRS frame on the 1993 FCRS

22

estimates can be seen as follows. Assumethat 1992 FCRS sample data are used toupdate the 1993 FCRS frame and thatthe two stage algorithm discussed in thisreport is used to redraw the sample. Therecords redrawn in the second stage willthen tend to have older control data thanthe ones they replaced. If the difference inthe age of the control data associated withthe records that are redrawn at the secondstage is related to the data collected fromthe records then bias will be introducedinto the FCRS estimates.

To show that the effect of this potentialbias on the 1993 FCRS estimates is small,consider a (highly unlikely) worst-caseexample. Suppose that the change inage of the control data causes the datacollected from the part of the samplethat is redrawn in the second stage tobe consistently 20 percent smaller (orlarger) than the data that would havebeen collected had the elements not beenredrawn. Note that this much bias inthe four percent of the sample redrawnat the second stage seems highly unlikely,since there is little reason to believe thatany significant amount of information fromthe 1992 FCRS sample is used to updatecontrol data prior to the 1993 FCRS framestratification. Further, it is unlikely thatslightly older or newer control data wouldproduce such a large difference in therelationship between the control data andobservations.

From the discussion above, the expandedcontrol data of the four percent of thesample that was redrawn in the secondstage ranged from 3.4 to 5.9 percent ofrespective totals. Making a worst caseassumption, assume that the expandeddata of the part of the sample redrawn inthe second stage represents five percent of

23

the estimate. Even under these extremeassumptions, redrawing the sample atthe second stage would cause only aone percent change (0.20 * 0.05 = 0.01)in the 1993 estimates. This changewould be undetectable in light of thecoefficients of variation associated with theFCRS estimates. Thus, even though thesecond stage of the algorithm cannot beguaranteed to be unbiased, it is highlyunlikely that any detectable bias will resultfrom redrawing the 1993 FCRS sample.

For the 1994 FCRS Estimates, If theSame Two Stage Algorithm is Used

If the same two stage algorithm is usedsequentially in two years, then the secondstage of the algorithm potentially canintroduce bias into the FCRS estimates,even when no information from theprevious year's FCRS sample is used toupdate the current FCRS frame. Withrespect to redrawing the 1994 FCRS, thesituation can be summarized as follows:

1. The first stage of the algorithm hasno potential to introduce bias into theFCRS estimates;

2. The second stage of the algorithm hasa potential to introduce bias into theFCRS estimates if any sample datafrom the 1993 FCRS, QAS, ALS, orCSS samples is used to update the 1994FCRS frame; however,

3. In 1994, less than three percent of theFCRS sample will be redrawn at thesecond stage of the two stage algorithm.This assumes that the 1994 FCRS hasthe same sample size as the 1993 FCRSand that the percentage redrawn in any

year is proportional to the expectedoverlap with the previous year's sample,which is approximately proportional forsmall sampling fractions to the productof 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 toupdate the 1994 FCRS frame opens the1994 FCRS estimates to potential bias justas it did in 1993. For the same reasonsthat were sighted for the 1993 FCRS, it isunlikely that any detectable bias will resultin 1994 from this source of potential bias.

However, in 1994 the use of 1993 QAS,ALS, and CSS sample data to update the1994 FCRS frame opens the 1994 FCRSestimates to another potential source ofbias. Since the 1993 FCRS sample wasredrawn to reduce its overlap with theother 1993 survey samples, when the partof the first stage 1994 FCRS samplethat overlaps with the 1993 FCRS isredrawn in the second stage to reduce itsoverlap with the 1993 FCRS sample, theresulting sample will be more likely tocontain farmers that were in one of theother 1993 surveys--hence more likely tohave their control data updated in 1993.Therefore, the part of the 1994 FCRSsample that is redravm at the second stageis more likely to have updated control datathan the frame population, and hence, maynot be representative of the population.

Thus, in 1994 and subsequent years, evenwhen no FCRS data from the previousyear's FCRS sample has been used toupdate the FCRS frame, the secondstage of the algorithm has a potential tointroduce bias into the FCRS estimates,since one cannot guarantee that thefarmers in a substratum do not differ by

24

the age of their control data. The nextsection presents a four stage algorithm thatshould help to limit this potential sourceof bias by restricting the later stage ofthe redrawing process to substrata thatincorporate both the original multivariatestratifications and two indicators of arecord's control data age.

For the 1994 FCRS Estimates, If aFour Stage Algorithm is Used

The four stage algorithm presented in thissection removes at each successive stagemore and more of overlap between the1993 and 1994 FCRS while maintainingat each stage, to the extent possible,the control data age characteristics ofthe sample. The four stage algorithm isderived from the components of the twostage algorithm as follows. First, use thefirst stage of the two stage algorithm toremove, to the extent possible, the overlapof the 1994 FCRS sample with the other1994 surveys' samples. Then, use thesecond stage of the two stage algorithmthree times with less and less restrictiveage dependent substrata to reduce theoverlap between the 1993 and 1994 FCRSsamples.

The substrata are made to depend on theage of the control values of the recordsthey contain through two age indicators:the last year Total Land In Farm, TotalCrop Land, or On-Farm Grain Storage,vas updated is used as an indicator orproxy for the age of a record's field cropcontrol values; and the last year AllCattle and Calves, Total Hogs and Pigs,or All Sheep was updated is used as anindicator or proxy for the age of a record'slivestock control values. The second stage

redraws the records of the 1994 FCRSsample that overlap with the 1993 FCRSsample within the substrata formed bycross classifying the records according tothe 1994 FCRS, 1993 FCRS, 1994 QAS,1994 ALS, 1994 CSS strata and the twoage indicators. The third stage redrawsthe records of the 1994 FCRS sample thatoverlap with the 1993 FCRS sample withinthe substrata formed by cross classifyingthe records according to the 1994 FCRSand 1993 FCRS strata and the two ageindicators. The fourth stage redraws therecords of the 1994 FCRS sample thatoverlap with the 1993 FCRS sample withinthe substrata formed by cross classifyingthe records according to the 1994 FCRSstrata and the two age indicators.

In the last three stages of this fourstage algorithm, each record that isredrawn has the same age indicator asthe record it replaces, which should limitthe potential for bias that might arisebecause of application of the algorithmin two consecutive years. In addition,at the second stage, the redrawn recordshave the same stratification with respectto all five surveys, at the third stagethe same stratification with respect to the1993 and 1994 FCRS surveys, and at thefourth stage the same stratification withrespect to the 1994 FCRS. The last threestages are progressively less restrictive.Hence, each stage provides progressivelymore overlap reduction and less protectionagainst potential bias. Thus, we see thatat each stage the gains in burden reductioncome at the expense of the loss of someprotection against bias.

Had this four stage algorithm been usedto redraw the FCRS sample in 1993, theoverlap between the 1992 and 1993 FCRSsamples would have been reduced at the

25

second stage from 466 to 273 (a 41 percentreduction), at the third stage from 273to 65 (a 44 percent reduction), and at thefourth stage from 65 to 32 (a 7 percentreduction). Tables B1, B2, and B3 ofAppendix B show a detailed breakdown ofthe burden reduction that would have beenachieved with the four stage algorithm ateach stage of the algorithm.

Tables B4, B5, and B6 of Appendix Bshow the number of farmers in each statethat would have been in the redrawn1993 FCRS sample at each stage withthe four stage algorithm that were also inthe 1992 FCRS sample. Tables B7, B8,and B9 of Appendix B show the U.S. levelcontrol variable estimates and coefficientsof variation derived from the sample ateach stage with the four stage algorithmthat were also in the 1992 FCRS sample.

The next section presents a five stagealgorithm that further restricts the recordsof each substrata to one FCRS FarmType. This additional restriction willhelp ensure that the age indicators aremore comparable with substrata, andconsequently, that the records of eachsubstratum are more alike with respect tothe expected current FCRS data.

For the 1994 FCRS Estimates, If aFive Stage Algorithm is Used

The five stage algorithm presented in thissection removes at each successive stagemore and more of overlap between the 1993and 1994 FCRS while maintaining at eachstage, to the extent possible, the controldata age and farm type characteristics ofthe sample.

The first stage of the algorithm is thesame as the first stage of the four stage

algorithm. The second, third, and fourthstages of the algorithm are obtainedfrom the corresponding stages of the fourstage algorithm by further restricting thesubstrata to one FCRS Farm Type. Thefifth stage is obtained from the fourth stageby substituting a single age indicator forthe two age indicators. The last year TotalLand In Farm, Total Crop Land, On-FarmGrain Storage, All Cattle and Calves,Total Hogs and Pigs, or All Sheep wasupdated is used at the fifth stage as a singleage indicator. Restricting the substrata toone farm type should help make sure thatthe age indicators are more comparablewithin the substrata. This should furtherlimit the potential for bias that might arisebecause of application of the algorithm intwo consecutive years. A sixth stage isadded to the five stage algorithm solelyfor the purpose of making comparisons.The sixth stage is obtained from thefifth stage by dropping the age indicatorsaltogether. The last five stages of thealgorithm are progressively less restrictive.Hence, each stage proyides progressivelymore overlap reduction and less protectionagainst potential bias. \\'hich means thatat each stage the gains in burden reductioncome at the expense of the loss of biasprotection. Note that, the sixth stageprovides no protection against bias arisingfrom differences in the age of the controldata.

Had this five (six) stage algorithmbeen used to redraw the FCRS samplein 1993, the overlap between the 1992and 1993 FCRS samples would have beenreduced at the second stage from 466to 285 (a 39 percent reduction), at thethird stage from ~8.S to 80 (a 44 percentreduction), at the fourth stage from 80to 41 (a 8 percent reduction), at the fifthstage from 41 to 32 !. a 2 percent reduction),

26

and at the fifth stage from 32 to 23 (a2 percent reduction). Tables B10, B11,and B12 of Appendix B show a detailedbreakdown of the burden reduction thatwould have been achieved with the fivestage algorithm at each stage of thealgorithm.

Tables B13, B14, and B15 of Appendix Bshow the number of farmers in each statethat would have been in the redrawn1993 FCRS sample at each stage with thefive stage algorithm that were also in the1992 FCRS sample. Tables B16, B17,and B l8 of Appendix B show the U.S. levelcontrol variable estimates and coefficientsof variation derived from the sample ateach stage with the five stage algorithmthat were also in the 1992 FCRS sample.

Theoretically, it would be simple to testthe second and latter stage of thesealgorithms for potential bias by either1) collecting data from the farmers in theFCRS year-to-year overlap in addition tothe data from redrawn farmers or 2) bysplitting the FCRS year-to-year overlapand only using half of it. To split the year-to-year FCRS overlap one would divide therecords that were redrawn at the secondand latter stage into pairs based on allthe available information, then randomlychoose one record from each pair to beredrawn. The other record from each pairthat would be used would be the recordselected at the end of the first stage ofthe algorithm. All tests would need to bebased on expanded data, since our interestis in potential for bias with respect tothe FCRS estimates. Thus, in practice,neither procedure would likely yield usefulinforllation, since at best one would haveno more than 400 records, which would bescattered over all strata in all states.

CONCLUSIONS

Redrawing the 1993 FCRS list framesample of 11,178 farmers reduced theburden on the individual farmer sampledby:

1. Decreasing the number of 1993 FCRSsamples that were in one or more of theother samples (1993 QAS, ALS, CSSor 1992 FCRS) from 4,561 to 1,966 (adecrease of 57 percent),

2. Decreasing the number of 1993 FCRSsamples that were in the 1992 FCRSsample from 469 to 29 (a decrease of94 percent), and

3. Increasing the number of 1993 FCRSsamples that are not in any of the otherfour surveys from 6,617 to 9,212 (anincrease of 39 percent).

The two stage algorithm used to redrawthe 1993 FCRS has very little potentialto introduce bias into the 1993 FCRSestimates. In fact, only at the secondstage, which involves less than four percentof the sample, does it have any potentialof introducing bias. At the second stage,the potential to introduce bias is limitedto those samples which have had their1992 FCRS sample information used toupdate the 1993 FCRS frame.

The primary reason that a two stagealgorithm was chosen over a single stagealgorithm for redrawing the 1993 FCRSwas to minimize the potential to introducebias into the FCRS estimates. A secondaryreason for the choice was that the two stagealgorithm also provides considerably moreburden reduction than the single stagealgorithm.

27

If the same two step algorithm is usedagain next year to redraw the 1994 FCRS,the potential to introduce bias into theFCRS estimates will increase. Thisincreased bias potential results from theuse of 1993 QAS, ALS, and CSS sampledata to update the 1994 FCRS frame whichtends to cause the 1994 FCRS sample tobe placed on records that have had theircontrol data updated recently.

A four stage algorithm and a five stagealgorithm were discussed that should helplimit the potential bias that may resultfrom the use of 1993 sample data toupdate the 1994 FCRS frame. Sincethe five stage algorithm places more ageindicator and Farm Type restrictions onthe substrata used in the latter stagesof the algorithm than either the two orfour stage algorithms it should provide themost protection against potential bias. Acomparison of the two, four, and five stagealgorithms using the 1992 and 1993 frameand sample data shows that they providesimilar levels of burden reduction.

Since any potential bias is restricted tothe latter stages of the redrawing processwith all algorithms, it will affect less thanthree percent of the sample (assuming thatthe 1994 FCRS sample is the same size asin 1993). With only three percent of thesample being redrawn in the latter stages itseems that under a worst-case example atmost a one percent bias would be expectedwith either the four or five stage algorithm.Hence, in comparison to the coefficients ofvariation associated with FCRS items, anybias should be undetectable.

RECOMMENDATIONS

The 1993 FCRS was redrawn using anew two stage algorithm in order to

substantially reduce respondent burden.The algorithm was performed by theResearch Division in cooperation withSurvey Management Division in a jointresearch and operations staff effort.

For The 1994 FCRS

Redra,v the 1994 FCRS sample with thefive stage algorithm. The use of the fivestage algorithm will limit to the extentpossible the potential for bias that resultsfrom the use of 1993 sample data to updatethe 1994 FCRS frame. Since the potentialfor bias in 1994 FCRS estimates is onlyslightly more than it was with 1993 FCRSestimates, the reduction in burden thatwill be obtained with the 1994 FCRSoutweighs the increased potential for bias.

For The 1996 Sample Select

Research Division is evaluating the twomethods described by Perry, Burt, andIwig (1993) for selecting multiple surveysamples to reduce burden on the individu-als selected in all samples. This work willbe completed in 199.5and at that time rec-ommendations will be made for incorporat-ing the results into the 1996 Sample Select.

REFERENCES

Perry, Charles R.. Jameson C. Burt, and\Villiam C. Iwig; ""Methods Of SelectingSamples In Multiple Surveys To ReduceRespondent Burden": Proceedings of theInternational ConfutTlce on EstablishmentSurveys; ASA; Alexandria, Virginia;June 1993.

28

Perry, Charles R., Jameson C. Burt,and \Villiam C. Iwig; "Redrawing the1993 Farm Cost and Returns Survey ListSample to Reduce Overlap with ThreeOther 1993 Surveys and the 1992 FCRS";1994 Proceedings of the Section on SurveyResw/'ch Methods; ASA; Alexandria,Virginia; 1994.

NOMINATION FORK

ROGER HERRIOT AWARD

Name of Nominee: Charles Perry, Jameson Burt

Mailing Addesss: 3251 Old Lee Highway, Room305, Fairfax, VA 22030

Telephone Number: (703) 235-5213

The Roger Herriot Award is intended to recognize unique and unusualcontributions to the solution of statistical problems encounteredin u.s. federal government statistical data collection programs andfor specific contributions in the introduction of new methods intofederal statistical data collection programs, data analysis, orstatistical program management. Describe below the unique andunusual characteristics of the contribution or the approach to theproblem upon which your nomination is based. Explain thesignificance of this work in relation to the Guidelines for theAward. Attach a copy of relevant documentation such as apublication, report, or other material .

• "". ,.', ...;, Co."'-

'.. ' ..~~f,f.:;"iReddcing·surVey burden on agricultural producers is a major concern for the.:::k>. :.'f~\tir~'.'/.»~<~c::·':i\'~?S:~'f~;",-, .':,.'::~~~?!'Nat:(cinal·~Agri·cu1.tliral.Statistics Service. Charles Perry~;and 'Jameson Burt

.;·C. --'~\::;:~'c_.#;.¥.;;".,,- ',. ~',.;s:,,"·"1"'';J;.'''''. ,.

. .• ::>;;'.~f11{'~:i~~e~\~~~!~ihiW~~1k~gesampling 'algorithm' i~f~~:tbe'Faci\Cci'~ts' and .Returns Survey

::1'<t~r~~j~~t:W~~;;-'is~~~d~~'~'ed annually u'sin~ a long ~d ~o~plex questionnaire":: ,.'~ .~~, J':<"- ·~~:.~t.r~.:~1~·;:T~·-·:~~'. ',.: :'~;"'Y'~~~.:" -

._' > '~~~:~tias~i~/'¢£b~~'S:'gfied-econoro·i~-?t'ritorinatlon•. :£'~:;';:::4li .-, : ':': .' "".1~.• - • ~~f:-:". '. -;i '.J<. ~~-~':'- - •

.": .'J\~":'-'.. ((:'.;r.o-E€~ . _ ~si:~tra:tifies3f1i:b'\fipOpulation into "cells" where all farm operations~.:;.~~~:~..,r::~~t&·.ji~:~~i~..·..~_·;;.':~j"~~.~:.\ ..., .• : ~_ •••.,. •••~~~~ •.•~ •• ,..; , ••.•• >~ •. ='"i. "t. t,:· '-~"~~;:;.:,. - :."

.. = ' ..;'11ave~·:similar,iici:'ictlltural characteristics. It then reallocates the sample within

these cells to limit any single farm operation being in a particular FCRSsurvey

across years.

continued on page 2

Nominator's Name: R. Ronald Besecker, Director, Research DivisionNational Agricultural Statistics Service

Address: 3251 Old Lee Highway, Room305. Fairfax, VA 22030

Telephone Number: (703) 235-5211---~-------------------------.'

MaiJ. To:I

Roger Herriot Award Committeec/o Daniel Kasprzyk4906 Colonel Contee PlaceUpper Marlboro, Maryland 20772-2875

The results were, that in the spring - 1994 survey, this procedure reduced by94 percent, the number of farm operators that were also in the previous FCRSsample. ~~en additional stages of the algorithm were used, 83 percent of the

sample was not in any other major probability survey during the current surveycycle year.

In 1995 an additional three stages to control bias were implemented (a total offive stages). This resulted in a reduction of 96 for operators selected in bothyears, and 81 percent would be contacted in only one probability survey duringthe year .

..- -.. ~

."

APPENDIX A: BURDENREDUCTION FOR A SINGLE

STAGE ALGORITHM

The following three tables give a detailedbreakdown of the burden reduction thatwould have been obtained had a singlestage algorithm been used to redraw the1993 FCRS sample. A comparison ofthese tables with Table 3A, 3B, and 3C,respectively, will show that the two stepalgorithm does a much better job ofreducing the overlap of the 1993 FCRSsample with both the 1992 FCRS sampleand the other three 1993 samples. Inparticular, had the single stage algorithmbeen used to redraw the 1993 FCRS,there would have been 171 farmers in the1993 FCRS sample that were also in the1992 FCRS sample; whereas, with the twostage algorithm, there were only 29 farmersin the 1993 FCRS who were also in the1992 FCRS sample.

29

U.S. Level Burden Reduction

Table Al. For All Strata Using a Single Stage Algorithm, U.S.: The Number of FCRSSamples and Percent of Total FCRS Sample by Sampling Configuration for the Initial andRedrawn 1993 FCRS Samples.

I--- - ----

!I Sampling Count Percent ChangeConfiguration t

--- f--

IInitial 1 Redrawn lnitial , Redrawn Count PercentI

I.---_. - I9 9

I3 2 9 9 9

I

iII F F 3 3 3

CombinationCCQAC

IIRRAL S

II

of Surveys S S S S s (#) (#) (%) (%) (#) (%) I

(1) (2) (3) I (4) (5)I

(6) (7) I (8) ,

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

I +34% !Total 6617 8853 59.2 79.2 +2236

93 FCRS plus on,' 1 0 0 0 1 1110 I 695 9.9 6.2 -415 I -37% i- --

1, other survey 1 0 0 1 0 336 113 3.0 I 1.0 -223 -66% I

--- __ u_

1 0 1 0 0 1966 I 964 17.6 8.6 -1002 I -51 % I.--~--

-71%1I 1 1 0 0 0 191 55 1.7 0.5 -136----- ----

Total 3603 ! 1827 32.2 16.3 -1776 -49% ,

I 93 FCRS plus two 1 0 0 1 1 741

38 0.7,

0.3 -36 -49% I,

- - ---other surveys 1 0 1 0 1 414 245 3_7 2.2 -169 I -41% I

I ---I 0 1 1 0 147 69 1.3 0.6 -78 -53% .

----~

! -59% I1 1 0 0 1 59 24 0_5 0.2 -35I - - - - -

i1 1 0 1 0 12 I 5 0.1 0.0 -7 -58%

- --- - - -- I1 1 1 1 0 0 137 43 12 OA -94 , -69% I

1

-----------+-----

-50% !Total 843 424 7_5 3.8 -419 II 93 FCRS plus three 1 0 1 1 1 45 30 0.4 i 0.3 -15 I -33%

--- --- "--- .-- --other surveys 1 1 0 1 1 6 I 3 0_1 0.0 -3 I -50%

, ,----331

--! , 1 1 1 0 1 24 0.3 ,

0.2 -9 -27% II

I 1 1 1 1 0 23 11 0.2 0.1 -12 I -52%II

f "'t--- ------.

1.0 I -36%'Total 107 I 68 0.6 -39

1 1 1 8,

6 0_1 0.1 -2 I -25%i

93 FCRS plus four 1 1 i

8 I

u_u_ -----other surveys Total 6 0_1 0.1 -2 -25%

Total 111,178 1_ 11.~~~_J_100.0 I 100.0 L 0 0% I

t Kate: The Sampling Configuration indicates the samplinf; pattern for the 93FCRS, 92FCRS, 93QAS,93ALS and 93CSS (Cattle and Sheep)_ For example, a 10001 indicates sample units selected for only the93FCRS and 93CSS.

30

Table A2. For Strata 90 and Above Using a Single Stage Algorithm, U.S.: The Number ofFCRS Samples and Percent of Total FCRS Sample by Sampling Configuration for the Initialand Final Redrawn 1993 FCRS Samples.

I

Sampling Count Percent ChangeConfiguration t Initial Redrawn Initial Redrawn Count Percent

, 9 9 I, 3 2 999 II

i F F 3 3 3

CombinationCCQACRRALS

of Surveys S S S S S (#) (#) (%) (%) (#) (%)

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

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

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 i 17.6 -319 -32%

1 1 0 0 0 98 39 2.6 1.0 -59 -60%!

Total 1760 1279 46.4 I 33.7 -481 -27%, I

1 o 0 1 1 52 31 1.4 0.8 -21 -40% i, 93 FCRS plus twoI

-31%other surveys I 1 0 1 0 1 293 201 7.7 5.3 -92

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% i

1 1 1 0 0 92 29 2.4 0.8 -63 -68%

I Total 586 336 15.4 8.8 -250 -43%

93 FCRS plus three i 1 0 1 1 1 36 26 0.9 0.7 -10 -28% !

other surveys I 1 1 0 1 1 4 2 0.1 0.1 -2 -50%I

-24%I 1 1 1 0 1 25 19 0.7 ! 0.5 -6

1 1 1 1 0 17 8 0.5 I 0.2 -9 -53%

Total 82 55 2.2 I 1.4 -27 -33% i!

93 FCRS plus four 1 1 1 1 1 6 4 0.2 I 0.1 -2 -33% iI

I other aurveys Total 6 4 0.2 0.1 -2 -33%

Total 3795 3795 100.0 100.0 0 0%

t 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 the93FCRS and 93CSS.

31

Table A3. For Strata 89 and Below Using a Single Stage Algorithm, U.S.: The Number ofFCRS Samples and Percent of Total FCRS Sample by Sampling Configuration for the Initialand Final Redrawn 1993 FCRS Samples.

I

- -~

Sampling Count Percent ChangeConfiguration t

-~~! Initial I Redrawn Lutial Redrawn Count Percent

i-~

9 9 !I

3 2 9 9 9 !

F F 3 3 3CCQAC I

I

Combination RRAL 5 I

of Surveys S 5 5 S 5 (#) (#) 1%) I (%) (#) (%)(1) (2) (3) (4) (5) (6) (7) (8)

I

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 I 193 8.0 I 2.6 -400 -67%.- I

I

other survey 1 0 0 1 0~

2.4 i 0.6 -135 i -76%'-

1 0 1 0 0 980· 297-- 13.3 1 4.0 -683 -70% II ._1 1 0 0 0 93

I 16 1.3 I 0.2 -77 -83%,--

Total 1843 548 25.0 ; 7.4 -1295 -70%

93 FCRS plus two 1 0 0 1 1 22 i 7 0.3 ! 0.1 -15I

-68%,, - I -- ---other surveys 1 0 1 0 1 121 I 44 1.6 ! 0.6 -77 -64%

- .

56 I1 0 1 1 0 17 0.8 i 0.2 -39 -70% ,--~- ~

1 1 0 0 1 12 5 0.2 I 0.1 -7 -58% I- .

0.0 I1 1 0 1 0 1 1 0.0 0 0%-. -- - ..

1 1 1 0 0 45I

14 0.6 I 0.2 -31 -69%- -. ------- --

i Total 257 88 3.5 i 1.2 -169 -660/0

93 FCRS plus three 1 0 1 1 1 9 i 4 0.1 0.1 -5 -56%-~- ------

other surveys 1 1 0 1 1 2 I 1 0.0 0.0 -1 -50% I--- .---~----'n

-38% iI

1 1 1 0 1 8 5 0.1 0.1 -3--

0.1 i! 1 1 1 1 0 6 3 0.0 -3 -50%! - .

i Total 25 I 13 0.3 I 0.2 -12 -48%

93 FCRS plus four 1 1 1 1 1 2 I 2 0.0 0.0 0 0% ''- +-------- - _. --

other surveys Total 2 2 0.0 0.0 0 i 0% I

Total 1 7383 7383 [100.0 I 100.0 0 I 0% i...-----_. ------~

I

I . - I

t 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: BURDENREDUCTION, OVERLAP

REDUCTION, AND BIAS FORTHE FOUR STAGE AND FIVE

STAGE ALGORITHMS

Tables Bl, B2, and B3 show a detailedbreakdown of the burden reduction thatwould have been achieved had the fourstage algorithm been used to redrawthe 1993 FCRS. The initial 1993 FCRSsample was redrawn at the first stagewithin the substrata formed by crossingthe four 1993 FCRS, QAS, ALS, andCSS stratifications to reduce to the extentpossible its overlap with the other three1993 surveys' samples. The part of the firststage redrawn sample that overlapped withthe 1992 FCRS sample was redrawn at thesecond stage within the substrata formedby crossing the 1992 FCRS strata; the1993 FCRS, QAS, ALS, and CSS strata;and the two age indicators to reduce tothe extent possible its overlap with the1992 FCRS sample. The part of the secondstage redrawn sample that still overlappedwith the 1992 FCRS sample was redrawnat the third stage within the substrataformed by crossing the 1992 FCRS strata,the 1993 FCRS strata, and the two ageindicators to reduce to the extent possibleits overlap with the 1992 FCRS sample.The part of the third stage redrawn samplethat still remained overlapped with the1992 FCRS sample was redrawn at thefourth stage within the substrata formedby crossing the 1993 FCRS strata and thetwo age indicators to reduce to the extentpossible its overlap with the 1992 FCRSsample.

Tables B4, B5, and B6 show the overlap ineach state between the 1992 FCRS sampleand the 1993 redrawn FCRS sample that

33

would have remain at each stage had thefour stage algorithm been used to redrawthe 1993 FCRS. Table B4 shows that thefour stage algorithm reduces the overlapat the end of the fourth stage to no morethan one in all but three states: Arizona,New Hampshire, and Rhode Island. Theoverlap in these three states account 72percent of the remaining overlap at the endof the four stage algorithm.

Tables B7, B8, and B9 show for eightpopulation control values the estimatedtotals and coefficients of variation thatwould have been associated with thesample at each stage had the fourstage algorithm been used to redraw the1993 FCRS. The U.S. level estimates aregiven in Table B7 for all strata; in Table B8for stratum 90 and above; and in Table B9for stratum 89 and below. These tablesshow that the samples are very similar ateach stage with respect to the estimatesderived from them. The estimates tendto fall at almost the same place in therespective confidence intervals; the sameis true for the estimated coefficients ofvariation.

Tables BID, Bll, and B12 show a detailedbreakdown of the burden reduction thatwould have been achieved had the fivestage algorithm been used to redrawthe 1993 FCRS. The initial 1993 FCRSsample was redrawn at the first stagewithin the substrata formed by crossingthe four 1993 FCRS, QAS, ALS, andCSS stratifications to reduce to the extentpossible its overlap with the other three1993 surveys' samples. The part of the firststage redrawn sample that overlapped withthe 1992 FCRS sample was redrawn at thesecond stage within the substrata formedby crossing the 1992 FCRS strata; the1993 FCRS, QAS, ALS, and CSS strata;

FCRS Farm Type; and the two ageindicators to reduce to the extent possibleits overlap with the 1992 FCRS sample.The part of the second stage redrawnsample that still overlapped with the1992 FCRS sample was redrawn at thethird stage within the substrata formedby crossing the 1992 FCRS strata, the1993 FCRS strata, FCRS Farm Type,and the two age indicators to reduceto the extent possible its overlap withthe 1992 FCRS sample. The part ofthe third stage redrawn sample that stillremained overlapped v·;ith the 1992 FCRSsample was redrawn at the fourth stagewithin the substrata formed by crossingthe 1993 FCRS strata. FCRS Farm Type,and the two age indicators to reduce tothe extent possible its overlap with the1992 FCRS sample. The part of thefourth stage redrawn sample that stillremained overlapped with the 1992 FCRSsample was redrawn at the fifth stagewithin the substrata formed by crossingthe 1993 FCRS strata. FCRS Farm Type,and the single age indicator to reduceto the extent possible its overlap withthe 1992 FCRS sample. The part ofthe fifth stage redrawn sample that stillremained overlapped with the 1992 FCRSsample was redrawn at the sixth stagewithin the substrata formed by crossingthe 1993 FCRS strata and the FCRS FarmType to reduce to the extent possibleits overlap with the 1992 FCRS sample.Note that the sixth stage is not reallya part of the five stage algorithm andthat it provides no protection against biasarising from differences in the age of thecontrol data. It is just being carriedalong to determine the amount of overlapreduction that could be obtained with noage indicator restrictions.

Tables B13, B14, and 81.5 show the overlap

34

in each state between the 1992 FCRSsample and the 1993 redrawn FCRSsample that would have remained at eachstage (including the extra sixth stage)had the five stage algorithm been usedto redraw the 1993 FCRS. Table B13shows that the five stage algorithm reducesthe overlap at the end of the fifth stageto no more than two in all but threestates: Arizona, New Hampshire, andRhode Island. The overlap in thesethree states account 66 percent of theremaining overlap at the end of the fivestage algorithm. Note that, if no ageindicator restrictions had been used theFCRS to FCRS overlap would have beenreduced only from 32 to 23.

Tables B16, B17, and B18 show for eightpopulation control values the estimatedtotals and coefficients of variation thatwould have been associated with thesample at each stage had the fivestage algorithm been used to redraw the199:3 FCRS. The U.S. level estimates aregiven in Table B16 for all strata; inTable B17 for stratum 90 and above; andin Table B18 for stratum 89 and below.These tables show that the samples arevery similar at each stage with respect tothe estimates derived from them. Theestimates tend to fall at almost thesame place in the respective confidenceintervals; the same is true for the estimatedcoefficients of variation.

A comparison of Tables Bl through B6 andTables BI0 through BIS with Tables 3Athrough 4C, respectively, shows that theburden reduction and FCRS to FCRSoverlap reduction achieved with the fourstage and the five stage algorithms is verysimilar to that achieved with the twostage algorithm. With the four stage andfive stage algorithms, there would have

been 32 farmers in the 1993 FCRS samplethat were also in the 1992 FCRS sample.With the two stage algorithm, there were29 farmers in the 1993 FCRS that werealso in the 1992 FCRS sample. With eachalgorithm the larger remaining FCRS toFCRS overlap tended to be in the samestates.

However, the extra restrictions placedon the redrawing process in the second,third, fourth, and fifth stage of the fivestage algorithm should cause it to have alower potential for biasing the 1994 FCRSestimates than the two stage algorithm.This is indirectly confirmed by observingthat the estimated totals and coefficientsof variations given in Tables B16, B17,and B18 tend to be almost the same forthe first, second, third, fourth, and fifthstage from the five stage algorithm.

35

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

Table Bl. For All Strata, D.S.: The Number of FCRS Samples and Percent of Total FCRSSamples by Sampling Configuration for the Initial, First Stage, Second Stage, Third Stage,Fourth Stage 1993 FCRS Sample.

Total

other surveys Total

0.3

a0.1

0.0

0.4

0.0

0.0

1.3

0.1

13.9

0.3

2.0

0.5

0.0

0.0

0.0 J2.9 i

(%)(12)

82.8

82.8

5.8

0.8

0.0 '

0.0

0.1

0.0

0.4

0.3, 13.9

0.3

2.0

0.5

0.1

0.0

0.1

3.0

0.3

a

0.1

0.1 :

0.2

0.0 i

0.2

0.1 !

0.5

0.2

1.8

0.5

0.3

0.0

0.5

3.3

5.4 5.7

0.7, 0.8

7.2

100.0 100.0 100.0

0.7

0.2

1.7

0.3

0.4

0.1

3.40.2

0.0

0.2

0.1

0.5

0.1

0.1

5.3

0.7

6._0_,_2.7

14.7

81.4 82.0 82.7

81.4 82.0 82.7

(%) (%) (%)

(9) (10) (11)

3.7 I

1.3

0.5

0.1 :1.2 '1.5 i

0.4

0.1

0.3 I

0.2 I1.0'

0.1 :

0.1

(%)(8)

59.2 I

59.2 :

9.9

3.0 '

17.6

1.7

32.2

0.7

7

33

a

2

423

3

34

643

89

(#)

(7)

33 '

33

87636

(#)

(6)

26

28

79

206 224 225--4-- "--- ..- ---r --- ~-

50 59 J 5932 +-'_.~ " _-n4:

---<---------- - - - ---5 1

51 10 4-- ------372 334 327

607

737i'~._.01 _ .._ 813148 33 11

1571 ' 155'7- -1556

9172! 9240 9250

9172; 9240 9250

(#)(5)

73375

26

2 2 (I

21 ' 2OT---·~ -9 9 I~;'-

581--57'-- 44

6, 6

6 6 :

9095

9095

597

74668305 '

1644

24 .I

189 I

391

446

(#) I

(4) .

12137

8431

45 !

6

33

23107

1

818

6617

6617 !1110

336

1966191

3603

74414

147 !

59 !

(#)(3)

11.178 11,178 11,178 11.178 11,178I

Count Percent___ n _

Initial I Stage 1 Stage ~~~ge_J .S~age 4 Initia! Stage I! Stage 2 Stage 3[ Stage 4:

11110---~------

Total

1 1 1 1 1

1 0 1 a 1

'Iota!

(2)

10011

110110

~!_~~_~_a 1,11010~--~------

11100~-----

'Iota!

10000I---_~---- _

10001i-I 0-01 arI-ol-o ail--1- a a ai-;r ota!

! Sampling

I'CCiOl1figu!~~ont9 932999

, F F 3 3 3CCQACRRALSSSSSS

1)3 FCRS plus four

1)3 FCRS plus three ~~_O_ 1_ 1 1

other surveys ! 1 1 a 1 1f---- -'11101

(1)

other surveys

other survey

1)3 FCRS plus two

1)3 FCRS plus one

Combinationof Surveys

1)3 FCRS alone

t Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS.93ALS and 93CSS (Cat tiE' 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 ofTotal FCRS Samples by Sampling Configuration for the Initial, First Stage, Second Stage,Third Stage, Fourth Stage 1993 FCRS Samples.

Sampling Count PercentConfiguration t Initial Stage 1 Stage 2 Stage 3 Stage 4 Initial. Stage 1 Stage 2 Stage 3 I Stage 4

9 9I3 2 9 9 9

1 F F 3 3 3

iI CCQA C ,

Combination IRRAL S

1

1

of Surveys i S S S S S (#) (#) (#) i (#) (#) (%) I (%) (%) (%) (%)i !(1 ) (2) (3) I (4) (5) (6) ! (7) (8) ! (9) (10) (11) (12), i

I 93 FCRS alone 1 0 0 0 0 1361 2260 2293 i 2332 2339 35.9 ' 59.5 60.4 61.5 61.6;

Total 1361 2260 ' 2293, 2332 i 2339 35.9 59.5 60.4 61.5 61.6

93 FCRS plus one, 1 0 0 0 1 517 459

1

4651

489 I 495 13.6 12.1 12.2 12.9 13.0

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

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

i 1 1 0 0 0 98 175 . 92: 22 6 2.6 4.6 2.4 0.6 0.2 !

I Total 1760 1175 1148 1152 i 1153 46.4 31.0 30.2 30.4 30.4.

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

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 I 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 23 231 29 29 0.9 0.6 0.6 0.8 0.8 Iother surveys 1 1 0 1 1 4 1 • l' 01 0 0.1 0.0 0.0 I 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 I 0 0.5 0.2 0.2 I 0.0 0Ii

i Total 82 46 45 361 34 2.2 : 1.2 1.2 0.9 0.9

93 FCRS plus four I 1 1 1 1 1 6 4 i 4 1 , 1 0.2 0.1 0.1 I 0.0 0.0

other surveys I Total 6 4 4 1 I 1 0.2 0.1 0.1 i 0.0 0.0, I

Total 3795 3795 . 3795 i 3795 I 3795 100.0 100.0 100.0 1 100.0 100.0I

t 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 the93FCRS and 93CSS.

37

Table B3. For Stratum 89 and Below, U.S.: The Number of FCRS Samples and Percent ofTotal FCRS Samples by Sampling Configuration for the Initial, First Stage, Second Stage,Third Stage, Fourth Stage 1993 FCRS Samples.

93 FCRS plus three,

Iotal

a ,0.0 I

0.0 ,

0.1 i

0.0 1

I0.0 1

2.9

0.1 1

5.5

0.1

0.5

0.2

0.0

a0.0

0.8 1

0.1 !

2.0 '

0.5

(%)(12)

100.0

0.1

a0.0

0.0

0.1

0.0 I

0.0

2.0

0.5 1

2.9

0.1

5.5

93.6 ' 93.6 I93.6 93.6 I

(%)(11)

100.0

0.0

0.0

0.1

0.0

0.2

0.0

0.0 I

0.0 1

0.1

0.9

1.9

0.5 ~2.6

0.8

5.7

0.0 0.1 i0.5 0.5 I0.2:~10.1 0.0 i

a !I

0.0

0.8

Percent

Stage 21Stage 31 Stage 411 :

! ', 1

i 1

! 1

I

0.1

0.0

0.2

0.0

0.0

1.9 1

0.4

2.3

1.8

6.3 I

0.0

0.4

0.2 i

~0.0 1

0.2 1

0.9

0.0 I

0.0 i

!

(%) I (%)(9) (10)

92.6 1 93.2

92.6 93.2

0.0!

8.0

2.4

13.3 i1.3

25.0 1

0.3

1.6

0.8 i

0.2 '0.0

0.6

3.5 I

0.1 !

0.0

0.1

0.1

0.3 :

0.0:

(%)(8)

71.2 i71.2

Initial i Stage 1

15

1

a2

59

4

a2

2

8

2

2

37

(#)

(7)

2

o

8

01 ,- -- -+----3'

1 1

-------

15

37

604

405 .

4

(#)

(6)

2

12 i

21I

.,...--~~----56! 11

673 !

1 :5,

3

423

3,

331

145

1

11

7383L~~8_3 ~. 7383 100.0 1 100.0 , 100.0

3,

12 1

2 !

2

65

3

1

5 1

169

130

4692

31

121

5

1

7383 I

(#) i (#)!

(4) (5)

(#)(3)

5256 I 6835

5256 6835

593 I 138 :

177 32 i

980

931843

1

22121

56 !

121

45,

257 !

912

8

6

252

217383 i

10111

1 1 a 1

1 1 1 aIotal

1 a a a 1~--- --_._-

10010

10100

11000

Total

10000

11111-i Total

Total

10011r----- --

10101

lalla---- ---

11001

aa

!-~~mpling

~~lIlfigUration t9 9

!32999F F 3 3 3CCQACRRALSSSSSS

(2)

Total

other surveys

other surveys

93 FCRS plus four

other surveys

other survey

(1)

93 FCRS plus one

93 FCRS plus two

93 FCRS alone

Combination

of Surveys

t 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 III the1992 FCRS Sample at Each Stage of the Redrawing Process.

I Overlap

State Initial I Stage 1 Stage 2 I Stage 3 Stage 4I

01: Alabama 6 : 4 4 204: Arizona 30 29 22 14 1105: Arkansas 9 14 : 5 206: California 26 21 13 208: Colorado 16 17 13 4 109: Connecticut 5 1 110: Delaware 3 2 1 I

12: Florida 11 I 10 5 2 213: Georgia 5 ! 4 4 1

I 16: Idaho 15 14 10 117: illinois 15 12 I 4 1

I 18: Indiana 6 13 4 ,

19: Iowa 23 I 22 13 120: Kansas 18 19 1121: Kentucky 7 6 522: Louisiana 12 15 7 2 123: Maine 3 224: Maryland 6 ! 5 4 1

i 25: Massachusetts 2 3 226: Michigan 11 14 I 4 127: Minnesota 21 18 13 2 !

28: Mississippi 13 I 12 4 1 I

29: Missouri 8 7 2 1 ! 130: Montana 2 7 531: Nebraska 16 16 10 232: Nevada 6 4 133: New Hampshire 9 7 7 6 634: New Jersey 2 3 336: New York 2 4 237: North Carolina 12 14 10 138: North Dakota 17 17 7 I

i 39: Ohio 9 9 1 1 140: Oklahoma 1 141: Oregon 8 7 4 1 142: Pennsylvania 9 6 344: Rhode Island 12 11 9 6 6 I

45: South Carolina 9 I 12 746: South Dakota 18 19 13 247: Tennessee 4 I 5 248: Texas 19 17 10 2

I 49: Utah 3 4 2I

50: Vermont 8 9 4 1 151: Virginia 4 4 3 2 I53: Washington 7 I 8 4 1 i 154: West Virginia 4 , 3 355: Wisconsin 2 3 1 156: Wyoming 15 12 11 I 1

I Total 469 466I

273 65 32 !

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

1 l

:~-3==L~ I7 I) 1 I

10 --r--'~__, 1 I8 1 ' I

16 ,_+ __ .21~_-_--~18 ,11 ~ ,

: -t-=' : , 2 I 1 I2 -+ - ---r---4

3

4-- -r--- 1 I I2

I 6 ,3 1 I I1~L .J~__+ 2, I,

~ --~=--~:----I--+--l--- ---, I

1~ _.~, 2 I I7 ~I 6 ' 63 3 !4 "-2~ !

-,-

11 8'~1~ -~=r-1 1: i=i~1 1 I: ,- ~------=+=-1

~~- - -----r14 9, 2, I

_c_ -, --=:=L I1~--1- -iu

i 2-~

1 ,_, 1 I J2 4 2112 3 ,~- 2' 1 1

-5 4 :>, 1 1,~_,_='-~'r, i : J__ u _

766

Overlap

State

: 01: Alabama104":-Arizona

05: Arkansas06: Califomia08: Colorado

~09: Connecticut.-10: Delaware

--12: Florida-

i- 13: Georgia16: Idaho

~J~ illinois, 18: Indianai 19: Iowar-20: Kansas

21: Kentucky~_22: Louisiana

23: Maine12TMarvlandc 25: Mas~achusetts

26: Michigan'-'27-:- Minnesota

28: Mississippi29: Missouri30: Montana

.---31: Nebraska32: Nevada

'-'33:- New Hampshire34: New Jersey

i 36: New York37: North Carolina38: l\"orth Dakota

--

39: Ohio40: Oklahoma- -

41: Oregon42: Pennsylvania45: South Carolina46: South Dakota47: Tennessee48: Texas49. Utah50: Vermont51: Virginia53: Washington54: West Virginia

,- 5S:-Wisconsin56: ,Vyoming

Initial

2177

23812846

123

1816472526

138

134722

1013

51

477

141

17

Stage 1 I Stage 2

2 ! 218 ~--1410 :;

-~-~189

I

IStage 3 i Stage 4 I

I 1I H 5 I

I 2 I

2 1 I

I

1

Cumulative Percent ReductIOn

Total 300I

305

1.7%

40

~89 !_~~~13,'.0% 85.3%' 94.0% I

Table B6. For Stratum 89 and Below: The Number of 1993 FCRS Samples by State thatwere 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 ! 104: Arizona 13 11 8 7 6 I

05: Arkansas 2 406: California 3 3 2 i

08: Colorado 8 8 5 209: Connecticut 4 1 110: Delaware 1 1 !12: Florida 3 6 3 1 1 1

13: Georgia 116: Idaho 9 7 4

i 17: illinois 3 2 I

18: Indiana 3 5 319: Iowa 5 6 220: Kansas 2 121: Kentucky 3 2 222: Louisiana 5 7 I 323: Maine 124: Maryland 1 126: Michigan 5 8 1

I 27: Minnesota 8 5 328: Mississippi 5 4 I 3 129: Missouri 8 6 2 1 130: Montana 2 5 4 I

31: Nebraska 3 4 1,

132: Nevada 2 1 I :33: New Hampshire 237: North Carolina 2 I 3 238: North Dakota 4 5 2

" 39: Ohio 4 3 I41: Oregon 4 3 ! 242: Pennsylvania 2 2 , 1 I44: Rhode Island 12 , 11 9 6 6

i 45: South Carolina 2 3 I 1 I

46: South Dakota 4 5 447: Tennessee 3 i 3 1 :

48: Texas 2 1 149: Utah 3 3 150: Vennont 6 5 251: Virginia 2 1 1 1 I

53: Washington 2 4 154: West Virginia 1 1 1 i

55: Wisconsin 2 2 1 1 ,

56: Wyoming 8 6 5 II I

: Total 169 161 i 84 21 14

I Cumulative Percent Reduction i 4.7% 50.3% 87.6% 91.7%

41

U.S. Level Control Value Estimates l~sing the Four Stage Algorithm

Table B7. For All Strata, U.S.: The Estimated 199:3 Population Control Variable Totals forthe Initial, First Stage. Second Stage1 Third Stage, and Fourth Stage 1993 FCRS Samples.

862521 47.04iI678.01 791.28 798.17 794.39 78944 78883 57.30.- .-----..-- - --

;15053' 14844 152.62 151.96 151.93 j 152.071 15228 152: 3 0.84

Estimated Tota.l Exact CV ofC'- ---

Initia.l ,StAge 11 Sh,ge 21 Sta.ge J I St.ea.ge 4Sa.mple: Sa.mple ! Sa.mple :Sa.mple : Sa.mple

36362 327.21 i 400.03 363541365.83 365.65 365 74 365 :\4._ue _

94758 902.34 992.81 992.67 990.911990.02 98742 985 :'0

0.88,

088 0.88·

1.071

1.06 ; i1.06,1

2.88 2.88 2.88

321 319 3,18 :

4081 4.08 4.09i

,

13.11 1330 13.30'

~5.41 5.43

Sta.ge 21 Sta.ge 3 Sta.ge .•

Sa.mple Sa.mPle: Sa.mple i

(%) , (%) . ('Yo) I

(13) I (14) (15);

2.451 2.43: 2.44:

,-,2.881

1.07

0.85

3.21

Estimated CV

2.31 2.46

3.05

2.98

1.11

5.331 4.08

13.02 ! 13.131I

5.22 5.31

IDlti •.l I Sla.ge 1

Sa.mple Sa.mple

('Yo) , ('Yo)(II) , (12)

2.89

2 78

9.97

6.07

32.59

13.90

EstimatedTotal

('Yo)(10)

!#1

8~4 :14

(#)

(B)

82, 19

(#)( 7)

(#) (#)(5) : (6)

573245-1:C9____ e __ u •••

106.15! 103901104.12 10214 10214

821.80 i 829 07: 828.11

588.76! 576.221 572.97I

889 19

8860 141.32

90% I 90%,

Pop. : Lower II UpperTotsl i Bound Bound(#J (#) (#)(2) i (2.) (4)

114 96

127 21__ .~_8.~1195.61 102.40 102.54 103.66 105 IJ l04f,.5

ControlVariablet

(I)

Tot •.1 Hogs &. Pig.

Tot .•.1 Land in Farm

, ,IAll Cattle &c Calvee 850 131 1\]: .07, I

._-----.-.

II Total Cropla.nd

lon-Farm Grain Storage

i Fa.rrn V.lue or Sale.

i All Sheep

rI Fa.rm Worker •. Hired

$1,000,000.000 for Farm Value Of Sales;10,000,000 bushels for On-Farm Grain Storage;10,000 worke;-s Farm Workers Hired.

t All missing control values were set to zero before any computations were performed. The units of measure for the populationtotals and their estimates are:1,000, 000 acres for Total Land:1,000,000 acres for Total Cropland;100,000 head for Cattle & Calves, Hogs & Pigs, and Sheep;

Table B8. For Stratum 90 and Above, U.S.: The Estimated 1993 Population ControlVariable Totals for the Initial1 First Stage, Second Stage, Third Stage, and Fourth Stage1993 FCRS Samples.

-"-~%:I. IlO%

-- - ---- ..-- --- ----Estimated Total Exact CV of Estimated CV

I--Initu.l : Sh'Ie 11 S1.~Ie :21 Sta.le 31 Sta.g:-;Control Pop. Lower Upper 1•• ,,,>1 1 S'.ge 1 S1.a.ge :2: S1.a.ge 3 Stll,.g" 4 Estimated.

Variablet Total Bound i Bound Sa.mple S&mple Sa.m.pl.e; Sa.mpl~ Sample Total Sample Sample Sample I Sa.mple I Sa.mple I

(#) ! !#) i (#) (#) (#) (#) (#) , #i ('Yo) ('Yo) ('Yo). ('Yo) I ('Yo) ] ('Yo) .,

(1) (2 ) (2 )I

(4 ) (5),

(6) (7) (8) ,9 J (10; (11) (12) I (13) I (14) . (IS),

! Toh.1 Land in Farm 200 12 160.57 239.67 196.58119254 191.38' 186.91 I B6~,2 11.98 5.19· 5.16 5.14 5.13 514.

I--

I__ n ___

2.261I Fa rm Valu e of Sale. 50 00 4826 : 51. 73 5077 5074 50.95 51.05 r~o <;'10 2 10 2.14 , 2.13 2 26 2.26--- .. - - i

! Total Cropland 87 84 52..34 122.33 81.811 8247 82.35 82.37 8212 2380 194 : 1.93 192 1.92 : 1.91I~.. --~- - -220.22! 221 58

- -- .--- .. ---i

3.98 !On·Farm Grain Storage 209 98 : 9R 54 221.41 222.99 222.68 222_~;2 330 3.96 ' 3.93 393 398-- --~+I --- ----. --

,,

7.93 iAll Cattle &: Calve. 28~ 97 251 17 320.77 286 42! 295 52 295.02 291.71 2~O f,O ,.38 8.30 ! 8.31 8.30 8.30---- - .. -- - . i------------._~------

Total Hog. 6£ Pig. 198 7S 11 J 57 283.98 19645.17703 175.51. 174.99 1~3~13 25.98 12.75 7.47 ! 7.48 I ,.491 ;-~~I ------ I ,

All Sb~.p 32 90 18.40 I 47 50 32.10 I 3326 ! 33.26 : ::n.49 .,~3 _4 9 26.76 25.68 25.101 25.10. 24.831 24 83;--- -c_ - ---

37 78t~~~-;--c;~,; 1

..Farm Worker. Hif'ed 45 0') 20. 34! 64 64 37 16: 3663

1

26.4 7 8.02!

8.04

-~~--,-_. ~----

$1,000,000.000 for Farm Value Of Sales;10,000,000 bushels for On-Farm Grain Storage;10, 000 worke~s Farm \Vorkers Hired.

t All missing control value" were set to zero before any computations were p,'rformed.totals and their estimates are:1,000.000 acres for Total Land:1,000.000 acres for Total Cropland;100.000 head for Cattle &: Calves. Hogs & Pigs, and Sheep;

The units of measure for the population

42

$1,000,000,000 for Farm Value Of Sales;10,000,000 bushels for On-Farm Grain Storage;to,ooo workers Farm Workers Hired.

Table B9. For Stratum 89 and Below, U.S.: The Estimated 1993 Population ControlVariable Totals for the Initial, First Stage, Second Stage, Third Stage, and Fourth Stage1993 FCRS Samples.

II 90% 90% Estimated Total Exact CV of Estimated CV

Control Pop. I Lower Upper In.itia.l Stage l' S1.a.ge2 Stage 3 r Sta.ge .• Estima.ted I Diti&l St&l'c 1 S'&g< ~ I Shg. 3 Sta.ge ",Variable-t Total Bound Bound Sa.mple S6mple· SlLmple i Sa.mph: I Sa.mple Total Sa.mple Sa.mple Sample Sa.m.ple Sa.mple

(#) (#) (#) (#) (#),

(#),

(#) (#) (%) (%) (%) (%) I (%) (%)(1 ) (2) (3) (4) (5) (6) (1) (8) (9) (10) (11) (12) (13) i (14) (15)

.152.1311416.92,

'Total Land in Farm 662.40 594.10 I 605.63 603.01 602.53 602.31 14.52 2.55 2.19, 2.18 2.16 2.16

I0.10 I,Val ue of Sale. 100.53 ' 99.36 i 101.11 101.19 i 101.19 101.12 101.23 101.23 0.11 0.68 0.68 0.68 ' 0.68

,

Total Cropland 215.18 264.14 281.43 281.13 283.36 283.30 283.37 283.22 2.56 1.32 1.26 1.26 1.25 1.25

,693.84 :

I3.66 !On-Farm Gra.in Stol' •.ge 137.60 181.31 112.45; 169.32 161.03 164.74 762.89 3.60 3.53 ! 3.54 3.54 ! 3.54

II

All Cattle &t. C•.lv •• 564.16 546.42 581.89 535.38 533.56 533.08 533.48 533.75 1.91 1.91 1.93 1.93 1.931 1.93I

Total Hog • .Ie Pig. 348.37 319.46 311.28 392.31 399.19 391.41 398.24 397.86 5.03 4.82 4.86! 4.86 4861

4.86 ~I

All Sheep 82.01 60.02 i 103.99 14.05 70.65 70.86 68.65 68.65 16.25 14.98 15.28 15.24 15.65 15.65,I I

Farm Worken Hired 82.221 16.701147.14 65.24 65.91! 65.89 66.81 66.67 48.30 6.801

6.94 6.95 6.90, 6.91I

t All missing control values were set to zero before any computations were performed. The units of measure for the populationtotals and their estimates are:1,000,000 acres for Total Land;1,000,000 acres for Total Cropland;100,000 head for Cattle & Calves, Hogs & Pigs, and Sheep;

43

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

Table BIO. For All Strata, U.S.: The Number of FCllS Samples and Percent of Total FCRSSamples by Sampling Configuration for the Initial, First Stage, Second Stage, Third Stage,Fourth Stage, Fifth Stage, Sixth Stage 1993 FCRS Samples.

7.3

0.0

0.0

0.0

13.8

0.3

2.1

0.5

0.0

0.0

0.0

3.0

0.3 I

o0.1

0.0,

0.4 '

82.7 I

82.7 I

5.7

0.8

(%)

(16)

0.0

0.0

0.3

o0.11

0.01

0.4

82.71

82 7

5.7!

0.8;

7.3

0.1

13.9

0.3

2.1

0.5

0010.01

0.0

3.0

(%)

(15 )

0.0

0.0

0.3

o0.1

0.0'

041

0.0

3.0

0.51

0.01

0.0:

5.7

0.8

7.3

0.2

13.91

0.31

2.1

82.7'

82.7

(%)

(14)

0.3i

2.1 '

0.5,

0.0

0.0

0.1.

0.0

0.1,

3.1

0.3'

010.11

00

0.4

82.5

82.5

5.71

0.8i

7.2

0.4

13.9

(%)

(13)

0.2

0.0

0.2

0.1

0.5

0.11

O.l!

0.3,

00

0.51

3.3!

81.9

81.9,

5.4

o 7,

661

1 4

14.2,

0.31

1.8

(%)

( 12)

021

0.0

0.2

0.1

0.5

o Ii

a.l!

81.4

81.4

5.3

0.7

6 a2.7

14.7

0.21

1 7

0.3

0.4

0.1

0.7,

3.41

0.41

0.1

0.3

1.3

0.5

0.1

1.2

7.5

0.7'

0.1

0.1

3.7

0.2

1.0

1. 7!

32.2!

59.2

59.2

9.9

3.0'17.6'

('Yo), ('Yo)I

(10); (] 1)

89

36

43

235

57

4

816

4

9249

1547

9249

638

1#)

(9)

(I 0_. ----~.

7 6

2

57

23 "

637

81410

9245

9245

1543

I#!

()

36

57234

5 " 3

337 338 336

34 34 35

813

19

1555

9240;

92401

6351

88

(7) I (8)

(#)

3201

631i

878001

41i

1559

351

231 '

55

7

1

16

345

(#)

I (6) I9227

1

9227

6,

6'

9

57

29

20649

31

5

52372,

261

2120;

91581

9158

607

80

738

160

1585

(#)

, (5)

24'

189

39,

H

6

73

375;

26

2

21

9158

1

616:

9095'

9095

597

H

668

305,

16H

45

6,

33

23

107

8'81

H

414

147;

59

12

137

843

6617

6617

(#) (#)

(3) ! (4)

,

Count Percent:

Ini1.u.1Sta.ge 1lShge 2 Sh.!'c 3ISta..ge -I Sh.g~ ":> S~a..g'"6 Inltl •.1StAge 1 Sta.ge :=/ISta.ge 3 Sh.ge 4 Sta.ge 5LSta.ge 61

II I,' j ~

, '

o ] 0

'J 9 9J " 3Q A CA L .1

( 2)

1 1 I) 1 I

1 1 1 0 0

1 1

1 0 1 1 1

Total

9 93 2F FC CR RS S >~ _ .:)

Sa-Jnpling

'Configuration t

, 1 0 0 0 1 1110 if=~=f-O_..!.-,~_ 336, 1 0 lOll 1966~-i~0=:~=') 191,

Total 36031

L_~ __l__ O _1

1 1 1 1 0~-----~

Total

~~l_~~l! Total

93 FCRS plu. two

93 FCRS alone

(1)

93 FCRS plue one

Combination

of Surveys

other .urvey

93 FCRS plu. thr-ee

93 FCRS plu. {our

other .ur"'eye

11,178111,178 11,178 11,178 ]1,178111.17' 11,178 100.0 100.01 100.0 100.0' 1000 100.()~

t 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 the93FCRS and 93CSS.

44

Table B11. For Stratum 90 and Above, U.S.: The Number of FCRS Samples and Percent ofTotal FCRS Samples by Sampling Configuration for the Initial, First Stage, Second Stage,Third Stage, Fourth Stage, Fifth Stage, Sixth Stage 1993 FCRS Samples.

I

Sampling Count Percent

Configuration t IDitia.l:St..~e 1 Sta.s:e 2 StILge 3 Sh.ge 4.Sta.S'c ~ Sta.ge 6 l:pitia.l Sta.gc 1 Sta.s:e 2 Sta.ge 3 St •.ge 41Stage 5 Stage 6

9 9 I !I

3 2 9 9 9

II F F 3 3 3: C c Q A CCombination R R A L S1 of Surveys

I

S S S S s (#) (#) (#) (#) (#) (#)i

(#) (%) (%) (%) ('Yo) (%) ('Yo) ('Yo)IIi (1) (2) (3) I (4)

i(5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)

iI 93 FCRS alone 1 0 0 0 0 1361 2260 2284' 2323 2334 2337 2339 35.9 59.5 60.21 61.2' 61.5 61.6 61.61 Total 1361: 2260 2284 23231 2334 2337 2339 35.9 59.5 60.2 61.2 61.5; 61.6, 61.6

93 FCRS plua ofte i 1 0 0 0 1 5171 459 465 484 488 490 491 13.6 12.1 12.2 12.8 12.9 12.9' 12.9 !

o1:her aurvey 1 1 0 0 1 0 159 42 46 51 52 52 52 4.2 1.1 1.2, 1.3 1.4 1.41 1.4'

1 0 1 0 0 986 499 548', 5931 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

I

93 FCRS plue two 1 0 0 1 1 52 22 26 31 32 32 32 1.4 0.6 0.7 0.8 0.8 08! 08:

ot her au rvey. i 1 0 1 0 1 293 1581 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 2.41 0.71 0.9 1.0 1.1 1.1' 1.1

I

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 '

I 1 1 1 0 0 92i 59, 40 13 3 3 1 2.4' 1.61 1.1 ' 0.3 0.1 0.1 0.0

i Total 586 310 3041 283 275 276 274 15.4 8.2 8.0 7.5 7.2, 7.3 7.2

I

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 survey. 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 0.41 0.2 0.1 0.1 0.11i i 1 1 1 1 0 17 6 6 1 01 0: 0 0.5 0.2 0.2 0.0 0 0 0

Total 82 46 i 45 34 331 331 34 2.2' 1.2 1.2 0.9 0.91 0.9 0.9 '

93 FCRS plus four 1 1 1 1 1 61 4 4! 1 1 1 1 0.2 0.1 0.11 0.01 0.0 0.0 0.0

01 ber au rvey. Total 6 4 4 11 1 1 1 0.2 0.1 0.1 : 0.0 O.O! 0.0 0.0

Total 3795: 3795! 3795 3795 3795 3795i 3795 100.0 100.0 100.0 100.0 100.0 100.0! 100.0

t 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 the93FCRS and 93CSS.

45

Table B12. For all Stratum 89 and Below, U.S.: The I\umber of FCRS Samples and Percentof 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

1

i Confl~,!~at~n t IXUha.liSta.ge 1 S\a.g~ 2ISta.I'C 3 Sta.ge 4~Sta.~5--=-t~~e 6 Inltla.llStAge 1 Sta.lc 2!Sta.ge 3lSta.ge " Sta.ge .5 Sta.ge 6

, g 9 , 1' I I3 2 9 ,. 9

F F 3 3 1, I

!, ,

CombinationC C Q A - ,

1,R R A L -

I

,

I

of Surveys S S S S - (#) (#) (#J

I

(#) (#1

I

(#J ,#1 (%) (%)

I

(%)

I

(%) (%) (%) I (%)

I

1

I

!(1 ) (2) (3)

,(4) (5) (6) ( 7) 18) i9) (10) (11 ) ( 12) ( 13) (14) (15 ) (16)

,

I

93 FCRS alone I 1 a 0 0 a 5256 68351 68741 6904 69061 69081 6910 71.21 92,6, 93.1 93.5 93.5 93.6 93.6L---.......-...~ __ ._ -I-I Total 5256 6835 68741 6904 69061 69081 6910 71.2 92.6 93.1 93.51 93.5 93.61 93.6 ,

93 YCRS plas one 1 0 0 0 I 593 138 1421 147 1471 147[ .. 147 8.01 1.9 1.9' 2.0: 2.0 2.0 2 0 ~iother- survey 1 0 0 I 0 177 32 341 36 36 36 37 2.41 0.4 0.5, 0.5! 0.5i 0.51 0.5

--I 0 1 a 0 980 169 1901 207 212 212 213 13.3 2.3 2.6 2.81 2.9 291 2.9

P2--0---.Cl- 0 93 130 I 611 15 8 61 3 1.3 1.8 0.8: 0.2, 0.1, 0.11 0.0 ;0-

I Tota.l 1843 469 4271 405 403 401 ' 400 25.0 63 5.8 5.5 5.5 54! 5.4

93 FCRS plus two L 1 a a 1 I 22 2 3, 4 4 4 4 0.3 0.0 0.0 0.1 0.1 o.li 0.1 !: -~ ----- ~: other aurvey. I 1 a 1 a I 121 31 331 38; 38 38 38 1.6 0.4 0.5 0.5 0.5 0.5: 0.5 ',

141, .. .---

1 a I I 0 56 12 161 17 ] 7 17 0.8 0.2 0.2 0.2 0.2 0.2 ~'------------- -~----- -- --

1 1 a a I 12 5 5' 1 1 1 I 0,2, 0.1, 0.1, 0.0 0.0' 0.0 0.0----- -----~- __ ,

O.O!I 1 1 0 1 0 1 1 11 0 0 0 a 0.0 0.0' 0) a 0 0-------1 1 1 0 0 45 14 121 3' 2 2 2 0,6! 0.2 0.2! 0.0 0.0 0.0, 0.0

.~

Tota.l 257, 65 68 62 62. 62 62 3.5, 0.9' 0.91 0.8. 0.8 0.8 08:

1 93 FCRS plu. three: 1 a I 1 I 91 3 3 5, 5' , 5 0.1 0.0 0.0 0.11 0.1 0.1 0.1! -----

21----

0.0'other .urvey. 1 1 a 1 1 1 1 a 0 a 0 0.0, 0.0 01 a 0, a----. +----~-- . ---<

1 1 I 0 I 8 5 5 3 3 :\ 2 0.1 0.1 0.1 0.01 0.0' 0.01 00:

, i 1 1 I I .J 61 31 3 2 2' 2 2 01 0.0 0.0 0.01 0.01 0.01 0.0 1~l-- ------- .-.-

0.1 125 12 12 10: 10; Iv 9 0.3 0.2 0.2, 0.1 0.1 0.1 :

93 FCRS plu. four 1 1 1 I I 2 2 2 2 2' " 2 a a 0.0 0.0 0.0 0.0; 0.0 0.0 :

21 --other aurvey. I Total 2: 2' 2, 2 2 2 a a 0.0 O.O! 0.0 0.0 0.0 0.0 ,

Tot •. 1 73831 7383 7383 7383 7383 7383 7383 100.0: 100.01 100.0j 100.01 10001

100.0 100.0 j----

t Note: The Sampling Configuration indicates the sampling pattern for the 93FCRS, 92FCRS, 93QAS,93ALS and 93CSS (Cat tie and Sheep). For example, a 10001 indicates sample units selected for only the93FCRS and 93CSS.

46

Table B13. For All Strata: The Number of 1993 FCRS Samples by State that were in the1992 FCRS Sample at each Stage of the Redrawing Process.

! Overlap iii

State Ini tial Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

01: Alabama 6 4 4 1 ,I 04: Arizona 30 29 22 12 I 9 9 9, 05: Arkansas 9 14 5 2 Ii 06: California 26 21 13 2 ,

08: Colorado 16 17 13 409: Connecticut 5 1 1 1 1 1

I 10: Delaware 3 2 1 ~I 12: Florida 11 ! 10 5 2 2 1! 13: Georgia 5 , 4 4 1i 16: Idaho 15 14 10 2 1

17: Illinois 15 12 5 1 1 1i 18: Indiana 6 13 5 1 1i 19: Iowa 23 22 13 2

20: Kansas 18 19 11 1 I

, 21: Kentucky 7 I 6 5 1 !

22: Louisiana 12 I 15 8 2 2 i23: Maine 3 2 l: !24: Maryland 6 I 5 4 1 1 125: Massachusetts 2 I 3 2 i26: Michigan 11 14 4 1 1 i

27: Minnesota 21 18 16 428: Mississippi 13 12 4 129: Missouri 8 I 7 2 1 1 I 1 II

30: Montana 2 I 7 5, ,31: Nebraska 16 i 16 9 332: Nevada 6 4 1 133: New Hampshire 9 I 7 7 6 6 6 634: New Jersey 2 3 336: New York 2 4 2 I

I 37: North Carolina 12 I 14 10 1 !I

38: North Dakota 17 l 17 8 1 I;39: Ohio 9 9 1 1 140: Oklahoma 1 141: Oregon 8 7 4 I42: Pennsylvania 9 I 6 3 ,

I

44: Rhode Island 12 11 11 6 6 6 645: South Carolina 9 12 8 2 2 2 146: South Dakota 18 19 13 I 247: Tennessee 4 5 2 148: Texas 19 17 12 ! 4

.

49: Utah 3 4 I 2 1 I

50: Vermont 8 9 5 2 2 2 151: Virginia 4 4 2 2 1 I

I

53: Washington 7 8 4 1 154: West Virginia 4 I 3 355: Wisconsin 2 3 2 1

, 56: Wyoming 15 12 11 2 2 2

Total 469I

466 285 ! 80 41 32 23i I

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

47

Table B14. For Stratum 90 and above: The Number of 1993 FCRS Samples by State thatwere m the 1992 FCRS Sample at each Stage of the Redrawing Process.

Overlap

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

~~=)---+---. ---+-~-2 l' 1--~- - -- ----

4 l--~---- ---.-----

6 l5 li----- ..

-~------+--------11 :2-------._-11 I

- ---------3 1

-------4 '2

1

447

108

1618482

436

1381 iI __ -.-

2 . 1 i

13 ~----:34 -~I7 7 I 7 f,2 3 I 3242

10 .1.._ 11 8-----13 I 12 65 I 6 11 1

4 47 47 914 14

1 217 16

1434216

3

i

I~~ __ '

I

2

2

3

2

III

I I

I I I

i 1 :---

66 6

i

-.--

- .. I I

1

1- I I 1----------t--

22

~ :J--.--~1

111

u. _

2 2----1 1n __ --

~=1= u:1=:ij6--- I 1

214 5 3

- -------5 :2---- ------11 :2

21810189

7

2253

7

217

23812846

123

1816

472526

138

I 01: Alabama----~04: Arizona05: Arkansas06: California08: Colorado09: ConnectiQ:,i---10: Delaware

--"--12: Florida

-- ---- -----13: Georgi,, _16: Idaho17: Illinois18: Indiarla--

-------~19: Iowa -- -----~-20: Kansas21: Kentucky22: Louisiana23: Maine24: Maryland25: Massachusetts26: Michi~a.:' _27: Minnesota28: Missi~!?~29: Missouri30: Montana31: ;\/ebraska

------

32: Nevada33: New Hampshire34: New Jersey36: New York ----

r 37: North -c-~oli;';~'I 38: North O.;:kota

--- .----39: Ohio40: Oklahoma41: Oregon__42: Pennsylvania45: South Caroliila46: South Dakota47: Tennessee48: Texas49: Utah

I 50: Vermont

i 51: VirginIa=:=53: Wasl1.i!lgto~ .

, 54: West Virginia55: Wisconsin

! 56: "Vyarning

Cumulative Percent Reduction

Total 300 305-1.7%

195

35.0%

54~2_0%

2392_3%

16

94.7%

11

95.1%

48

Table B15. For Stratum 89 and below: The Number of 1993 FCRS Samples by State thatwere in the 1992 FCRS Sample at each Stage of the Redrawing Process.

I Overlap I

IState Ini tial Stage 1 Stage 2 I Stage 3 Stage 4 Stage 5

IStage 6

I 01: Alabama 4,

2 I 2 104: Arizona 13 11 8 7 6 6 6

! 05: Arkansas 2 4 i06: California 3 3 2 ,

08: Colorado 8 8 6 2 ,

09: Connecticut 4 1 1 1 1 110: Delaware 1 i 112: Florida 3 6 3 1 1 113: Georgia 1 I

I 16: Idaho 9 7 4 I 1 117: illinois 3 2 i18: Indiana 3 5 4 1 1

I 19: Iowa 5 6 2 I !

, 20: Kansas 2 1 I21: Kentucky 3 2 2

,

, 22: Louisiana 5 7 4I 23: Maine 1

24: Maryland 1 1I 26: Michigan 5 8 1

27: Minnesota 8 5 3 I

I 28: Mississippi 5 4 3 1 ,29: Missouri 8 6 2 1 1 1

,

30: Montana 2 5 I 4 I

31: Nebraska 3 4 1 !

32: Nevada 2 133: New Hampshire 2

I 37: North Carolina 2 3 2I 38: North Dakota 4 5 I 2 ,

I 39: Ohio 4 341: Oregon 4 I 3 242: Pennsylvania 2 2 144: Rhode Island 12 11 11 6 6 6 6 ,

45: South Carolina 2 I 3 1 i, 46: South Dakota 4 5 4

47: Tennessee 3 3 1 148: Texas 2 1 1 I

49: Utah 3 ,3 1,

50: Vermont 6 5 I 3 i51: Virginia 2 1 1

,1

53: Washington 2 ! 4 1 I , I I54: West Virginia 1 1 1 ! ,

55: Wisconsin 2 2 1 I 1 i56: Wyoming 8 6 5 1 1 1

Total 169 I 161 90 I 26 18 16 12I

I

Cwnulative Percent Reduction 4.7%I

46.7% i 84.6% 89.3% 90.5% 92.9% 1

49

u.s. Level Control Value Estimates Using the Five Stage Algorithm

Table B16. For All Stmta, U.S.: The Estimated 199·3Population Control Variable Totals for theInitial, First Stage. Second Stage, Third Stage, Fourth Stage, Fifth Stage, and Sixth Stage 1993FCRS Samples.

On~Fllrm.GraUl Slor~ 947.58 9(i~.34 ~1.S1 992_67 990.91 989.171992.01 990.66 990 4b 9!-lO4'4

13.421 13.42 I 13.39 j

5.41 1 5.41 1 ',.40

1.11

2.98

5.22

5.33 :

3.051

E.!ltimated CV

lnil,.] ISla,,, I S'all:":l 51"1I:~ 31 51"'11" 4 151 .•.,,<1' 5 i 51 •. ,;" G ,

S~;t~l"IS~;;I<I''I S~;~"1 S~;'~', : S~;~I'I: S~;PI" ! S~;';"I

(13) : (141 (15): (I6) (17) (18) 1 (19) ;

2.31 2.46' 2.451 2.451 ~~~

0.86 0.85 0.88~ 0_88 I 0.88 I 0.880.84

2.78

2.89

9.97

6.07

:;7,30

1,1.9D

32.59

Exact CV of

&Itimated

Total

(%1(121

]5190 IS190

790.67 790 1'>9,

--r----

101 IS 101.:19

364.50 364 48

S I ••,e 4 .$t&I\"!. "~t&,:~I.

S••mpl" S,ullpl •. : S.l.l'fll,J ••

(#1 (#1

(10) I")

Estimated Total

(#)

(51

141.31 106.15,103.90

(.¢I(I)

19,-,.61 102.40 102.54 i 103.75; 104.50 i 104.45 104 47 104.~,8

1#1

(31

(#)(2)

90% 90%

Pop. Lower Uf'per Inlti,.]

Total Bound! Bound S.mplt'

5-17.15 457 I:'" &1;' 1Z 588.76 576.Z2

363 62: 3:'7.21 I 400.03 363.54

114.96 88.60

127.21 I :>8,SO

862.521 4704, 167S 01 791.28

150.53 I 148,44 152.6Z 151.96

Control

Variablet

(1)

All Sh..,..,p

Tot.J Land 111 Farm

All Caltl~ '" C.}VoeA 850.13 SII 1)7" &S:1.19 821.80 i 829.07 1825 44 ! 830.78 831.88 J 832 10 &3:: 38

Fllrm Value or Salea

! Farm Work'il!r'8Hil"L>d

t All missing control values were set to zero before any computations were performed. The units of measure for the population totalsand their estimates are:L000.000 acres for Total Land;1.000.000 acres for Total Cropland;100.000 head for Cattle &: Catv"s. Hogs &. Pigs. and Sheep:

$1,000. nOD. OOU for Farm Value Of Sales;10,000. dad bushels for On-Farm Grain Storage:10,000 worker·, [-"',rrn \Vorkers Hired.

Table B17. For Stratum 90 and Above, U.S.: The Estimated 1993 Population Control \/ariableTotals for the InitiaL First Stage, Second Stage, Third Stag",. Fourth Stage, Fifth Stage, and SixthStage 1993 FCRS Samples.

~---- --Exact: CV of E5timated CV

E~hmated :1 . IIMI, •. ] S~il.Ii<l' 1 I St"II" ~ Sh."" 3 51.,,<1''' 5t&,I;<I' ~ I 5\ •.,.." (, I

Total S.mol.1 S.mPl.1 S.mpl. , S.mol. , S.mPI.\ S.mpl. : S.mpl.

1%) ('iI) 1 (%1 ('iI), ('iI) '('iI) (%) I (%)

(12) (13) : (14) 1 (15) 1 (16) , (17) i (18) (19)

11.98 0.191 5,16 I 5.151 5.24 5.24 5.241 0.231

-----~_ ..

2.131 2.25

12.10 2.14 2.25 : 2.251 2.25 2.25

23.80 1.94 1.93 1.921 1.91 i 1.91 1.91\ 1.90---------j

3.3ll 3.96 3<93 3.93 I 4.0:! 4.03 4.04 ! 4.04

7.38 7.93 8.30 ! 8.32 I 8.27 8.24 8.24 i 8.24 I

25.98 12.75 ' 7.47 [ 7.46 7.42 7.47 7.47 ! 7.47

26.76 2:).68 25.10 I 25.]0 26.05 I 2,•.361 25.36 2.>.20 I

2647 8.02 8.04 8.70 8~ 8.67 8.66 867 :" ~~

295.6ZI1Y,).'4.--+- ---~--

J 74 ,~lh 174.~,"

37.61 37 is

btimated Total

220.22 221.58 121.93! 222.88 l222.91

286.42 129.3.52 291.921294.52 I 2'95.42

196.45 i 177.03! 176.28 i 175.7] i 174.56

32.101 33.261 33.261 31.671 32.74

37.16! 36.63: 37.73~ 37701 37.19,

IlIlllal I 51"'1I:~ I . 5t.I<I' 21' 51 •. ,." 3 ~ St •. (~ 4 , 51'&'1[" 5 I 5t"'l!:~-'

S~;'I'1 S~;I" S~;"'IS~;~l' I S~;;'I S~~'l" , S~~~,.

(5) 1 (6) I (7) I (S) I (9) ,1101 111i

196.58: 192.541191.111188.35, 188.56 IllS." 18ii 71

50.771 so. 74! 50.781 50.641 50.65! ~~t~i-·S-~~~;

81.81 I 82.47 82.11 \ 81.321 81.34 81.17 .SU,'

50.00 48.2b 51.73

87.84153 ,~ 12233

.--- -209.98 ]98 :)4 ".:21 41

~~-

285.971251 17 :)20 ?7

198.76 : ] 13 ..')7 053 98

32.95 18AU 4750., ..--

90% 90%

POP'l Lower i t;pper

Total Bound Bound

(#) (#) ,#)

(2) (3) I (41

200.12 160.57 i ~39.67

(1)

farm Worker-. Hi,,><t

Control

Variablet

Total Ho~ A. Pilo;'ll

F••.rm Valu'l' or 5••.1_

, All Cattle A£ Calve ••

ITotal LII.S1-d In Farm

i Total Cropland

t All missing control values wer<>set to zero before any computations were pcrior·ned. The units of measure for the population totalsand their estimates are:

1.000.000 acres for Total Land.1. 000. 000 acres for Total Cropl,i!ld100.000 head for Cattle &.: ('"heo. Hogs &. Pigs. and Sheep;

$1.000. OOO.lIrJll f'r Farm Value Of Sales;10.000.000 bmhc.s for On-Farm Grain Storage;10.000 worbTs FUIll Workers Hired.

50

$1,000,000,000 for Farm Value Of Sales;10,000,000 bushels for On-Farm Grain Storage;10,000 workers Farm Workers Hired.

Table B18. For Stratum 89 and Below, U.S.: The Estimated 1993 Population Control VariableTotals for the Initial, First Stage, Second Stage, Third Stage, Fourth Stage, Fifth Stage, and SixthStage 1993 FCRS Samples.

90% 90% &ltimated Total Exact CV of Estimated CV

Control Pop. i Lower Upper !tnli.) E!:timated Imtiolol i S'AKe 1 S••• ,' 5 •••• 3 5 •••• 'I5•••• > Siale 61Variablej Total ,Bound Bound Sample Total s.mPl'l S.mpl, Sample, S.mple I Sal11ph, S.•.mpj•.. S.•mple

(#)I

(#) (#) (%) (l'.) (%) (%) I (%) (%) (%) (%)I

(I) (2) I (3) (4) (12) (13) I (14) (15) (16) I (17) i (18) (19)

I662.40 i -152.13I To~al Land i.n FartD 1476.92 74.52 2.55 2.77 2.77

ValUe! Qf S.l4!. 100.53 0.71 0.70 0.68

Tot.1 Cropland 275.78 2.56 1.32

On-Farm Grain Stor.~ 737.60 " 767.75 3.60 3.66

All Cattle &:. Calvl8 564.16 . 536.64 1.91 1.97,

i Tolal Hogtl .It.Pip 348.37 I 396.78 5.03 4.82 i

All Shfl:p 82.01 60.02 103.99 68.43 16.25 14.98

'F.rm Wo ••k~nl Hired 82.22 ]6.70 ]47.14 66.80 48.30 6.80 6.94)

j All missing control values were set to zero before any computations were performed. The units of measure for the population totalsand their estimates are:1,000,000 acres for Total Land;1,000,000 acres for Total Cropland;100,000 head for Cattle & Calves, Hogs & Pigs, and Sheep;

51