United StatesDepanment ofAgriculture

StatisticalResearchService

Estimatesand StatisticalResearchDivisions

SRS Staff ReportNumber YRB-8S-02

April 1985

Simplifying SoybeanObjective YieldEstimationRobert Battaglia and Jack Nealon

ABSTRACT

CONTENTS

SIMPLIFYING SOYBEAN OBJECTIVE YIELD ESTIMATION By RobertBattaglia and Jack Nealon, Statistical Research Division, Sta-tistical Reporting Service, U.S. Department of Agriculture,Washington, D.C. 20250. April 1985. Staff Report No. YRB-85-02.

This report justifies the replacement of the operational soy-bean objective yield estimator with an alternative estimatorthat is easier to understand and use, less susceptible toplant-handling effects, and slightly more precise. Analysisindicates that in most cases yield estimates from the alterna-tive estimator are not significantly different from the onenow used •

••••******.*.***.*.******************************************* ** This report was prepared for limited distribution to the ** research community outside the U.S. Department of Agricul-** ture. The views expressed herein are not necessarily *• those of SRS or USDA. *• **************************************************************

pageSU~ARY •••••••••••••••••••••••••••••••••••••••••••••••••••• i iINTRODUCTION ••...•.•..••....•••••••.•••••.•••.......•....... 1ESTIMA TORS •••.••••••••••••••••••••.••••••••••••••••••.•••.•• 2ANAL YS IS •••••••••••••••••••••••••••••••••••••••••••••••••••• 4RECOMMENDATION ••••••••••••••••••••••••••••••••••••••••.••••• 8REFER.ENCES •••••••••••••••••••••••••••••••••••••••••••••••••• 8AP PEND IX •••••••••••••••••••••••••.•••••••••••••••••••.•.•.•• 9

SUMMARY This report recommends the replacement of the operationalyield estimator in the soybean objective yield program withone that is computationally simpler, easier to understand, andpermits simple verification of unusual yields by field officepersonnel. The alternative estimator is less susceptible tobias that might be introduced by repeated handling of plantsin the samples and is slightly more precise in most instances.An analysis of soybean objective yield data from 1981 to 1984for the 15 States in the program showed few significantdifferences between the operational and alternative estima-tors.

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INTRODUCTION

SIMPLIFYING SOYBEAN OBJECTIVE YIELD ESTIMATION

Robert Battaglia and Jack Nealon 1/

Yield estimation from objective yield surveys is based onrelatively simple and straightforward observations of themature crop. Two units, which make up an objective yield sam-ple, are laid out randomly in each selected field and har-vested by the enumerator when the crop is mature. Yield peracre is then computed based on counts, .measurements, andweights from the two units.

The statistical procedures used to forecast or estimate yieldat maturity in objective yield surveys are sometimes unneces-sarily complex. This complexity can'affect the survey resultsby exposing the yield estimates ,to additional nonsamplingerrors. The operational yield estimator for the soybeanobjective yield program uses a complicated statistical pro-cedure to estimate yield at maturity. This complexity hascreated three problems:

(1) Those involved in collecting the data, editing, andsetting the yield estimate do not understand the opera-tional estimator.

(2) The yield estimate for each sample is very difficult tocompute manually. Data collected both in the field and inthe lab must be weighed together based on the variabilitybetween the pod counts from the two units in each sample.Because of the computational complexity of this estimator,unusual yields cannot be easily verified by field officepersonnel.

(3) The operational estimator uses field counts from thetwo 6-inch sections in each unit. Research has shown thisprocedure to be susceptible to bias in some States due torepeated plant handling [2,3]. 2/

Methods Staff and Yield Research Branchobjective yield procedures whenever

desirepossible,

to simplifyin order to

1/ The authors are mathematical statisticians with the Statis-tical Reporting Service, U.S. Department of Agriculture.2/ Numbers in brackets refer to literature cited in the Refer-ences at the end of the report.

ESTIMATORS

minimize the effects of nonsampling errors and to make theprocedures easier to understand. The purpose of this report isto justify the use of an alternative yield estimator in thesoybean objective yield program. This estimator is mucheasier to understand, makes it easier to verify unusualyields, and is less susceptible to pOSSible bias from handlingthe plants in the samples.

This report discusses the operational and alternative yieldestimators and compares the yield estimates from these estima-tors using soybean objective yield data from 1981 to 1984. Ifthe yield estimates are statistically the same for most com-parisons, we will recommend the alternative estimator be usedin future surveys. If the yield estimates are statisticallydifferent in many cases, we will recommend that research beconducted to uncover why the yield estimates differ betweenthe two estimators before a decision is made whether to usethe alternative estimator operationally.

This section describes the o~3rational and alternative yieldestimators. The only difference between the two estimators isthe source of measurements on the number of pods with beans.Both estimators require row width measurements to compute thenumber of pods with beans per 18 square feet component ofyield [4]. The current survey design and computer summary pro-grams require the "reported" value from each sampled field tobe "yield per acre" in bushels. Subsequently this value willbe referred to as "yield". Yield at maturity for a soybeanobjective yield sample can be calculated using the followingformula:

(Pods with beanS) * (Weight of beans per) * (cOnVerSiOn)per 18 SQ. ft. pod with beans factor

where the number of pods with beans per 18 square feet isestimated from field (Form B) and/or lab (Form C) data, weightof beans per pod with beans is calculated using lab data, andthe conversion factor converts the weight per 18 square feetto bushels per acre. The operational and alternative yieldestimators differ only in how they estimate the number of podswith beans per 18 square feet. The operational estimator usespod counts from both Forms 8 and C while the alternative esti-mator relies solely on Form C pod counts. A description ofeach yield estimator follows.

Ooerational Estimator

The operational yield estimator requires that pods with beansper 18 square feet be estimated from Form 8 and Form C data.The Form 8 estimate of pods with beans per 18 square feet for

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;

a sample is based on the enumerator's plant counts in the 42-inch rows, the row width, and the number of pods with beanscounted in the 6-inch sections [5]. In formula notation, theestimate of pods with beans per 18 square feet based on Form Bdata is:

(A1 * B1) + (A2 * B2)

2

where Ai is the number of plants per 18 square feet in unit ibased on the counts in the two 42-inch rows in unit i, and Biis the number of pods with beans per plant in unit i based onthe counts in the two 6-inch sections in each row in unit i.

The Form C estimate of number of pods with beans is currentlybased on lab data from the 3-foot section of the first row ofeach unit [5]. In formula notation, the estimate of pods withbeans per 18 square feet based on Form C data is:

P1 + (P1 * W2 / W1)

2

where P1 is the estimate of number of pods with beans per 18square feet for unit 1 based on the lab count in the 3-footsection of row 1 in unit 1, and (P1 * W2 / W1) is a type ofratio estimate of pods with beans per 18 square feet for unit2 derived by adjusting the pod estimate for unit 1 (P1) by theratio of the weight of pods and beans in unit 2 (W2) to theweight of pods and beans in unit 1 (W1). This estimateassumes that the ratio of the number of pods with beans tototal weight of beans and pods is the same for the two unitsand is used in lieu of actually counting the pods with beansfor unit 2.

Next. the operational estimator weights together the Form Band C estimates of pods with beans for each sample based ontheir relative variances [4]. Relative variance is synonymouswith the coefficient of variation squared. The relative vari-ances are based on the variation between the pods with beansestimates from each of the two units in a sample. Since thepod estimate for unit 2 from Form C is derived, it is notreally appropriate to derive a relative variance based on theForm C counts. In formula notation, the operational estimatorfor pods with beans per 18 square feet for a sample is:

(Pads with beanS)

P * per 18 sq. ft. +(Form B)

3

(Pads with beanS)

(1-P) * per 18 sq. ft.(Form C)

ANALYSIS

where P is the relative variance of the pods-with-beans esti-mate from Form C divided by the sum of the relative variancesof the pods-with-beans estimates from Forms Band C for thesample. That is, P is a weight between 0 and 1 that isassigned to the Form B estimate of pods with beans for thesample. The weight given to the pods-with-beans estimate fromForm C is (1-P). The weights assigned to the Form B or C esti-mates differ from sample to sample depending upon the relativevariances between the units in each sample. Overall, however,the average weights assigned to the Form Band C estimates areabout .45 and .55. respectively. Therefore. the operationalestimator relies very heavily on both the Form Band C esti-mates.

Finally. the operational yield estimate for each sample isderived by multiplying the weighted estimate of pods withbeans per 18 square feet by the weight of beans per pod andthen expanding this product to bushels per acre.

Alternative Estimator:

The alternative yield estimator, hereafter referred to as theForm C yield estimator, relies solely on Form C pod counts.To arrive at yield per acre, the Form C estimator simply takesthe weight of beans from the 3-foot section in row 1 of eachof the two units. adjusts this weight to the standard moisturecontent. and expands this product to bushels per acre. There-fore, the Form C estimator does not rely on the Form B countsand the complex weighting scheme to calculate yield at matu-rity for each sample. This results in an estimator that ismuch easier to understand and greatly Simplifies the verifica-tion of unusual yields by field office personnel. Also. theForm C estimator is less susceptible to potential bias causedby handling the plants, since it does not rely on the fieldcounts from the 6-inch sections. It should be mentioned. how-ever, that even though the counts of pods with beans fromForms Band C would no longer be needed to estimate yield atmaturity if the Form C estimator is adopted. these counts willstill be needed in the objective yield program to make yieldforecasts when the crop is not mature.

This section compares the soybean yields at maturity from theoperational and Form C estimators. Soybean objective yielddata from 1981 to 1984 for the 15 States in the program wasused in the analysis. Yield per acre at maturity was derivedfor each sample using the operational and Form C estimators.Table 1 shows the mean difference between the Form C andoperational yields for each year when the data is combinedover all 15 States. The mean difference is expressed inbushels per acre. The yield estimates were matched for eachsample and a paired t-statistic was used to test if the meandifferences were significantly different from zero.' A two-

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tailed alternative hypothesis was used. This test is the usualmethod employed by SRS. Problems with its application due toviolations of simple random sample and normality assumptionsare being addressed by Fecso [1].

For 3 of the 4 years, the Form C and operational estimateswere virtually the same. In 1982, however, the Form C yieldestimate was about one-half bushel lower than the operationalestimate. This difference was significantly different fromzero and represents a 1.6-percent decrease in yield. Eventhough the difference in 1982 was significantly different fromzero it resulted in a yield estimate that was closer to theofficial Board figure. For the other years the mean differenceaccounted for less than 1 percent of final yield.

In 1981 and 1982, the operational yield estimate from the 15States was slightly higher than the Form C estimate, while in1983 and 1984 it was lower. In 1981 and 1982, the soybeanobjective yield survey started around October 1 in 9 of the 15States while in 1983 and 1984 the survey started around Sep-tember 1 in these states. Also, the number of counts madeeach month in the 6-inch sections was reduced from 10 to 6 in1982. Therefore, the Form B counts were least susceptible toplant handling effects in 1982. This fact might possibly havecaused the operational estimator to behave differently in1982, thereby contributing to the significant difference.

Table 1: Mean difference between operational and alternativesoybean yield estimates for 15 States combined, 1981-84.

Year

1984198319821981

Samplesize

1568156814061415

Meandifference 1/

(bushels)

.12

.18-.52-.21

Significancelevel

.46

.22

.01

.24

1/ Form C yield minus the operational yield.

Table 2 shows the mean differences by State. The sample sizesfor each State are listed in the Appendix. An asterisk intable 2 denotes that the paired t-statistic was significantlydifferent from zero at the .05 significance level.

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The Form C and operational yield estimates were not signifi-cantly different for 53 of the 60 comparisons. With multipletests--60 tests in table 2--we expect some significant differ-ences to be erroneously stated due to type 1 error. Assumptionviolations can also increase the number of tests that appearto be significant. Therefore, the seven significant differ-ences shown are probably not cause for alarm, especially sincethe differences were not consistently positive or negative.

The main reason for showing the yield differences for eachstate is to look for patterns in the comparisons. In general,the Form C yield estimates were not higher or lower than theoperational yield estimates. The Form C estimates were lowerthan the operational estimates, however, for all 4 years inIowa and South Carolina.

Table 2: Mean difference between soybean yield estimatesby State, 1981-84 1/.

Bushels

State

AlabamaArkansasGeorgiaIllinoisIndianaIowaLouisianaMinnesotaMississippiMissouriNebraskaNorth CarolinaOhioSouth CarolinaTennessee

1984

-.321.78 •-.011.24 •1.40- .59-.29- .68

.65-.11-.46

-1.04-.37

-1.10.60

1983

.59

.32-.08

.61

.52-.621.821 .40 •

-1 .42 •.45.58

-.37.18

-1.24 •.04

1982

-2.05-.72.79

-.52-1 .17-.69

.78-.26-.70

.57-1 .291.09-.92

-2.03 •-1.11

1981

.87-.31

.56-.211.00

-1 •57 •.40

-.09.55

-.44.55

-.40-.84

-2.06.17

1/ Asterisk denotes significantly different fromzero at the .05 significance level.

The results in tables 1 and 2 indicate that replacing theoperational estimator with the Form C estimator will not sig-nificantly change the level of the objective yield estimate atmaturity in most instances. For cases where the level ischanged considerably, we recommend that the Crop ReportingBoard rely on the Form C estimate rather than the operationalestimate.

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The coefficients of variation (CV's) were compared between thetwo yield estimators in each state for the 1984 survey todetermine if the Form C estimator was as precise as the opera-tional estimator. The CV's are shown in table 3. In 13 ofthe 15 States, the Form C estimator was as precise or slightlymore precise than the operational estimator. At the 15-Statelevel, the CV's for the Form C and operational yield estima-tors were 1.21 and 1 .24 percent, respectively.

Table 3: Coefficients of variation for operationaland Form C estimators, 1984 survey.

---------------------------------------------------State

Coefficient of VariationOperational Form Cestimator estimator

AlabamaArkansasGeorgiaIllinoisIndianaIowaLouisianaMinnesotaMississippiMissouriNebraskaNorth CarolinaOhioSouth CarolinaTennessee

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6.34.27.43.73.72.74.63.54.44.35.54.93.97.05.0

Percent6.14.17.53.63.42.74.53.34.44.34.94.83.66.25.1

RECOMMENDATION

REFERENCES

We recommend adoption of the Form C yield estimator to esti-mate yield at maturity for future soybean objective yield sur-veys. This estimator is computationally simpler. easier tounderstand. simplifies the verification of unusual yields byfield office personnel. is less susceptible to plant-handlingeffects and is slightly more precise.

[1] Fecso. Ron. "Test Statistics for Objective Yield SurveyData," Memo to F. Vogel, U.S. Department of Agriculture, Sta-tistical Reporting Service, April 22,1985.

[2] Nealon, Jack. "198~ Soybean Validation Study," StatisticalReporting Service. U.S. Department of Agriculture, 1985.

[3] Nelson, D.C •• "Soybean Objective Yield Destructive Count-ing Study," Statistical Reporting Service, U.S. Department ofAgriculture, 1980.

[~] U.S. Department of Agriculture. Statistical Reporting Ser-vice. "Forecasting and Estimation Models." Objective YieldSupervising and Editing Manual, Section 150. 198~.

[5]198~.

• Soybean Objective Yield Enumerator's Manual.

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APPENDIX Number of soybean objective yield samplesharvested by enumerators. 1981-84.

---------------------------------------------------State 1984 1983 1982 1981---------------------------------------------------

Alabama 81 83 60 65Arkansas 127 121 124 112Georgia 67 87 61 54illinois 155 159 160 160Indiana 107 96 105 94Iowa 131 150 138 152Louisiana 91 97 73 76Minnesota 102 99 89 90Mississippi 103 100 96 117Missouri 142 141 135 127Nebraska 83 77 56 55North Carolina 92 86 63 72Ohio 113 101 112 102South Carolina 93 93 64 65Tennessee 81 78 70 74---------------------------------------------------

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