United States

Department of

Agriculture

National

Agricultural

Statistics

Service

Methodology Division

SEDMB Staff Report

Number SEDMB 23-01

May 2012

Revised January 2023

THE YIELD

FORECASTING

PROGRAM OF

NASS

The Summary, Estimation, and 

Disclosure Methodology Branch
THE YIELD FORECASTING AND ESTIMATING PROGRAM OF NASS, by the Summary, 

Estimation, and Disclosure Methodology Branch, Methodology Division, National Agricultural 

Statistics Service, U.S. Department of Agriculture, Washington, D.C., January 2023. NASS Staff 

Report No. SEDMB 23-01.

ABSTRACT

The National Agricultural Statistics Service (NASS) is responsible for estimating production of 

most crops grown in the United States. Additionally, early season forecasts are prepared for the 

major crops. NASS conducts several surveys to obtain the basic data needed to fulfill this 

obligation. These surveys are a mix of grower interviews and objective field visits employing 

sophisticated survey sample designs and statistical methodology.

Large surveys designed to measure acreages are used to define prescreened subsampling 

populations for the yield surveys. These surveys and the subsampling techniques are described,

and the data collection procedures are also outlined. Summary formulas are given, and regression 

techniques employed in the forecasting process are discussed in detail.

Each survey produces indications of prospective yield which commodity specialists must interpret 

to arrive at the official forecast or estimate of NASS and the USDA. This paper discusses in detail 

the process of producing these indications by the Summary, Estimation, and Disclosure 

Methodology Branch and outlines the review process used by the commodity specialists in the 

Crops Branch. A brief discussion of acreage estimates is included to the extent that they impact 

sampling and the calculation of production.

KEY WORDS

Yield, Forecast, Estimate, Regression, Outlier.
TABLE OF CONTENTS

THE YIELD FORECASTING PROGRAM OF NASS

CHAPTER 1 - OVERVIEW.........................................................................................................1

CHAPTER 2 - SAMPLE DESIGNS ............................................................................................4

CHAPTER 3 - AGRICULTURAL YIELD SURVEYS ...........................................................10

CHAPTER 4 - GENERAL YIELD FORECASTING PROCEDURES .................................20

CHAPTER 5 - CORN OBJECTIVE YIELD METHODS.......................................................28

CHAPTER 6 - SOYBEAN OBJECTIVE YIELD METHODS ...............................................44

CHAPTER 7 - COTTON OBJECTIVE YIELD METHODS .................................................60

CHAPTER 8 - WHEAT OBJECTIVE YIELD METHODS ...................................................77

CHAPTER 9 - PREPARATION OF OFFICIAL STATISTICS.............................................93
CHAPTER 1 OVERVIEW

THE YIELD FORECASTING PROGRAM OF NASS

1

CHAPTER 1 OVERVIEW

Introduction

Each month, the U.S. Department of Agriculture publishes crop supply and demand estimates for 

the Nation and the world. These estimates are used as benchmarks in world commodity markets 

because of their comprehensive nature, objectivity, and timeliness. The statistics that USDA 

releases affect decisions made by businesses and governments by defining the fundamental 

conditions in commodity markets. When using USDA statistics, it is helpful to understand the 

forecasting and estimating procedures used and the nature and limitations of crop estimates.

Several agencies within USDA are responsible for preparing world crop statistics. The National 

Agricultural Statistics Service (NASS) and the World Agricultural Outlook Board (WAOB) have 

crop statistics among their primary focus. NASS forecasts and estimates U.S. crop production 

based on data collected from farm operations and field observations. The WAOB is responsible 

for monthly forecasts of supply and demand for major crops, both for the United States and the 

world, and follows a balance sheet approach to account for supplies and utilization. The major 

components of the supply and demand balance sheet are beginning stocks, production, domestic 

use, trade, and end-of-season carry-out stocks. Forecasts and estimates of U.S. crop production 

are independently prepared by NASS, while U.S. and foreign supply and demand forecasts are 

developed jointly by several USDA agencies with WAOB coordinating.

This paper is dedicated to the crop production estimating program of NASS. A brief discussion 

of acreage estimation is followed by a detailed presentation of yield forecasting and estimating.

This paper examines the NASS process from sample design to data collection to summarization 

and data interpretation.

Definitions

Several variables, key to forecasting and estimating crop production, are defined below:

Planted acreage: Acreage planted for all purposes includes: (a) acreage planted that has been or 

will be harvested; (b) acreage planted and replanted to the same crop (only the first planting is 

included); (c) acreage planted and later plowed down, grazed, or abandoned; (d) volunteer 

acreage, only if the acres will be harvested; and (e) acreage planted on land enrolled in 

Government diversion programs.

Harvested acreage: Acreage harvested includes: (a) all acres already harvested or intended for 

harvest and (b) the same crop acres (such as hay) harvested two or more times for the same 

utilization from the same planting are included only once.

Biological Yield: The gross or total amount of a crop produced by plants expressed as a rate per 

unit; for example, bushels per acre.
CHAPTER 1 OVERVIEW

THE YIELD FORECASTING PROGRAM OF NASS

2

Net Harvested Yield: The portion of total crop production removed from the field, expressed as 

a quantity per unit of area, and derived by deducting harvesting and other losses from the 

biological yield.

Production: The total quantity of an agricultural commodity recovered or removed from the 

field. In other words, net harvested production computed as harvested acres times net harvested 

yield.

Preparing NASS Production Forecasts

Crop production forecasts and estimates have two components -- acres to be harvested and yield 

per acre. A full program of forecasts and estimates includes determining acres planted at the 

beginning of the growing season, estimates of acres to be harvested for grain, forecasts of yield 

during the season, and final acres and yield after harvest. For example, corn and soybean planted 

acreage estimates are made using data obtained from a survey of farmers conducted during the 

first two weeks in June. Expected corn and soybean yields are obtained monthly using the Ag 

Yield survey in August and two different types of yield surveys September through November.

Acres to be harvested for grain are measured in June and monitored through the season. Final 

acreage and yield are measured in December.

Two types of crop forecast surveys are conducted, a grower-reported survey and objective 

measurement surveys. The survey of growers, the Agricultural Yield Survey (AY), covers all 

major field crops included in the NASS estimating program. Growers in the sample are asked, 

monthly, to provide their assessment of yield prospects for the crops they grow. The objective 

measurement surveys, known as Objective Yield (OY) Surveys, cover wheat, corn, soybeans, 

and cotton. The OY surveys consist of a sample of fields in which counts and measurements are 

made of plants in random plots laid out in each field.

Data collected from the yield surveys reflect seasonal growing conditions and weather events as 

of the first of the month. An historical accumulation of monthly OY data collected under a 

variety of growing conditions is an invaluable forecasting asset. The implicit relationship 

between OY data and seasonal growing conditions is also explicitly evaluated using temperature 

and precipitation relative to “normal”. Departures from normal are evaluated not only for the 

current year but for the range of historic years under consideration. An assumption of "normal"

conditions is always held for the remainder of the growing season. Data collected from AY

surveys also reflects seasonal growing conditions and weather events up to the first of the month. 

AY datasets have also been accumulated over time and form an integral part of yield forecasting. 

In the context of AY surveys, the influence growing conditions and weather events have had 

upon this year’s yield is given by the respondent’s collective perception, judgment, and 

experience gathered over some given period of time.
CHAPTER 1 OVERVIEW

THE YIELD FORECASTING PROGRAM OF NASS

3

NASS does not attempt to predict future weather conditions or events. Long-range weather 

forecasts are not used in any forecast models and growing conditions and weather events after 

the first day of the month are evaluated in the following months forecast. A significant change in 

conditions or a weather event between the survey period and the report release date such as a 

killing freeze, serious heat wave, beneficial rains, etc., will not alter the forecasted values based 

on conditions existing on the first day of the month. NASS policy requires forecasts to be based 

on conditions as of the first of the month, the period which corresponds to data collected in the 

OY and AY surveys.
CHAPTER 2 SAMPLE DESIGNS

THE YIELD FORECASTING PROGRAM OF NASS

4

CHAPTER 2 SAMPLE DESIGNS

Acreage and final production estimates for the major field crops are based on data collected from 

a set of quarterly surveys designed to measure these items. The two yield forecasting surveys 

documented in this manual use a subsample of operations and fields identified during these 

quarterly surveys. Grower-reported yield surveys cover most major field crops included in the 

NASS estimating program and are referred to as the Agricultural Yield Survey (AY). Objective 

measurement surveys are conducted for corn, cotton, soybeans, and winter wheat and are 

referred to as Objective Yield Surveys (OY).

Sampling Frames

The sample designs for these surveys utilize two different sampling frames. The area frame is 

defined as the entire land mass of the United States and ensures complete coverage of the U.S. 

farm population. The list frame is a roster of known farmers and ranchers and includes a profile 

of each operation indicating the size of the operation and what commodities have historically 

been produced. The main strengths of the area frame are its completeness and stability. The 

weaknesses are its inefficiency for crops grown in small regions and its cost to build and collect 

data. The list frame can be sampled more efficiently (commodity specific, if necessary) and data 

can be collected using less expensive methods (e.g., mail, telephone, or web). The list frame does 

not provide complete coverage of all farms and is not stable since farming arrangements are 

constantly changing.

The area frame is stratified by land use for efficient sampling. All land in each State is classified 

into land use categories by intensity of cultivation using a variety of map products, satellite 

imagery, and computer software packages. These land use classifications range from intensely 

cultivated areas to marginally cultivated grazing areas to urban areas. The land in each use 

category is further divided into segments ranging in size from about 1 square mile in cultivated 

areas to 0.1 square mile in urban areas. Different sampling rates are applied to different strata 

with intensely cultivated land segments selected with a greater frequency than those in less 

intensely cultivated areas.

All AY samples are selected from respondents to the March or June Agricultural Survey. 

Objective Yield survey samples for corn, cotton, and soybeans are selected from the June Area 

Survey (JAS) tracts having the commodity of interest. Objective Yield survey samples for winter 

wheat are selected from March Agricultural Survey respondents with winter wheat planted for 

harvest as grain.

Objective Yield samples are selected as soon as possible following the final summary of the 

March Agricultural Survey or JAS. For geographic representation of the samples, the records are 

first sorted by state, district, county, segment, tract, and crop. The sample select programs use 

probabilities proportional to size to select a systematic random sample of acres from the reported 

acres (multiplied by the inverse of the sampling fraction) of the parent survey. The selected acres 
CHAPTER 2 SAMPLE DESIGNS

THE YIELD FORECASTING PROGRAM OF NASS

5

are used to determine sample fields. Two counting areas (plots) are then randomly selected in 

each field.

The following example displays the area design for Nebraska. This frame was built with seven 

land-use strata covering all 77,157 square miles. Each stratum is mutually exclusive and 

independent. The stratum labeled commercial is made up of urban areas and the non-agricultural 

contains mostly protected forest land. The expansion factors are inverses of the sampling 

fractions. Note the allocation of the samples favors the more intensely cultivated areas with 200

of 207 segments falling in the first three strata. Strata with little or no agriculture are lightly 

sampled.

Nebraska – 2019 JAS samples

Stratum Square

Miles

Segment 

Size

Segments 

in Frame

Sample 

Size

Exp 

Factor

Stratum Definition

11 22,878 1 22,867 200 114 >75% Cultivated

12 9,480 1 9,452 70 135 51-75% Cultivated

20 12,084 1 12,037 63 191 15-50% Cultivated

31 465 0.25 1,850 2 925 Agri-Urban

32 66 0.1 657 2 329 Commercial

40 5,147 2 2,567 6 428 0-15% Cultivated

42 26,775 4 6,690 12 558 <15% Cultivated

50 262 pps 16 2 8 Non-Agricultural

Total 77,157 56,136 357

The Agricultural Survey list frame sample is selected using a multivariate probability 

proportional to size (MPPS) sampling scheme. Each list frame record is assigned a measure of 

size based on historic data for multiple specified commodities. The MPPS design makes it very 

easy to target samples sizes for the commodities of interest. The desired number of samples for 

each commodity can be controlled with a minimum overall sample size. The MPPS design 

makes it easier to change samples to meet the needs of the crops program changes. The MPPS

design is a more efficient design because operations will have a more optimal probability of 

selection based upon their individual commodities and size.
CHAPTER 2 SAMPLE DESIGNS

THE YIELD FORECASTING PROGRAM OF NASS

6

The strata from a previously used stratified design are not being used for sampling, however they 

are still used for nonresponse adjustments and item level imputation. Stratification for the

Agricultural survey sample is based on the frame data for total cropland, on-farm grain storage 

capacity, and some rare or specialty crops (for each State). An example of the nonresponse 

stratification for Illinois Agricultural Survey is shown below.

ILLINOIS 

Agricultural Survey Strata

Strata Boundaries

97 Capacity 500K+

95 Cropland 7,000+

79 Cropland 2,500-7,499

78 Capacity 50K-499,999

73 Sorghum 1+

72 Cropland 600-2,499

66 Capacity 10K-49,999

65 Cropland 100-599

62 Capacity 4K-9,999

Multiple frame statistical methodology has been developed that captures the efficiency of the list 

frame and uses the area frame to measure incompleteness. This methodology was developed 

jointly by NASS and Iowa State University with provisions to account for each farm or land area 

once and only once. The survey process requires a check of all operations found in the area 

sample against the entire list frame. Area operations not found on the list comprise the sample 

from which incompleteness is measured.

Acreage and Final Production Surveys

The basic data for all NASS acreage estimates and final production estimates are collected on the 

quarterly Agricultural Surveys. These surveys also cover the quarterly grain stocks data 

requirements. NASS views the annual cycle of these surveys beginning in June with September, 

December, and March completing the cycle. Each survey employs multiple frame methodology.

All surveys have list samples of about 70,000 operations. These samples are replicated, and 
CHAPTER 2 SAMPLE DESIGNS

THE YIELD FORECASTING PROGRAM OF NASS

7

replicates are rotated from quarter to quarter with about 60 percent of the sample retained from 

one quarter to the next. This scheme allows for response burden management while keeping the 

ability to measure quarter to quarter change using matched reports.

The June Area survey (JAS) features complete enumeration of an area sample of about 9,000

segments. The June area sample forms a stand-alone survey from which a set of unbiased 

indications are generated. They can also be married to the respective list samples to provide 

another set of unbiased multiple frame indications. The September, December and March area 

frame samples include only tracts that were not eligible to be included in the list frame crops 

population. These tracts are referred to as non-overlap (NOL) tracts. Approximately 5,000 area 

non-overlap tracts are sampled in these follow-on quarters. 

Survey content differs each quarter to meet the varying requirements of the estimating program.

The June and March surveys also define subsampling populations for the yield forecasting 

surveys. The following table outlines key data items collected on each survey, the yield surveys 

subsampled from them, and from which frame the subsample is drawn.

Survey Items Measured Surveys Subsampled

June Planted acres of spring planted crops.

Acres harvested and to be harvested for 

spring crops and winter wheat.

Ag Yield (Aug. - Nov.) (list)

Corn Objective Yield (area)

Soybean Objective Yield (area)

Cotton Objective Yield (area)

September Final harvested acres and yield of small 

grains.

None

December Seeded acres of winter wheat (new crop).

Final harvested acres and yield for spring 

crops.

None

March Planting intentions for spring planted 

crops. Winter Wheat acres for harvest as 

grain.

Ag Yield (May - August) (list)

Winter Wheat OY (multiple frame)

Estimates of planted acres, made at the beginning of the season, include some acres left to be 

planted at the time of the survey. Generally, these fields do get planted and planted acreage 

estimates are not changed during the crop season. Occasionally, the planting season runs 

extremely late causing abnormally large intentions in the data or some weather event alters 

grower plans after the data are collected. When this happens, NASS may re-visit these farms 

during late July to determine what was actually planted. If necessary, planted and harvested 
CHAPTER 2 SAMPLE DESIGNS

THE YIELD FORECASTING PROGRAM OF NASS

8

acreage estimates are revised and published in the August Crop Production report.

Yield Forecast Surveys

As noted previously, there are two types of crop yield surveys conducted to obtain data for yield 

forecasting, the grower-reported yield surveys or the Agricultural Yield Survey, and objective 

measurement surveys, or the Objective Yield Surveys.

Agricultural Yield Surveys

Grower reported surveys, called the Agricultural Yield Surveys (AY), cover most of the field 

crops estimating program. The survey covers most crop yield data needs for each State. The AY 

program begins in May using a sample drawn from the list portion of the March Agricultural 

Survey. This sample is used each month through August and focuses on the small grains: wheat, 

oats, barley, and rye. The second AY sample is drawn from the list portion of the June 

Agricultural Survey. This survey is conducted monthly from August through November and 

includes numerous row crops like corn, cotton, and soybeans, as well as hay, tobacco, and 

oilseeds.

The AY survey uses a multivariate probability proportionate to size (MPPS) sample design, with 

list frame data used to determine a unit’s selection probability. A more detailed description of 

this sample design is provided in “Chapter 3 - Agricultural Yield Surveys”.

Sample size targets are set for each commodity in AY. The overall sample size varies, depending 

upon the month, from a maximum of 20,000 in August, to a minimum of 3,500 in June. In AY, 

targeting is especially important for the commodities that are considered rare commodities or 

specialty crops. 

Objective Yield Surveys

Objective measurement surveys, called Objective Yield (OY), are conducted for corn, cotton, 

soybeans, and winter wheat. These surveys are very costly and are conducted only in the top 

producing States. The States in the OY program usually produce more than 75 percent of the 

U.S. total. For each commodity, a series of monthly net yield forecasts culminates in a final net 

yield at maturity

As noted in the previous table, all OY samples except winter wheat are drawn from an area 

frame parent survey. JAS data are collected and recorded at the tract level, multiplied by the 

inverse of the sampling fraction, and summed to obtain State totals. OY fields are selected 

systematically from the acres of the crop of interest. In other words, OY samples are selected 

with probability proportional to size, making them self-weighting samples. The detail of the 
CHAPTER 2 SAMPLE DESIGNS

THE YIELD FORECASTING PROGRAM OF NASS

9

recorded area data allows sample selection at the tract level. During the interview with the farm 

operator, enumerators randomly select fields within the selected tract. Tracts with large acreages 

or expansion factors may be selected for more than one sample. Separate plots are laid out for 

each sample within a field up to four samples.

Winter wheat acres are collected at the farm level on the March Agricultural Survey

questionnaire, multiplied by the inverse of the sampling fraction adjusted for nonresponse, and 

totaled in the summary program. Farms are selected probability proportional to size (expanded 

acres). Fields are selected proportional to size within farm by the enumerator during an interview 

with the farm operator making this, too, a self-weighting sample. Farms and fields within farms 

may be selected more than once.
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

THE YIELD FORECASTING PROGRAM OF NASS

10

CHAPTER 3 AGRICULTURAL YIELD SURVEYS

The Agricultural Yield Survey (AY) collects farmer assessments of yield prospects monthly, 

through the growing season. A sample of farmers who reported planting the crops of interest on a 

parent survey (March or June Agricultural Surveys) are asked to predict their final yield for those 

crops. The AY fills the yield forecasting needs of most field crops in the NASS estimating 

program and provides data for all individually published State forecasts. In other words, this 

survey provides yield indications to ensure the entire program is covered. 

The AY survey uses a multivariate probability proportionate to size (MPPS) sample design, with 

list frame data used to determine a unit’s probability of selection. A more basic PPS sample 

design has their units selected by size depending on the proportion of the commodity of interest 

the operation has in comparison with other operations on the list frame. The MPPS sample 

design is similar to a traditional PPS sample design, but there are multiple commodities or frame

items used to determine a unit’s probability of selection. The MPPS design makes targeting of 

samples to the desired commodities much easier, improves the sampling efficiency over the 

traditional stratified design, and simplifies sample designs when there are multiple commodities.

In the MPPS sample design, a sample size is targeted for each commodity of interest that has 

frame data available. A unit’s resulting probability of selection is determined by the commodity 

that has the largest proportion of the total and the sample size for that commodity.

The AY samples are drawn from respondents in list strata in the March and June Agricultural 

Surveys. A small grains (SG) sample, to be used May through August, is drawn from the March 

Agricultural Survey from respondents who reported having a small grain crop of interest. A row 

crops (RC) sample, to be used August through November, is drawn from the June Agricultural 

Surveys from respondents who reported having a row crop of interest. All records to be included 

in the AY SG sample were used only in the March quarter of the Agricultural Surveys (with 

respect to June through March survey year). In a similar fashion, all records to be included in the 

AY RC sample were used only in the June quarter of the Agricultural Surveys (with respect to 

the June through March survey year). Excluded from the AY sampling are operations in the 

largest (preselect) list strata, as well as the non-overlap area tracts – farms identified through our 

area frame that were not on the list frame.

Since in some months (August in most states, for example) the AY sample includes operations 

from both samples, a composite weighting methodology was developed. Using such an approach

allows maximum use of the information obtained from AY responses. That is, information about 

SG crops that was obtained from AY RC only sample records can have that SG information used 

in AY SG survey indications. Similarly, information about RC crops that was obtained from AY 

SG only sample records can have that RC information used in AY RC survey indications. Under 

the MPPS sample design, stratification is not used at all as an underlying component. The strata 

are used, however, in computing nonresponse adjustment weights. 
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

THE YIELD FORECASTING PROGRAM OF NASS

11

Data Collection

The reference date of every AY survey is the first of the month. The data collection period must 

span the first, and States are expected to collect data as close to this reference date as reasonable.

In practice, the data collection period begins around the 25th of the previous month and ends no 

later than the 7th of the survey month. This amounts to about seven working days with 

allowances for weekends. 

Survey instruments are prepared in paper and electronic forms. Most data are collected in the 

electronic form using Computer Assisted Telephone Interviewing (CATI) techniques. Many 

States will collect some data by mail; however, the short data collection period limits this 

activity. A small number of samples are interviewed face to face due to special reporting 

arrangements or other considerations. Computer Assisted Self Interviewing (CASI) via the 

internet began with the 2006 crop year.

The complete questionnaire for AY includes acres for harvest and yield for each crop of interest.

For most crops, planted acres will also be asked in either the initial month of the survey - May 

for SG and August for RC, the first month the crop appears if it is not asked in the base month, 

or the first time an operator is interviewed. Actual survey instruments are customized for each 

month in each State. Some differences may also exist between the paper and CATI version.

Acreage responses are retained in the dataset from month to month and these items are not asked 

on later interviews. The acreage questions are printed on all paper versions of the questionnaire 

and enumerators are responsible for managing the flow of the interview and recognizing when to 

ask the acreage questions and when to skip them. The CATI software easily tracks previously 

reported data and manages the flow of the interview accordingly. The paper and CATI versions 

also include a question on whether each crop has been harvested and the reported yield is final.

Once harvested, the yields for those crops are not asked on subsequent interviews but are brought 

forward and used in subsequent month’s summaries. The AY survey has an additional ability to 

measure harvested acreage changes during the crop year due to extreme weather conditions when 

necessary. This distressed acres sub-survey estimates the current acres for harvest versus 

previously reported acres for harvest and can be targeted at specific crops and States.

The small grains are surveyed May-August and the row crops August-November. The small 

grains and row crops probability samples overlap in August. A single survey instrument is 

prepared, and respondents are asked all questions regardless of the sampling base.

States are expected to achieve a minimum response rate of 80 percent. In order to meet this 

minimum level, States are expected to conduct a telephone follow-up for operations that have not 

responded. States must also monitor response by crop to determine the amount of follow-up 

necessary to achieve 50 complete reports for major crops. 
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

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Analysis

All AY data are processed through an interactive edit program as the first step in data review.

This edit performs all within-record data (micro level data) checks. Data from paper versions are 

manually reviewed, key entered, and merged with CATI data. Any CASI data is also merged 

with the CATI data prior to editing. The edit program checks that reported data are within 

absolute limits, compares acres reported on AY and the parent survey, and compares yields 

reported by the same reporting unit in consecutive months. This ensures data review is consistent 

across States. States provide customized edit limits for their data. Most of the edit checks are also 

performed by the CATI software during the interview which allows enumerators to probe for 

additional information and correct errors when suspect values are recorded.

The next step is an across-record (macro level data) review of the raw data via the Interactive 

Data Analysis and Review Tool (iDART). Reported data for all responses are listed for each crop 

as well as data expanded by probability weights. This allows statisticians to examine data 

distributions and to identify extreme values that may overly influence the summary results. Data 

are displayed graphically by district so statisticians can also analyze yield relationships 

geographically within their State. Statisticians re-examine these values before allowing them to 

pass to the summary. Some follow-up may be necessary to validate a response. If the data are 

deemed correct, no action is taken.

iDART displays extreme differences between surveys. In May and August, AY acreage values 

are compared to acres reported on the parent survey for review. Similarly, month-to-month yield 

differences are displayed beginning in June for small grains and in September for row crops.

The output is displayed in graphical and tabular form. The graphs show the frequency 

distribution of the positive data while the tabulations show actual record level data

Summarization

The AY summary program is really two summaries combined. The first part is a probability 

summary that applies a combination of the appropriate MPPS sample weight and a nonresponse 

adjustment to produce an indication with associated measurable statistical error. The second part

is a non-probability indication which pools the complete reports from all respondents for each 

crop within an Agricultural Statistics District (ASD). These respondents’ yields are then 

reweighted based on their harvested acres and the acres in their respective ASD for that specific 

crop. This produces an indication but, because of a lack of probability sampling design, has no 

measurable error associated with it. The probability and non-probability indications are both 

sorted by ASD prior to output for comparative purposes.
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

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13

Probability Summary

The probability summary computes three types of indications:

1. Average expected yield.

2. The ratio of yields reported on consecutive AY surveys.

3. The ratio of any two acreage items from the AY, the parent survey, or both.

Average expected yield

Average expected yield is defined as the expected total production divided by the total acres 

standing for harvest. For an individual report, production is acres for harvest times expected yield 

per acre. 

The nonresponse weight is calculated using the Agricultural survey stratum each respondent is 

associated with and is based on the total number of expected respondents within the stratum 

divided by the total number of complete respondents. The k

th stratum nonresponse weight would 

be calculated as:

wnrk =

∑ wMPPSi

Nk

i=1

∑ wMPPSu

nk

i=1

where

wnrk= nonresponse weight for stratum k

Nk = total sample size for stratum k

nk = number of complete responses within stratum k

wMPPSi= MPPS weight for sample i within stratum k

wMPPSu= MPPS weight for complete responses u within stratum k

The total probability weight for the i

th individual record within stratum k would then be the 

product of the MPPS weight and the nonresponse weight:

wi = wMPPSiwnrk

where

wi = total weight for record i

wMPPSi= MPPS weight for record i

wnrk= nonresponse weight for stratum k

Production is the product of reported current month yield and harvested acreage: 
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

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14

pi = Yihi

where 

pi = production for record i

Yi = record i yield

hi = acres of harvested or to be harvested for record i

Production is calculated for each ASD using the total probability weight and production for each 

record, then summed to the State using the following formula:

PS = ∑∑ piDwiui

NiD

i=1

ND

j=1

where

PS = production for State S

ND = number of ASD in State S

NiD = total number of sampled records in ASD D

piD = production for record i in ASD D

wi = total weight for record i

ui = 1 if sample i is complete, else 0

Similarly, the total number of acres harvested or to be harvested is determined for each ASD and 

summed to the State:

HS = ∑∑ hiDwiui

NiD

i=1

ND

j=1

where

HS = acres harvested or to be harvested for State S

ND = number of ASD in State S

NiD = total number of sampled records in ASD D

hiD = acres harvested or to be harvested for record i in ASD D

wi = total weight for record i

ui = 1 if sample i is complete, else 0

The average expected yield for the State would be:

Ŷ

S =

PS

HS
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

THE YIELD FORECASTING PROGRAM OF NASS

15

where

Ŷ

S = average expected yield for State S

PS and HS were previously described

Ratio of Yields

The ratio of yields reported on consecutive AY surveys quantifies the change in the collective 

judgment of the respondents. Computations are made by converting the current and previous 

month’s sample reported yields to a sample level production value using the last reported acres 

for harvest and the total weight wi . ASD and State totals are obtained for each month and the 

ratio of current over previous provides the measure of change. The b

th complete value is1 if 

complete for current and previous month, and 0 if not complete for both months. The equation 

for State S:

RS =

∑ ∑ yiDc

hiDc

NiD

i=1 wibi

ND

j=1

∑ ∑ yiDp

hiDp

NiD

i=1 wibi

ND

j=1

where

RS = ratio of current month’s expected yield to previous month’s expected yield for

 State S

ND = number of ASD in State S

NiD = total number of sampled records in ASD D

yiDc= current expected yield for record i in ASD D

hiDc= current acres harvested or to be harvested for record i in ASD D

wi = total weight for record i

bi = 1 if sample i is complete for current and previous month, else 0

yiDp= previous expected yield for record i in ASD D

hiDp= previous acres harvested or to be harvested for record i in ASD D

Ratio of two acreage items

The ratio of any two acreage items from AY and the parent survey offers several key indicators.

Any ratio of AY reported acres to the acres reported on the parent survey provides a link 

between the AY and the parent survey. Every AY probability sample unit matches a parent 

survey response. This affords the opportunity to calculate ratios of acres reported on both 

surveys. The acres used vary between crops. For most crops ratios of harvested acres are 

computed, for a few crops planted acres are used, and a few crops have both. Acreage ratios 

provide an assessment of the presence or absence of reporting errors in the data used to 

determine the AY subsampling population. This ratio is expected to be near 1.0. Deviation from 

1.0 can indicate a reporting error and/or changes in growing conditions such as delayed planting.
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

THE YIELD FORECASTING PROGRAM OF NASS

16

In a drought year, harvested to previous harvested ratios provide an indication of increasing 

abandonment. Under these conditions, reporting errors become confounded with true change in 

the acreage level. The AY survey is not designed to provide clean measurement of current year 

acreage changes; however, it can provide limited information about current acreage changes.

The general formula for the ratio between surveys for State S is shown below. Note that the 

current AY weights apply in all instances.

AS =

∑ ∑ aiDc

NiD

i=1 wibi

ND

j=1

∑ ∑ aiDp

NiD

i=1 wibi

ND

j=1

where

AS = ratio of current month’s acreage to the parent survey acreage in State S

ND = number of ASD in State S

NiD = total number of sampled records in ASD D

aiDc= current acreage for record i in ASD D

wi = total weight for record i

bi = 1 if sample i is complete for current and previous month, else 0

aiDp= parent survey acreage for record i in ASD D

The formula for the harvested to planted acreage ratio for State S is:

HS

PS

=

∑ ∑ hiD

NiD

i=1 wibi

ND

j=1

∑ ∑ piD

NiD

i=1 wibi

ND

j=1

where

HS

PS

= ratio of acres harvested to acres planted in State S

ND = number of ASD in State S

NiD = total number of sampled records in ASD D

hiDc= acres harvested for record i in ASD D

wi = total weight for record i

bi = 1 if sample i is complete, else 0

piDp= acres planted for record i in ASD D

Although all calculations in the probability summary are performed within design stratum, the 

printed output presents the results by ASD. This facilitates the interpretive process by making it 
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

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17

easier to compare AY results to other data sources reported by ASD. Temperature, precipitation, 

and crop progress data provide additional evidence to support the AY indications to build a 

complete picture of current conditions. An additional analytical benefit is gained from the ability 

to see a geographic breakdown.

The summary program derives yields and ratios by expanding the sample level data and grouping 

the samples by ASD. Key variables are summed to obtain ASD totals and the yields and ratios 

are computed. It is important for commodity analysts to remember that even though the summary 

shows the results by ASD, the calculations performed at the sample level follow the design 

strata.

Non-Probability Summary

The non-probability portion of the summary treats the pooled dataset as a simple random sample.

The data are partitioned by ASD. Sample weights are 1.0 for all reporting units. Reported yields 

are weighted by acres for harvest when computing ASD means. ASD means and ratios are 

weighted to the State level using externally provided historical district harvested acreage 

estimates. 

The same three types of indications are calculated. The non-probability formulas similar to the 

probability at the ASD level, with design weights (wi) eliminated. State level formulas use the 

ASD level calculations and then applies external weights.

Average expected yield

Average expected yield is a weighted average of reported yields with harvest acres serving as 

weights. The yield for ASD D would be calculated as follows:

Ŷ

D =

∑ yiD

NiD

i=1

hiDki

∑ hiDki

NiD

i=1

where

Ŷ

D = expected yield for ASD D

NiD = total number of sampled records in ASD D

yiD = yield for record i in ASD D

hiD = parent survey acreage for record i in ASD D

ki = 1 if sample i is complete, else 0

Ratio of Yields

Similarly, the ratio of yields reported on consecutive AY surveys is:
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

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18

RD =

∑ yiDc

NiD

i=1

hiDki

∑ yiDp

hiDki

NiD

i=1

where

RD = ratio of current to expected yield to previous month’s expected yield for ASD D

NiD, hiD, and ki were previously described

yiDc= current yield for record i in ASD D

yiDp= previous yield for record i in ASD D

Ratio of two acreage items

The ratio of acreage items between AY and the parent survey and the harvested to planted ratio

for ASD D are derived as:

AD =

∑ aiDc

ki

NiD

i=1

∑ aiDp

ki

NiD

i=1

where

AD = ratio of current month’s acreage to the parent survey acreage in ASD D

NiD = total number of sampled records in ASD D

aiDc= current acreage for record i in ASD D

ki = 1 if sample i is complete for current and previous month, else 0

aiDp= parent survey acreage for record i in ASD D

The formula for the harvested to planted acreage ratio for ASD D is:

HD

PD

=

∑ hiD

NiD

i=1

ki

∑ piD

NiD

i=1

ki

where

HD

PD

= ratio of acres harvested to acres planted in ASD D

NiD = total number of sampled records in ASD D

hiDc= acres harvested for record i in ASD D

ki = 1 if sample i is complete, else 0

piDp= acres planted for record i in ASD D
CHAPTER 3 AGRICULTURAL YIELD SURVEYS

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19

State Level Estimates

The ASD level non-probability estimates shown above are weighted to the State level using 

external weights. These external weights are derived from historical district harvested acreage 

estimates. Let ED denote any ASD level non-probability estimate shown above. The State S level 

estimate, Ew is:

Ew =

∑ wDED

ND

i=1

∑ wD

ND

i=1

where

Ew = weighted State S estimate ED

ND = total number of ASD in State S

wD = external weight for ASD D

ED = ASD D level non-probability estimate 

Survey Bias

Note that AY data are the respondents’ expected yield. The crop may not be mature and ready 

for harvest for another several weeks after the respondent has been contacted. Experience has 

shown these responses tend to be conservative (biased down). Under drought conditions, this 

bias gets much larger as respondents’ perceptions of a crop are influenced by current weather 

conditions. Therefore, the interpretation phase of the review must recognize this tendency and 

factor it into the final deliberations.
CHAPTER 4 GENERAL YIELD FORECASTING PROCEDURES

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20

CHAPTER 4 OBJECTIVE YIELD SURVEY AND 

GENERAL YIELD FORECASTING PROCEDURES

This chapter presents basic sampling, data collection, and mathematical methods commonly 

employed to forecast the yield and production of any economically valuable agricultural crop. 

The sampling review will emphasize the reliance objective yield survey forecasts have to a welldefined population and the traditional sampling methods employed in objective yield studies. 

Data collection will focus on the plant characteristics and measures commonly collected for 

objective yield programs. Finally, the mathematical methods review will center on 

mathematical/statistical estimation principles common to forecasting any crop’s yield and 

production. 

Sampling

NASS currently expends federal funds to forecast crop yields in 24 of the lower 48 states. NASS 

also supports yield forecasting for fruits and nuts in Florida and California. For most crops, yield 

forecasting begins with partitioning each states’ land area into uniquely identifiable pieces called 

segments. The resulting collection of segments is a complete population of all land area in each

state and is referred to as an “Area Frame”. This painstaking segmentation of land area into 

uniquely identifiable segments makes possible the selection of a probability-based sample of 

crop acres for objective yield (OY) field enumeration. 

The most important statistical result of area frame construction is that any crop acre can be 

assigned a known inclusion probability for OY studies. For annual crops like corn, NASS’s 

Area Frame explicitly identifies and separates each corn acre from every other possible 

utilization and makes probability calculations possible. For perennial crops like Florida citrus, a 

Citrus Area Frame allows separation of citrus acres from other possible utilizations allowing 

probabilities of selection to be established. The effort required to identify and separate each type 

of utilization from another is a common feature of agricultural area frames. In return for the 

effort, statistically defensible estimates of crop yields are obtainable. 

Accurate inferences from probability-based surveys require the construction of a sampling 

population and, in addition, a method to select a representative sample from that population.

Probability proportional to size (PPS) is the most common statistical method employed by NASS 

for selecting crop acres to be included in objective yield studies. Since a given crop acre is most 

often embedded within an individual field composed of multiple acres, PPS sampling ensures 

that a proper accounting is made for the size of field. In agriculture a field is one, continuous 

acreage of land devoted to the same use. Since fields are the unit of selection for objective yield 

studies and because fields vary in acreage, PPS sampling is ideally suited to selecting a sample 

that perfectly reflects the population characteristics of the particular crop. For example, 

employing PPS sampling implies a crop field accounting for twice the percentage of total state 

corn acres relative to a neighboring corn field, will also carry twice the probability of selection as 
CHAPTER 4 GENERAL YIELD FORECASTING PROCEDURES

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21

the neighbor. The representative acre selected from a sampled field is finally accomplished with 

simple random sampling. Since a selected acre is too large for complete enumeration, a selected 

sample will be enumerated and expanded up to the one-acre level.

Data Collection

A full OY survey collects data at different times during the growing season. The following 

paragraphs describe the data collected and the how the data are used in the forecasting and 

estimating process.

During the initial OY survey, the operator is asked to verify the acreage reported in the parent 

survey. This is accomplished on a field-by-field basis. Changes may be due to recording or 

reporting errors in the parent survey, failure to fulfill planting intentions, or switching to other 

utilizations. Other data concerning the crop, for example planting date and use of genetically 

modified seed, are collected at this time. The final question asks for permission to enter the 

sample field and make counts and measurements through the growing season. 

The initial visit to the sampled acre involves precise selection of plants from which fruit counts,

measurements, and maturity determinations are to be made for the remainder of the growing 

season. Each sample is identical in its dimensions according to crop. Extra precautions during 

sample layouts ensure the exact same plants are revisited in subsequent months. Plant counts and 

a variety of plant characteristics collected from these samples will be used to forecast gross yield 

and the components of yield such as number of fruit and weight per fruit. The final visit obtains 

all harvestable yield, which will determine final gross yield. The counts and measurements from 

all visits are added to a five-year historical database which will be used to forecast gross yields 

the following season.

After the farmer has harvested the sample field, postharvest gleaning data are collected. All unharvested fruit and loose grains are gleaned from specially prepared plots that are separate from 

the original sample plot. The calculations from these plots will be used as a deduction from gross 

yield which provides a net yield number. Before gleanings data become available, a five-year 

average harvest loss is assumed for the calculation of net yield.

Models

Linear statistical models are used extensively in forecasting and estimating crop yields and 

production. Other methods employed are variable plots, scattergrams, and tables. The basic 

agronomic model used to conceptualize final net yield per acre is:

Y = (F * W)-L
CHAPTER 4 GENERAL YIELD FORECASTING PROCEDURES

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22

where

Y = the population net yield per acre,

F = the population average number of fruit per acre,

W = the population average net fruit weight per unit, in industry standard moisture, and

L = the population average harvest loss per acre. 

This model can be estimated as follows:

First, forecast the average number of fruit per sample as

fi = β0 + β1xi + εi

Where fiis the estimate for average number of fruit for sample i, β0 and β1 are historic 

coefficients estimated by ordinary least squares from five years of data, xiis some characteristic 

such as plant count for sample i, and εiis an error term exhibiting classical properties. Each fiis 

expanded to the acre level after the forecast is made.

Secondly, forecast the average weight of fruit per unit as:

wi = β2 + β3zi + εi

Where wiis the estimate for average weight of fruit per unit, e.g., weight of corn per ear, weight 

of soybeans per pod, weight of cotton per boll, weight of wheat per head, etc., β2 and β3 are 

historic coefficients estimated by ordinary least squares from five years of data, ziis some 

characteristic such as average fruit size from sample i, and εiis an error term exhibiting classical 

properties. Each wiis converted to industry standards for moisture when required.

Third, forecast the average yield loss per sample as:

L̅ =

1

NL

∑Li

NL

i

Where Li is the historic sample harvest loss in the i

th sample expanded to one acre, then summed 

from the first sample to the NL sample and divided by NL which gives L̅, the average historic loss 

per acre. After the current years’ final harvest, each sample’s harvest loss reflects this years’ loss 

statistics.

Finally, substitute each component back into the agronomic model:
CHAPTER 4 GENERAL YIELD FORECASTING PROCEDURES

THE YIELD FORECASTING PROGRAM OF NASS

23

Equation 1. y̅ =

1

N

∑(fi ∗ wi

N

i

– L̅)

Where y̅ is now an estimate of the population average net yield per acre in industry standard 

moisture and volume.

The models used to forecast fruit count and fruit weight above may also be independently 

evaluated from the general agronomic model as in: 

Equation 2. f̅=

1

N

∑fi

N

i

Where f̅is now an estimate of the population average number of fruit per acre, or:

Equation 3. w̅ =

1

N

∑wi

N

i

Where w̅ is now an estimate of the population average fruit weight per unit in industry standard 

moisture.

Component forecasts, represented by equations 2 and 3, are evaluated with statistical plots, 

charts, and scatter grams to assist statisticians forecasting yields. Analysts will investigate

component fruit counts and weights relative to the current years growing conditions and compare 

to previous years’ conditions. An in-depth examination is made relative to potential impacts of 

outliers on component forecast and in turn on net yield forecasts. In addition to component 

forecasting, other more esoteric relationships are examined during the course of yield 

forecasting. 

Regressed to Board Indications

Time series models are also estimated for each aggregate using the expression: 

Yt = β4 + β5y̅t + εt

Where Yt, is the known population final net yield per acre in time period t, β4, and β5 are 

coefficients to be estimated using fifteen years of data, y̅tis the average net yield aggregate from 

Equation 1 for time period t , and εtis an error term exhibiting classical properties. Individual 

years’ that have absolute studentized deleted residuals (see Neter, Wasserman, and Kutner [2], 

page 406) greater than three are not used for estimating β4 and β5. Similarly, other models are 
CHAPTER 4 GENERAL YIELD FORECASTING PROCEDURES

THE YIELD FORECASTING PROGRAM OF NASS

24

estimated, such as:

Ft = β6 + β7f̅

t + εt

Where Ft, is the known population final fruit count per acre in time period t, β6, and β7 are 

historic coefficients to be estimated from fifteen years of data, f̅

t

is the aggregate average 

number of fruit per acre from Equation 2 for time period t , and εtis an error term exhibiting 

classical properties.

Strengths and Weaknesses of Each Model

The strength of the sample level models is that each model is estimated at every level of 

maturity, for example the sample level model estimating fruit count per acre, as given above 

was:

fi = β0 + β1xi + εi

which is estimated for each crop maturity classification. For example, corn has six forecasting 

classes, thus up to six equations are estimated for every month and geographic area represented 

in the survey. A similar set of equations are estimated for weight of fruit per unit by maturity 

class. If xi is one plant characteristic used to forecast fruit count per acre, but ri is an alternative 

plant characteristic, which can also predict fruit count per acre, the process repeats. This 

approach to estimation allows for a high degree of complexity. The weaknesses of sample level 

models are that plant measurements are very sensitive in nature and require extra caution in their 

collection and the data typically exhibit large variation within and across years. 

A statistical benefit of aggregate level models like Equations 1, 2, and 3 is the reduction in mean 

variation of net yield, or fruit count, or fruit weight as sample sizes increases across all maturity 

classes. Additionally, aggregated survey means are well correlated with general changes in 

agricultural technology across time. Disaggregated sample level models cannot capture 

technological change from relatively short five-year time periods, limited geographic area, and 

single maturity classifications. Another advantage for aggregate models is that their dependent 

variables have very small measurement error due to end of year administrative data. A noted

weakness of aggregated models is that maturity levels across many years are never equal as of a 

date certain on the calendar. By their nature, aggregated models also have few degrees of 

freedom. 

Acreage Indications

Acreage adjustment ratios are another byproduct of objective yield surveys. Data collected in the 

initial interview may be compared to data obtained in the parent survey. Acreage adjustments are 

not the main purpose of OY surveys and thus are not designed for great precision but to detect 
CHAPTER 4 GENERAL YIELD FORECASTING PROCEDURES

THE YIELD FORECASTING PROGRAM OF NASS

25

gross changes in acreage.

There are three acreage adjustment ratios:

1. The R1 ratio is a harvest intentions ratio. For crops sampled from the area frame, it is the 

ratio of total acres intended for harvest in the tract to total acres planted in the tract. 

Acres intended for harvest are reported on the initial OY interview and acres planted are 

reported on the base survey. 

2. For cotton, the R2 is the ratio of planted acres to the planted acreage from the JAS. Thus, 

the R2 measures the change in planting intentions for cotton since the JAS.

3. The abandonment ratio is used each month to adjust for samples destroyed or abandoned, 

that is, "lost" samples. The numerator of the ratio equals the total number of lost 

samples, and the denominator is the total number of samples, including lost samples. An 

active sample is where harvest has occurred or is expected to occur.

Model Based Yield Indication

The Agricultural Statistics Board (ASB) examines each indication to decide the best 

forecast in any given month. One such indication introduced in 2015 is a model-based 

yield indication that combines the farmer reported survey, the objective yield survey, and 

a linear covariate model with crop condition, weather data, and trend as predictor 

variables. This additional indication has proved to be a valuable piece of information 

when forecasting crop yields. The ASB’s procedures for selecting the official forecast has 

not changed; however, this new indication provides additional insight in considering the 

official forecast for any given month. Currently, winter wheat, corn, soybeans, and cotton 

have this model-based yield indication. There are no plans to introduce any other crops.

Three components are used to generate this indication: farmer reported survey, objective 

yield survey, and a linear regression model using crop condition, weather data, and trend 

as predictor variables. The linear regression will be hitherto referred as the covariate 

model. The farmer reported survey and the objective yield survey are adjusted for bias for 

each state and for each month. In most cases, the farmer reported survey is adjusted 

upward while the objective yield survey is adjusted downward. This bias is an average 

bias comparing the final ASB yield to those respective indications for that month.

The covariate model has four predictor variables that are regressed to the final ASB yield. 

The simplest of these is a trend variable. Because crop yields have shown a strong linear 

trend upward, this trend variable is simply the forecasting year minus a constant for easy 

calculation. Monthly average temperature and precipitation observed in the prior month 
CHAPTER 4 GENERAL YIELD FORECASTING PROCEDURES

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26

are also used as predictors. For corn, only July weather data are used for this covariate 

model because July is the most crucial month for corn development. For soybeans, July 

weather data are used for the August forecast whereas August weather data are used for 

the September and later forecasts. For wheat, the weather data used are specific to the 

state because weather across the wheat speculative region is quite different. The final 

predictor variable in this model is the crop condition measures from the NASS weekly 

Crop Condition report. For corn, only the percentage of good to excellent corn in week 30 

is used for all forecasting months. For soybeans, week 34 is used for each month. Wheat 

varies by state. The following table shows a timeline for updating the covariate model for 

wheat.

May Covariates June Covariates July Covariates August Covariates

State/

FIPS

Week 

#

Weather 

Month

Week 

#

Weather 

Month

Week 

#

Weather 

Month

Week 

#

Weather 

Month

CO 8 15 April 21 May 21 May 21 May

IL 17 15 April 19 May 19 May 19 May

KS 20 15 April 19 May 19 May 19 May

MO 29 15 April 19 May 19 May 19 May

MT 30 15 April 19 May 24 June 24 June

NE 31 15 April 21 May 21 May 21 May

OH 39 15 April 21 May 21 May 21 May

OK 40 15 April 17 April 17 April 17 April

TX 48 15 April 17 April 17 April 17 April

WA 53 15 April 22 May 22 May 22 May

A model is also calculated at the speculative region level. The covariate component is 

simply a weighted average of the state level covariates with weights being the harvested 

acreage. The survey components are directly inputted from the summaries of those 

respective surveys which generate a speculative regional yield. Because the speculative 

region has less variability, each state’s model-based indication must be adjusted to match 

the speculative region as a whole. 

Given all three indications (the bias adjusted farmer reported survey, the bias adjusted 

objective yield survey, and the covariate model), weights are then assigned to each 

indication to calculate a single model-based yield indication. These weights are 

determined by how well each indication does at predicting the final ASB yield. The 

weights are determined in proportion to the inverse of the variance for each indication 

according to the formula below:
CHAPTER 4 GENERAL YIELD FORECASTING PROCEDURES

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27

wk =

1

Vk

⁄

1

VOY

⁄ + 1

VAY

⁄ + 1

VCOVAR

⁄

Where k in {OY, AY, COVAR}.

Generally, the weights for the covariates and farmer reported survey are the greatest early 

in the forecasting season. As the season progresses, more weight is assigned to the farmer 

reported survey and the objective yield survey as less weight is attributed to the 

covariates. The covariate model all but drops out in the last two months of the season as 

more weight is given to each of the two survey indications.

For more information on this indication please refer to the paper “A Bayesian Hierarchical 

Model for Combining Several Crop Yield Indications” by Cruze (2016).

Remotely Sensed Empirical Model Indication

The latest indication considered by the ASB, introduced in 2019, is a within-season, remotely 

sensed-based corn and soybean yield estimation. This indication is made available to the ASB 

from August through October and uses a linear regression model for prediction as a function of 

the Normalized Difference Vegetation Index (NDVI) values accumulated over the growing 

season. The NDVI measurements come from NASA’s Moderate Resolution Imaging 

Spectroradiometer (MODIS) which provides a landscape-level snapshot of vegetation conditions 

every eight days. The imagery is refined further by constraining it to crop-specific areas via an 

ancillary bitmask image derived from the NASS Cropland Data Layer. Ultimately, the NDVI 

data are averaged to the state or regional area of interest annually and related to the NASS 

historically published yields going back to 2002, the start of the MODIS era, to build the 

empirical model. The image handling is currently performed through the USDA supported 

NASA Global Agricultural Monitoring website and statistical aspects undertaken within NASS.
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

THE YIELD FORECASTING PROGRAM OF NASS

28

CHAPTER 5 CORN OBJECTIVE YIELD METHODS

This chapter presents basic sampling, data collection, and mathematical methods utilized to 

estimate U.S. corn yield and production. The sampling review will emphasize NASS’s unique 

Area Frame and its suitability for sample selections intended to measure U.S. corn yields. Data 

collection will focus on the variety of data collected and how data collection changes as corn 

crop maturity changes. The mathematical methods review will center on mathematical/statistical 

estimation of final corn yields utilizing measurable plant characteristics observed at specific 

points during the growing season. The end results of careful sampling, data collection, and 

mathematical methods are numeric indications suitable to establishment, and/or revision, of U.S. 

corn acreage, yield, and production.

Sample Design

Corn Objective Yield (COY) surveys are conducted in Illinois, Indiana, Iowa, Kansas, 

Minnesota, Missouri, Nebraska, Ohio, South Dakota, and Wisconsin. On average, over the last 

three years, these ten states produced more than 80 percent of the U.S. corn crop. As described 

in Chapter 2, NASS partitions each of these states’ land area into approximately one square mile 

pieces and calls the pieces segments. The resulting collection of segments is referred to as the 

“Area Frame”. This painstaking segmentation of land area into uniquely identifiable segments 

makes possible the selection of a probability-based sample of U.S. corn acres. 

Probability based surveys require the explicit identification and separation of all elements 

contained in a population of interest. For yield surveys like COY, the most important result of 

constructing a population of corn acres is that any acre of corn, in a given state, can be assigned a 

known probability of selection. This result allows statistical samples to be extracted, population 

parameters to be estimated, hypotheses to be tested, and inferences to be made. NASS’s Area 

Frame is the vehicle that transports us from a very large population of U.S. corn acres to a 

representative sample of U.S. corn acres. The sample is both statistically defensible and 

economically feasible to enumerate. The procedure for identifying every U.S. corn acre is to 

first, select a subsample of Area Frame segments, and secondly, to account for all agricultural 

activity occurring within those segments. Each selected segment will have all its acres inspected 

by and accounted for by professional enumerators with assistance from the owner/operator. In 

this manner, a new listing of corn acres is constructed each year. This listing is the COY sample 

population. No other purveyor of U.S. corn estimates can construct such a sample population. 

Accurate inferences from a probability-based survey require the construction of a sampling 

population and, in addition, a means to select a representative sample from that population. The 

statistical method used to select corn acres to be included in COY is probability proportional to 

size (PPS). In statistics, this method ensures a representative sample is selected when sample 

elements vary in their size. A simple explanation should be given as to how sample elements in 

the corn acres population can differ in size. During constructing of the corn acres sample 
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

THE YIELD FORECASTING PROGRAM OF NASS

29

population, the explicit identification and separation of corn acres, from all other acres, is made 

according to fields. In agriculture a field is one, continuous acreage of land devoted to the same 

use. Therefore, the sample elements in the corn population are fields. Since fields of corn vary in 

acreage, the sample selection method of PPS ensures the probability of selection is adjusted for 

field size. For example, employing PPS sampling, a corn field that is twice the size of its 

neighbor will also be twice as likely to be included in the sample. After the determination of 

which fields are included in the sample, the representative acre is selected with simple random 

sampling designed to give every acre in the selected field, an equal chance of selection. Since a 

selected acre is too large for complete enumeration, a selected sample will be enumerated and 

expanded up to the one-acre level.

In mid-July of each year, professional statisticians in the ten COY states train field enumerators 

to properly identify and prepare selected samples for data collection. Generally, enumerators will 

have many years of experience in COY data collection and are well qualified to conduct their 

assignments. Practical field training is also available through relationships developed among 

individual enumerators and their supervisors. Overall, the preparation for data collection is 

rigorous and includes quality control processes that continue through the corn growing season. In 

late July, field enumerators will begin visiting and enumerating samples and will continue 

personal visits at monthly intervals throughout the season until final harvest. 

Each sample consists of two units (or plots) to be utilized in forecasting final net yield per acre. 

Each unit consists of two parallel 15-foot sections of row. During each visit, enumerators count 

or measure each required plant characteristic, the required characteristics being determined 

according to the units’ maturity level. For example, at early maturities enumerators will count 

plants and measure row spacing. At later maturities, ear lengths, diameters, and weights are 

measured and recorded. After each data collection period, a forecast of each unit’s final net yield 

is constructed. Essentially forecasts of corn yields depend on two items: One, the current year’s 

measurable plant characteristics and, two, the historic relationship between plant characteristics 

measured in the past, at the same level of maturity, and final plant characteristics that result in 

harvestable yield. Each item is needed to forecast a samples final net yield per acre. In cases 

where one or the other of the two required items is missing, a five-year average of the final plant 

characteristic is substituted. During some early forecasts there may be no plant characteristic that 

NASS measures that can be related the final plant characteristic. Ear weight is the prime 

example. In these cases, historic averages are used to forecast final net yield.

Data Collected

Field enumerators count and measure several items within or near the units. The size of the unit 

(square feet), the number of ears, grain weight, and harvest loss. The following lists the data 

items collected and what it is used to measure.

Data items used to measure the size of each unit:
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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Distance between two rows (one row middle)

Distance between five rows (four row middles)

Data items used to forecast or estimate the number of ears:

Number of stalks in each row

Number of stalks with ears or silked ear shoots in each row

Number of ears and silked ear shoots in each row

Number of ears with kernel formation

Data items used to forecast or estimate grain weight:

Kernel row length from the first five ears beyond the unit in a specified row 

Ear diameter at a point one inch from the butt on the same five ears beyond the unit

Weight of the first five ears in the dent stage (when the sample reaches this maturity)

Weight of shelled grain from the five dent stage ears

Moisture content of grain from the five dent stage ears

Field weight of all ears in the two units at maturity (crop cutting)

Lab weight of sample of four mature ears harvested

Weight of grain shelled from the four mature ears

Moisture content of shelled grain from the four mature ears

Data items used to estimate harvest loss:

Distance between two rows (one row middle)

Distance between five rows (four row middles)

Grain weight of ears between Row 1 and Row 3

Grain weight of loose kernels between Row 1 and Row 2

Maturity Categories

At each visit, the enumerator makes maturity assessments within the units and a maturity 

category is established for the sample. If necessary, ears outside the unit may be husked to make 

this determination. Forecast equations are derived using data collected during the previous 5-

years for each maturity in each month. The maturity definitions used by the enumerators are:

Maturity Definition

1 - no ear shoots No ears or ear shoots are present.

2 - pre-blister Ear shoots are present with some silks showing. Most silks are yellow to 

white in color. Spikelets contain little or no liquid.
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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3 - blister Most silks protruding from husks are beginning to turn brown. Spikelets 

have swollen and contain clear to white liquid.

4 - milk Silks protruding from husks have turned brown and dry. Plant or shuck is 

green. Ears are erect. Kernels contain a milk-like substance and show 

little or no denting.

5 - dough Shucks starting to take on a light rust color. Ears beginning to lean away 

from stalks. About half the kernels are dented and contain a milk or 

dough-like substance. Maturity line has not moved halfway to the cob on 

a majority of the kernels.

6 - dent Shucks are dry but not opening up. Nearly all kernels are dented. 

Maturity line on kernels has not reached the cob.

7 - mature Shucks are dry and opening up. Ears are hanging down from the stalk. 

Maturity line on kernels has reached the cob.

Analysis of Raw Data

In the following sections estimation at the sample level is discussed. All sample level regression 

equations are derived from the previous 5 years' survey data using multiple regression 

techniques. Certain influential data points (i.e., "outliers") are excluded from the dataset prior to 

deriving the coefficients. These influential data points are identified using a "deleted residual" 

analysis or the "Cook's D" statistic (Belsley, Kuh, and Welsch, [4]). There is usually very little 

change in the regression equations from year-to-year because roughly 80 percent of the data for 

each class were used in the analysis the previous year. Classes that do change significantly from 

one year to the next are usually those with very few observations. If a class has little data and a 

plausible forecast equation cannot be derived, the equation from the previous year is used.

Forecasting and Estimating Number of Ears for Sample Fields

The mathematical expression for calculating the number of ears per acre from a sample plot is 

straightforward, i.e., a specific count of ears per 60 linear feet and a measurement of average row 

spacing for the sample results in a unique value of ears per acre. The formula for calculating the 

number of ears per acre is:

ears per acre = (ears in sample plots) (43,560)

(60) (average row space)
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Where 43,560 is the number of square feet in an acre, 60 is the total length of rows in two units, 

and average row space is the sum of the two 4-row space measurements divided by 8.

In the equation above, forecasts for ears per acre are dependent on the number of ears in the 

sample plots. Should the ears in a sample plot not be observable due to immaturity, then a 

forecast of the final number of ears before farmer harvest is required. NASS bases this prediction 

on the historic relationship between observable plant characteristics and the eventual outcome for 

number of ears. NASS carefully considers which plant characteristics are used to make ear count 

forecasts based on the historic performance of the particular plant characteristic in question. 

When samples are in maturities categories 1-4, two models are used to forecast the number of 

ears in each sample. The first model uses five years of historic data to estimate the relationship 

between final ears per sample and the historic stalk count from the same month. 

yi = β0 + β1xi + εi

where xi is the number of stalks in sample i, yi is the final number of ears for sample i, and εi are 

random departures from the relationship. The coefficients β0 and β1 are estimated by ordinary 

least squares from data collected during the previous five years. This model produces historic 

results with R2’s typically in the 80 to 90 percent range for all states. The second model uses five 

years of historic data to estimate the relationship between final ears per sample and the ratio of 

stalks with ears to total stalk counts per sample. This model may be represented by,

yi = β2 + β3zi + εi

Where zi is the number of stalks with ears or silked ear shoots (maturity category 1-4) divided by 

the total number of stalks in the sample, yi is the final ratio, measured at or before maturity 

category 4, of stalks with ears to total stalks and εi are random departures from the relationship. 

The coefficients β2 and β3 are estimated by ordinary least squares and a forecasted number of 

ears per sample is formulated by dividing the current count of stalks with ears by the predicted 

value of the ratio. This model produces R2’s that are much lower than the simple stalks model 

and, in addition, are generally variable across states and within states across maturity categories. 

The forecast models for ears per sample are a weighted combination of the two regressions.

Model 1: yi = β0 + β1xi + εi

Model 2: yi = β2 + β3zi + εi
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A composite is constructed for forecasting ears per sample as follows:

Ŷ

i =

R1

2

(ŷi1) + R2

2

(ŷi2)

R1

2 + R22

where, Ŷ

i

is the weighted forecast of ears per sample from Model 1 and 2, and R1

2 and R22

 are 

the multiple correlation coefficients for Model 1 and 2 respectively. Typically, the performance 

of Model 1 completely dominates Model 2.

Samples classified in dough stage or higher use the actual count of ears with evidence of kernel 

formation as the forecasted number of ears in the sample. Also, for the final visit to the sample, 

the actual ear count is used, regardless of the maturity category.

Forecasting and Estimating Grain Weight Per Ear for Sample Fields

Corn is no exception to the general rule of objective yield surveying, i.e., successfully 

forecasting fruit weight is more difficult than forecasting fruit count. Therefore, it should be no 

surprise that over the course of time and program development, one model has been successfully 

employed for ear count predictions whereas multiple models are utilized forecast final weight per 

ear. The sensitivity of final net yield to grain weight per ear necessitates a careful consideration 

of all plant characteristic which may contribute to successfully forecasting final grain weight per 

ear. 

When samples are in maturity categories 1 and 2 the grain weight per ear will be forecasted to 

the final utilizing the 5-year historical average grain weight per ear. For the September 1 survey, 

this average is computed from all samples with final lab grain weights during the last 5-years. 

For the October 1 and later surveys, this average is computed using only samples that were in 

maturity category 1 or 2 (no ear shoots and pre-blister stage) for October 1 or later surveys from 

the last 5-years. The October 1 historic average is rarely used.

Corn samples in maturity categories 3 through 6 use historic regression models to forecast final 

grain weight per ear. There are currently three models calculated that are based on the following 

plant characteristics: kernel row length, ear volume, and maturity code 6 harvested ears. Kernel 

row length measurements are taken just beyond the 15-foot count section of each unit. Kernel 

row length measures the average length of five cobs from one inch above the butt to the end of 

the cob. These measurements, collected over a series of years, can be utilized to forecast future 

sample grain weights. Ear volume measures are calculated by combining kernel row length 

measures with cob diameter measurements. These too are historically related to final grain 

weights. Lastly, maturity code 6 harvested ears are collected just beyond the 15-foot count 
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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34

section and are then laboratory weighed and adjusted to 15.5 percent moisture. These MC6 

weights are also related to final grain weights by means of regression.

In general, the form of the three models discussed above is:

wti = β0 + β1xi + εi

Where xi is the average kernel row length for sample i or the computed volume measurement of 

the ears in sample i, or the MC6 grain weight for sample i. wti is the final grain weight for sample 

i and εiis a random departure from the relationship. The coefficients β0 and β1 are estimated by 

ordinary least squares from the previous five years of data.

Parameter estimates (β0 and β1) are calculated for each maturity category in each month for each 

State. Each of these models exhibits significant variation but, in general, each improves in 

predictive ability over the course of a growing season. R2‘s are in the 20’s, 30’s and 40’s for ear 

volume and slightly less for kernel row length. The R2for MC6 weights does show the expected 

improvement given the later maturity, however, by statistician standards, has considerable 

remaining variation. Ultimately, it is difficult to make both an early and confident prediction of 

final grain weights per ear utilizing kernel row length, ear volume, and MC6 weights. 

A sample is enumerator harvested when three or more ears of the first ears beyond a unit are 

mature or the farmer intends to harvest the sample within three days. If a final harvest sample is 

missed by an enumerator, its most recent forecast is perpetuated. The average field weight per 

ear is an average of the combined ear weight (cob and kernels) from all ears harvested in sample 

i:

Field Wt = [

Total wt of ears

count of ears ]

A conversion must be made to adjust this field weight to a shelled ear weight at 15.5 percent 

moisture. The conversion factor is calculated in one of two ways:

1. When lab data are available, the adjusted weight per ear is calculated by:

Wt

Ear = Field Wt ∗ [

ws

w4 − b

] ∗ [

1 − mi

100

. 845 ]
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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35

where, for sample i, ws is the weight of all grain shelled from four ears, w4 is the weight of four 

ears (including cob), plastic bags and rubber bands (as mailed), b is the weight of plastic bags 

and rubber bands, mi is the moisture content of the shelled grain, and .845 = (100 - 15.5/100) 

adjusts to standard moisture.

2. If lab data are not available, a 5-year historical average shelling fraction and moisture 

adjustment is applied to the average field weight.

Independent Variables used in Sample Level Forecasts and Estimates

The following table summarizes the data items used to estimate or forecast the number of ears, 

weight per ear and harvest loss for each of the 7 maturities:

Maturity Number of Ears Weight per Ear Harvest Loss

1 No ears or ear shoots Stalks 5-year average 5-year average

2 Pre-blister Stalks 5-year average 5-year average

3 Blister Stalks Kernel row length/

Volume

5-year average

4 Milk Stalks Kernel row length/

Volume

5-year average

5 Dough Ears with kernels Kernel row length/

Volume

5-year average

6 Dent Ears with kernels Kernel row length

Grain weight per ear

5-year average

7 Mature Ears with kernels Grain weight per ear Realized Harvest Loss

 Final Ears with kernels Grain weight per ear Realized Harvest loss
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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Forecasting Yield for Sample Fields

The gross yield for sample i is calculated by:

GŶi =

ŷi ∗ wt ̂i

56

Where ŷiis the forecasted or final estimate for ears per acre, wt ̂iis the forecasted or final 

average grain weight per ear in pounds at 15.5 percent moisture, and 56 converts the numerator 

to bushel per acre

State Average Forecasts and Estimates

The sample level gross yield forecasts are averaged to the State level. Since the sample is selfweighting, the simple mean of the sample forecasts is an unbiased estimate of the State gross 

yield. Therefore, gross yield for a State is given as G̅,

G̅=

1

NG

∑Gi

NG

i

where

G̅ = State mean gross yield

NG = number of samples with gross yield forecasts (estimates)

Gi = gross yield for sample i

The standard error of G̅is:

SG̅= √∑

(Gi − G̅)

2

NG(NG − 1)

NG

i

Simple means are also appropriate for Stalks per Acre, Ears per Acre, and Harvest Loss. No 

weighting is required when calculating State level averages for these items:

State Average Stalks per Acre =  (Sample Field Stalks per Acre) / NG

State Average Ears per Acre =  (Sample Field Ears per Acre) / NG
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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State Average Harvest Loss =  (Sample Field Harvest Loss) / NL

The State average grain weight per ear is calculated using a weighted mean. The weighting 

variable is the sample field Ears per Acre.

State Average Grain Wt per Ear =  (sample field grain weight * sample field ears per acre)

 /  (sample field ears per acre)

Harvest Loss

Harvest loss data are collected from every fourth sample. If less than 10 samples have current 

harvest loss data then harvest loss, L, is the 5-year average harvest loss, expressed as a 

percentage of gross yield. This 5-year average is used during the early months of the forecast 

season. 

AVG. PERCENT LOSS = 100* (1/5) *  (Avg Loss in bu. / Avg Gross Yield in bu.)

The percentage loss is applied to the current year gross yield indication to calculate an indicated 

loss per acre.

INDICATED HARVEST LOSS = AVG. PERCENT LOSS * INDICATED GROSS YIELD

Later in the season, when 10 or more samples have harvest loss data, sample harvest loss 

calculations are made with the following expression:

Li =

(we + 2wg) (1 − (

mi

100)) ∗ 43,560

(R̅

i

)(453.6)(60)(56)(.845)

Where Liis the forecasted harvest loss of sample i, we is the weight of ears between Row 1 and 

Row 3 for sample i, wg is the weight of grain between Row 1 and Row 2 for sample i, R̅

i

is the 

average row spacing, sample i, (sum of the two 4-row space measurements divided by 8), mi is 

the moisture content of the shelled grain for sample i, and the following conversion factors:

453.6= conversion of grams to pounds

43,560 = square feet per acre

60 = row feet in 2 units

56 = pounds of corn in a bushel

.845 = converts to standard moisture (15.5) percent.
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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State average harvest loss is calculated using data from the individual samples as:

L̅ =

1

NL

∑Li

NL

i

Where Li is the harvest loss in sample i and NL is the number of harvest loss samples and 

standard error of harvest loss can be understood as:

SL̅ = √∑

(Li − L̅)

2

NL(NL − 1)

NL

i

State Level Net Yield

Net yield for the State is computed by subtracting the estimated State level harvest loss from the 

mean of all sample level gross yield forecasts and estimates. Thus, estimated average net yield 

is:

Y̅ = G̅− L̅

Where G ̄ and L ̄ are State level gross yield and state level harvest loss

The standard error of the estimate is:

SY̅ = √SG̅

2 + SL̅

2 −

2

NG

COV(G, L)

Where SL̅ and SG̅were defined previously, and

COV (G,L) = 

N

L



1

(Gi- G )(Li- L )

NL-1
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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39

When less than 10 Form E's are completed, and historical average loss is used, the standard error 

is:

SY̅ = SG̅

Production for the State

Production (P) for the State is the product of estimated State level net yield and acres to be 

harvested for grain:

P = (Aharv) ( Y̅),

with standard error:

SP = √(Aharv

2

)(SY̅

2

) + (Y̅2)(SAharv

2

) + (SY̅

2

)(SAharv

2

)

Gross Yield for Samples with Incomplete Data

Gross yield is forecasted from the current month's survey data. In some cases, current data are 

unavailable and data from a previous month may be used to forecast gross yield, or no gross 

yield is forecasted for the sample. The specific cases are discussed below.

Refusals

If the farmer refuses permission to enter the field, the sample is lost for the season. In this case 

the yield for this sample is left missing. Consequently, the refused sample contributes nothing to 

the State level average yield. Stated another way, the assumption is made that if the sample had 

not been a refusal, its gross yield would have been equal to the State's average gross yield.

Inaccessible Samples

Occasionally, some samples are inaccessible due to scheduling or field conditions. If data from a 

previous visit are available, the previous forecast is carried forward. Otherwise, the sample is 

excluded from gross yield calculations. The sample must still be intended for harvest as grain.

Early Farmer Harvest
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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If a sample is harvested by the farmer before current data can be collected, the previous month's 

predicted yield is brought forward. 

Lost, Abandoned, Destroyed Samples

If a sample is lost, abandoned, destroyed, and so forth, no gross yield is computed for the sample. 

The sample contributes nothing to the sample-level yield indication.

Removing Bias from State Level Calculations

Forecasts of state or regional yields are inherently subject to differ from the final, 

administratively-determined, yield. The difference is due to weather and crop conditions yet to 

be encountered at the time the forecast is made, the difference between weather and crop 

conditions in the current year and the historic weather and crop conditions utilized to predict 

current yields, and systematic non-sampling errors which contribute to forecast error. NASS 

makes every attempt to minimize the impact of these three sources of error by means of 

administratively determine final values. These final, sometimes referred to as official, values are 

used as dependent variables to estimate an ordinary least squares equation with the averages 

calculated from objective yield samples as the independent variable. For example, each state will 

have an administratively-determined, official corn yield for all previous years. To forecast the 

official corn yield for the current year, NASS regresses the objectively determined State level 

average corn yields from previous years to the corresponding official corn yields. This process 

provides a historical context for weather, biases, and non-sampling errors. 

The regression equation is:

yi = β0 + β1xi + εi

where yi is the official state yield and xi is the calculated State average net yield, β0 and β1 are 

historic least squares estimates, and εiis a random departure from the relationship.

Computational Examples

Sample Field Yield Examples

Suppose data have been collected for the following four samples. Calculations of gross yield 

will be demonstrated. The maturity categories are defined earlier in this chapter.
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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1. Sample 1

Maturity category 1, no ear shoots

Stalk count 79

8-row space width (ft.) 20.3

Historical 5-year avg grain weight per ear (lbs.) 0.29

Suppose regression models for samples with no ear shoots are:

Ears = 8.6 + 0.86 (stalk count)

Grain Wt = Historical average grain weight

Then

Ears = 8.6 + 0.86 (79) = 76.54 ears

Grain Wt = 0.29 pounds

Then forecasted gross yield for sample 1 is:

Gross Yield= [ (76.54)(0.29)(43560) ] / [ (56)(15)(20.3)/(2) ] = 113.4 bu/acre

2. Sample 2

Maturity category 3, blister

Stalk count 81

8-row space width (ft) 20.3

Average kernel length (in.) 5.8

Ears Model = 7.2 + 0.87 (stalk count)

Grain Wt = 0.23 + 0.02 (kernel row length) 

Therefore,

Ears = 7.2 + 0.87 (81) = 77.67 ears

Ears Model = 89 / [ 1.2 + 0.09 * (76 / 81) ] = 69.29

Grain Wt = 0.23 + 0.02 (5.8) = 0.346 lbs

and Gross Yield = [ (73.65)(0.346)(43560) ] / [ (56)(15)(20.3)/(2) ] = 130.2 bu/acre
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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3. Sample 3

Maturity category 5, dough

Ears with kernel formation 70

8-row space width (ft) 19.5

Average kernel length (in.) 5.2

Suppose regression models for samples in dough stage are:

Ears = count of ears with kernel formation

Grain Wt = 0.10 + 0.04 (kernel row length)

Therefore,

Ears = 70 ears

Grain Wt = 0.10 + 0.04 (5.2) = 0.308 lbs.

and

Gross Yield = [(70)(0.308)(43560) ] / [ (56)(15)(19.5)/(2) ] = 114.7 

bu/acre

4. Sample 4

Maturity category 6, dent

Ears with kernel formation 50

8-row space width 20.3

Ears husked with grain 22

Field weight of husked ears (lbs.) 12.1

Wt. of ears in sealed bags (grams) 1042.2

Wt. of bags and rubber bands (grams) 45.2

Wt. of grain at moisture test(grams) 758.9

Moisture content (percent) 25.0

Suppose models for enumerator harvested samples are:

Ears = count of ears with kernel formation

Grain Wt = (field wt per ear)(fraction dry grain wt of 

field wt) / (0.845)

Therefore,
CHAPTER 5 CORN OBJECTIVE YIELD METHODS

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Ears = 50 ears

Field weight per ear = 12.1 / 22 = 0.55 lbs

Fraction dry weight of field weight = [ (758.9)(1-(25.0/100)) ] / [ (1042.2 - 45.2) ] 

= 0.571

Grain Wt = [ (0.55)(0.571) ] / 0.845 = 0.372 lbs.

And,

Gross Yield = [ (50)(0.372)(43560) ] / [ (56)(15)(20.3)/(2) ] = 95.0 bu/acre
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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44

CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

This chapter presents basic sampling, data collection, and mathematical methods utilized to 

estimate U.S. soybean yield and production. The sampling review will emphasize NASS’s 

unique Area Frame and its suitability for sample selections intended to measure U.S. soybean 

yields. Data collection will focus on the variety of data collected and how data collection 

changes as soybean crop maturity changes. The mathematical methods review will center on 

mathematical/statistical estimation of final soybean yields utilizing measurable plant 

characteristics observed at specific points during the growing season. The end results of careful 

sampling, data collection, and mathematical methods are numeric indications suitable to 

establishment, and/or revision, of U.S. soybean acreage, yield, and production.

Sample Design

Soybean Objective Yield (SOY) surveys are conducted in Arkansas, Illinois, Indiana, Iowa, 

Kansas, Minnesota, Missouri, Nebraska, North Dakota, Ohio, and South Dakota. On average, 

over the last three years, these eleven states produced more than 80 percent of the U.S. soybean 

crop. As described in Chapter 2, NASS partitions each of these states’ land area into 

approximately one square mile pieces and calls the pieces segments. The resulting collection of 

segments is referred to as the “Area Frame”. This painstaking segmentation of land area into 

uniquely identifiable segments makes possible the selection of a probability-based sample of 

U.S. soybean acres. 

Probability based surveys require the explicit identification and separation of all elements 

contained in a population of interest. For yield surveys like SOY, the most important result of 

constructing a population of soybean acres is that any acre of soybeans, in a given state, can be 

assigned a known probability of selection. This result allows statistical samples to be extracted, 

population parameters to be estimated, hypotheses to be tested, and inferences to be made. 

NASS’s Area Frame is the vehicle that transports us from a very large population of U.S. 

soybean acres to a representative sample of U.S. soybean acres. The sample is both statistically 

defensible and economically feasible to enumerate. The procedure for identifying every U.S. 

soybean acre is to first, select a subsample of Area Frame segments, and secondly, to account for 

all agricultural activity occurring within those segments. Each selected segment will have all its 

acres inspected by and accounted-for by professional enumerators with assistance from the 

owner/operator. In this manner, a new listing of soybean acres is constructed each year. This 

listing is the SOY sample population. No other purveyor of U.S. soybean estimates can construct

such a sample population. 

Accurate inferences from a probability-based survey require the construction of a sampling 

population and, in addition, a means to select a representative sample from that population. The 

statistical method used to select soybean acres to be included in SOY is probability proportional 

to size (PPS). In statistics, this method ensures a representative sample is selected when sample 
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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45

elements vary in their size. A simple explanation should be given as to how sample elements in 

the soybean acres population can differ in size. During constructing of the soybean acres sample 

population, the explicit identification and separation of soybean acres, from all other acres, is 

made according to fields. In agriculture a field is one, continuous acreage of land devoted to the

same use. Therefore, the sample elements in the soybean population are fields. Since fields of 

soybeans vary in acreage, the sample selection method of PPS ensures the probability of 

selection is adjusted for field size. For example, employing PPS sampling, a soybean field that is 

twice the size of its neighbor will also be twice as likely to be included in the sample. After the 

determination of which fields are included in the sample, the representative acre is selected with 

simple random sampling designed to give every acre in the selected field, an equal chance of 

selection. Since a selected acre is too large for complete enumeration, a selected sample will be 

enumerated and expanded up to the one-acre level.

In mid-July of each year, professional statisticians in the eleven SOY states train field 

enumerators to properly identify and prepare selected samples for data collection. Generally, 

enumerators will have many years of experience in SOY data collection and are well qualified to 

conduct their assignments. Practical field training is also available through relationships 

developed among individual enumerators and their supervisors. Overall, the preparation for data 

collection is rigorous and includes quality control processes that continue through the soybean 

growing season. In late July, field enumerators will begin visiting and enumerating samples and 

will continue personal visits at monthly intervals throughout the season until final harvest. 

Each sample consists of two units (or plots) to be utilized in forecasting final net yield per acre. 

Each unit consists of two parallel 3.5-foot sections of row partitioned into a 3-foot section and a 

6-inch section. During each visit, enumerators count or measure each required plant 

characteristic, the required characteristics being determined according to the units’ maturity 

level. For example, at early maturities enumerators will count plants and measure row spacing. 

At later maturities, lateral branches, flowers, and pod weights are measured and recorded. After 

each data collection period, a forecast of each unit’s final net yield is constructed. Essentially 

forecasts of soybean yields depend on two items: One, the current year’s measurable plant 

characteristics and, two, the historic relationship between plant characteristics measured in the 

past, at the same level of maturity, and final plant characteristics that result in harvestable yield. 

Each item is needed to forecast a samples final net yield per acre. In cases where one or the other 

of the two required items is missing, a five-year average of the final plant characteristic is 

substituted. During some early forecasts there may be no plant characteristic that NASS 

measures that can be related the final plant characteristic. Pod weight is the prime example. In 

these cases, historic averages are used to forecast final net yield.

Data Collected
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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46

Field enumerators count and measure several items within or near the units. The size of the unit 

(square feet), the number of pods, pod weight, and harvest loss. The following lists the data items 

collected and what it is used to measure.

Data items used to measure the size of each unit:

Distance between two rows (one row middle)

Distance between five rows (four row middles)

Data items used to forecast or estimate the number of pods:

Number of plants in each section of each row

Number of main stem nodes in the 6-inch section

Number of lateral branches in the 6-in section

Number of dried flowers and pods in the 6-inch section

Number of pods with beans in the 6-inch section

Data items used to forecast or estimate bean weight per pod:

Weight of beans harvested by enumerator

Moisture content of beans harvested

Data items used to estimate harvest loss:

Distance between two rows (one row middle)

Distance between five rows (four row middles)

Weight of beans gleaned from harvest loss units

Moisture content of beans gleaned

Maturity Categories

At each visit, the enumerator makes maturity assessments within the units and a maturity 

category is established for the sample. Forecast equations are derived using data collected 

during the previous 5-years for each maturity in each month. The maturity definitions used by 

the enumerators are:

Maturity 2, Pods set, leaves still green, or earlier

Maturity 3, Pods filled, leaves turning yellow

Maturity 4, Pods turning color, leaves shedding

Maturity 5, Pods brown, almost mature or mature
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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In analysis, these categories are further refined into 10 forecasting categories, based on the 

counts made by the enumerators. The 10 forecasting categories form a more homogeneous 

grouping and are defined as:

0 No plants present in either row of the 6-inch section

1 Field maturity 2, no pods with beans in 6-inch section and the ratio 

of total fruit to main stem nodes is less than .20.

2 Field maturity 2, no pods with beans in 6-inch section and the ratio 

of total fruit to main stem nodes is between 0.20 and 1.75 

inclusive.

3 Field maturity 2, no pods with beans in 6-inch section and the ratio 

of total fruit to main stem nodes is greater than 1.75.

4 Field maturity 2, pods with beans are present in the 6-inch section 

and the ratio of pods with beans to total fruit is less than 0.05.

5 Field maturity 2 and the ratio of pods with beans to total fruit is at 

least 0.05 but less than 0.20.

6 Field maturity 2 and the ratio of pods with beans to total fruit is at 

least 0.20 but less than 0.65.

7 Field maturity 2 and the ratio of pods with beans to total fruit is at 

least 0.65 but at most 0.85.

8 Field maturity 2 and the ratio of pods with beans to total fruit is 

greater than 0.85, or Field maturity 3 (and plants present in the 6-

inch section).

9 Field maturity 4 and plants present in the 6-inch section.

10 Field maturity 5, regardless of whether there are plants in the 6-

inch section.

Analysis of Raw Data

In the following sections estimation at the sample level is discussed. All sample level regression 

equations are derived from the previous five years' survey data using multiple regression 

techniques. Certain influential data points (i.e., "outliers") are excluded from the dataset prior to 

deriving the coefficients. These influential data points are identified using a "deleted residual" 

analysis or the "Cook's D" statistic (Belsley, Kuh, and Welsch, [4]). There is usually very little 

change in the regression equations from year-to-year because roughly 80 percent of the data for 

each class were used in the analysis the previous year. Classes that do change significantly from 

one year to the next are usually those with very few observations. If a class has little data and a 

plausible forecast equation cannot be derived, the equation from the previous year is used.

Forecasting Gross Yield

Forecasting soybean yields is somewhat different, but follows similar patterns, to corn and cotton 

yield forecasting. The difference results from two features of soybeans: one, their typical row 
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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48

space pattern and two, their fruit size and count. Soybean producers exhibit more variation with 

respect to row spacing than either corn or cotton producers. This variation is a direct result of 

soybeans flexibility to be used as either a single or double crop. Another unique feature of 

soybeans that alter yield forecasting patterns is fruit size and counts. Corn ears are large and 

most often singular to individual plants. Even cotton bolls are large compared to soybean pods 

and cotton’s fruit counts are not unmanageable. On the other hand, individual soybeans pods are 

much smaller, more prolific, and therefore, more difficult to count. In addition, other plant 

characteristics for soybeans are almost unmanageable due to prolific counts, e.g., flowers. These 

two differences alter the methods NASS employs to count and measure soybeans. The most 

important change is a reduction in the size of the count area for soybean samples. Another 

change is the conversion of all soybean sample measures to a common denominator of 18 square 

feet. 

The forecast for soybean yield per acre is expressed as follows:

Gross yield per acre = (pods per 18 square feet)*(weight per pod)* (43,560)

 (18)(453.6)(60)

Where 43,560 is the number of square feet in an acre, 60 converts pound of beans to bushels, and 

453.6 converts grams to pounds.

In the equation above, forecasts for gross yield per acre depends on the number of pods per 18 

square feet and the weight per pod. Should the pods per 18 square feet in a sample plot be 

unobservable due to immaturity, then stochastic models are employed to “predict” the number of 

future pods per 18 square feet. The prediction is based on the historic relationship between past 

observable plant characteristics and the eventual outcome for pods. These historic models are 

stochastic because a range of potential pods per 18 square feet exists for each value of the 

observable plant characteristic. NASS gives careful consideration to plant characteristics that are 

proven performers in terms of prediction and forecasting. Table 1 illustrates the plant 

characteristics utilized for predicting gross yields at alternative time and maturity levels:
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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Table 1. Soybean Objective Yield Models

Sample Level Models

models based on previous 5 years

Forecasting 

Category

maturity 2

maturity 

3,4 maturity 5

1

Fruit/

Node

0 to .2

2

Fruit/

Node

.2 to 1.75

3

Fruit/

Node

1.75+

4

Pods/

Fruit

0 to .05

5

Pods/

Fruit

.05 to .2

6

Pods/

Fruit

.2 to .65

7

Pods/

Fruit

.65 to 

.85

8

yellow

9

brown

10

enumerator 

harvested

Pods per 

Plant

Sep

Plants,

Nodes

Plants, 

Laterals

Laterals,

Fruit

Plants,

Laterals

Laterals,

Fruit

Laterals,

Fruit,

Pods Pods Pods Pods 

Pods

Oct Pods Pods Pods 

Nov

Weight per pod 5-year average Lab Data

fruit = blooms + dried flowers + pods
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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To form a complete gross yield expression, a value is needed for pods per 18 square feet which is 

only observable at or just before harvest. Therefore, yield forecast made before final harvest 

require some method to forecast final pods per 18 square feet. NASS forecasts pods per 18 

square feet with the following expression:

Pods per 18 square feet = Final Plants per 18 square feet * Final Pods per Plant

But ‘Final Plants per 18 square feet’ is also unobservable before harvest, as well as ‘Final Pods 

per Plant’. NASS forecasts these two subcomponents in the following manners. 

1. Forecasting Final Plant Count per 18 Square Feet

A simple linear (one variable) regression model is used to forecast the final number of plants per 

18 square feet. The form of the model is:

yi = β0 + β1xi + εi

The independent variable, xi, is the current period, total plant count in the 3-foot and 6-inch 

sections of unit i and yi is the final plant count from the same area. These counts are available 

from previous years’ data collections and therefore are available to calculate parameters β0 and 

β1 by ordinary least squares. As might be expected, the R2’s from this model, in any state, is 

rarely below 90 percent.

If the forecasted number of plants exceeds the number obtained during the monthly visit, the 

forecast is replaced with the monthly visit value. A negative forecast is replaced with zero.

2. Forecasting Final Pods per Plant

The final number of pods per plant is forecasted using one or two variable regression models. 

The independent variables used to predict pods per plant depend upon the forecasting category of 

the unit and are shown in Table 1. There are five possible forecasting variables:

V1 = Plants per 18 square feet (the same variable used to forecast the final number of plants 

per 18 square feet)

V2 = Main stem nodes per plant

V3 = Lateral branches with blooms, dried flowers, or pods per plant

V4 = Blooms, dried flowers, and pods per plant

V5 = Pods with beans per plant

Thus, the general form of the model is:

yi = β0 + β1V1 + β2V2 + β3V3 + β4V4 + β5V5 + εi
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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51

where three or four of the coefficients (β1, β2, β3, β4, β5) are zero. y is the final (at-harvest) 

number of pods per plant in the 6-inch section for sample i.

If a unit is classified as forecasting category 0, no counts are possible in the 6-inch sections so 

there are no forecasting variables. The average number of pods with beans per plant in all other 

forecasting categories (1-10) is substituted for units in category zero. In all States separate 

averages are computed for "wide" row units (row width at least 1.5 feet, broadcast, or blank) and 

narrow row units (row width less than 1.5 feet) for category zero substitutions.

Recall the expression for final gross yield given above was:

Gross yield per acre = (pods per 18 square feet)*(weight per pod)* (43,560)

 (18)(453.6)(60)

Together, the two sub-component forecasted values for final plants per 18 square feet and final 

pods per plant may be used to forecast a final pods per 18 square feet. Now, if a final weight per 

pod is also known, the yield may be calculated. Unfortunately, the final weight per pod is 

unknown until just before, or at, harvest. As Table 1 shows, weight per pod is forecasted at a 5-

year average over all forecasting categories, allowing for shifts in the five-year average 

according to whether the sample has wide or narrow row spacing. The average is carried until 

laboratory data make the weight per pod final. 

State Average Forecasts and Estimates

The sample level gross yield forecasts are averaged to the State level. Since the sample is selfweighting, the simple mean of the sample forecasts is an unbiased estimate of the State gross 

yield. Therefore, gross yield for a State is given as G,

G̅=

1

NG

∑Gi

NG

i

where

G̅ = State mean gross yield

NG = number of samples with gross yield forecasts (estimates)

Gi = gross yield for sample i
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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52

And the standard error of G̅is:

SG̅= √∑

(Gi − G̅)

2

NG(NG − 1)

NG

i

Simple means are also appropriate for Pods per 18 Square Feet, Plants per 18 Square Feet, 

Harvest Loss, etc. No weighting is required when calculating State level averages for these 

items:

Harvest Loss

For one quarter of the samples, an additional plot is laid out near each unit and gleaned after 

farmer harvest of the field. If less than 10 harvest loss samples have been completed for a State, 

a 5-year historical average (bu/acre) is the State-level estimate of harvest loss. When a sampling 

gleaning has been completed, harvest loss (bu/acre) is computed for each sample as follows:

Li =

(wloose/thres) (1 − (

mi

100)) ∗ 43,560

(3)(R̅

i

)(453.6)(60)(.875)

Where wloose/thres is the weight of loose and threshed beans, mi is moisture, and R̅

i

is the 4-row 

spacing for unit 1 plus the 4-row spacing for unit 2, divided by 2. If a unit is broadcast, 6.0 is 

used for its 4-row space width.

These sample-level harvest loss estimates are averaged to the State level, with mean

L̅ =

1

NL

∑Li

NL

i

Where Li = harvest loss in sample i, and NL = number of harvest loss samples.

And the standard error is given by SL̅ = √∑

(Li−L̅)

2

NL(NL−1)

NL

i
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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53

State Level Net Yield

Net yield for the State is computed by subtracting the estimated State level harvest loss from the 

mean of all sample level gross yield forecasts and estimates. Thus, estimated average net yield 

is:

Y̅ = G̅− L̅

Where G ̄ and L ̄ are the State level gross yield and state level harvest loss respectively.

The standard error of the estimate is:

SY̅ = √SG̅

2 + SL̅

2 −

2

NG

COV(G, L)

Where SL̅ was defined previously, and

SG̅= √∑

(Gi − G̅)

2

NG(NG − 1)

NG

i

When less than 10 Form E's are completed, and historical average loss is used, the standard error 

is:

SY̅ = SG̅

Production for the State

Production (P) for the State is the product of estimated State level net yield and acres to be 

harvested for grain:

P = (AHARV)(Y̅)

with standard error:

SP = √(Aharv

2

)(SY̅

2

) + (Y̅2)(SAharv

2

) + (SY̅

2

)(SAharv

2

)

COV (G,L) = 

N

L



1

(Gi- G )(Li- L )

NL-1
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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Removing Bias from State Level Calculations

Forecasts of State level yields are inherently subject to differ from the final, and in most cases 

administratively-determined, yield. The difference is due to weather and crop conditions yet to 

be encountered at the time the forecast is produced, the difference between weather and crop 

conditions in the current year and the historic weather and crop conditions utilized to predict 

current yields, and also systematic non-sampling errors which contribute to forecast error. NASS 

makes every attempt to minimize the impact of these sources of error by means of 

administratively determine final values. These final, sometimes referred to as official, values are 

used as dependent variables and are related to corresponding State level averages of net yield to 

estimate historic linear regression equations. For example, each state will have an 

administratively-determined, official soybean yield and a State level soybean yield for all 

previous years. To forecast the official soybean yield for the current year, NASS takes the State 

level average soybean yields from previous years surveys and regresses them to the 

corresponding official soybean yields. This process provides a historical context for weather, 

biases, and non-sampling errors. 

The following table shows the variety of independent and dependent variables for which historic 

biases are evaluated:

Dependent variable Independent variable

Official Final Yield

September - average number of pods per acre

October - December - average net yield per 

acre

Final Number of pods per acre

September - December - average number of 

pods per acre

Final weight per pod

September - average number of pods per acre

October - December - average weight per pod

Final Harvest Loss

September - November - average of previous 

5 years harvest loss

December - Harvest Loss for current year

Laboratory Weight Measures

Bean weight per pod is calculated using the harvested data from the sample. The weights from 

both units are combined, so only one weight is calculated for the sample. 
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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55











WC

NC 









WB

W12 









1.0-(moisture content /100)

0.875

where

Wc = weight of the pods and beans from Row 1 of the 3-foot section of Unit 1. If there are 

no plants in Row 1 of Unit 1, then Row 2 is used. If that is also blank, then the same 

process is applied to Unit 2.

Nc = the number of pods with beans from the row counted above.

W12 = weight of pods and beans from Row 1 of the 3-foot sections of Units 1 and 2.

WB = weight of the threshed beans form Row 1 of the 3-foot sections of Units 1 and 2.

0.875 = conversion to 12.5 percent moisture (1.0 - .125).

Number of Pods with Beans per 18 Square Feet is computed for each unit from the harvested 

data:

Unit 1: (W1)(Nc)(18)

 ───────────────────────

 (Wc)(3)(4-row space width)/(4)

Unit 2: (W2)(Nc)(18)

 ───────────────────────

 (Wc)(3)(4-row space width)/(4)

Where

Wi = weight of pods and beans from Row 1 of the 3-foot section of Unit i (i = 1 or 2),

Nc and Wc were defined previously, and the expression “(3)(4-row space width)/(4)” is the area 

of the rectangular unit formed by Row 1 of the 3-foot section and its row middle. If the unit is 

broadcast, a 4-row space of 6.0 is used.

Example

Suppose Unit 1's pods are counted in the lab, and the following data are obtained:

Wc = 103.2 grams = W1

Nc = 221

WB = 134.8 grams

W12 = 236.4 grams

moisture content = 10.6 percent
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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56

4-row space width = 11.0 feet

Then, the estimated weight of beans per pod is:

(103.2)(134.8) (1-(10.6/100)) 

───────────────────── = 0.272 grams.

(221)(236.4) (0.875)

The estimated number of pods per 18 square feet is:

(103.2)(221)(18)

────────────────────── = 482.18 pods/18 square feet.

(103.2)(3)(11.0)/(4)

Then the estimate of gross yield for the unit is:

(482.18)(0.272)(43560)

────────────────────── = 11.66 bu/acre

(18)(453.6)(60)

Gross Yield for Units with Incomplete Data

Gross yield is forecasted or estimated from the current month's survey data. In some cases, 

current data are unavailable and data from a previous month may be used to compute gross yield, 

or no gross yield may be computed for the unit. The different cases are discussed below.

Refusals

If the farmer refuses permission to enter the field, the sample is lost for the season. In this case, 

the yield for this sample is left missing. Consequently, the refused sample contributes nothing to 

the State-level average yield. Stated another way, the assumption is made that if the sample had 

not been a refusal, its gross yield would have been equal to the State's average gross yield.

Inaccessible Samples and Units

Occasionally, some or both units are inaccessible due to scheduling or field conditions. If data 

from a previous visit are available, the previous forecast is carried forward. Otherwise, the 

sample is excluded from gross yield calculations. The sample must still be intended for harvest 

as beans.

Early Farmer Harvest
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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57

If a previously laid out unit is harvested by the farmer before current data can be collected, the 

previous month's predicted yield is brought forward. 

Lost, Abandoned, Destroyed Units

If a unit is lost, abandoned, destroyed, and so forth, no gross yield is computed for the unit. The 

unit contributes nothing to the sample-level yield indication.

Computational Examples

An example will now be given showing how gross yield per acre is forecasted for a sample. 

Assume that the following data were obtained for a sample.

Sample Data

Unit 1 Unit 2

Field maturity 2 2

Four-row space measurement (ft.) 12.8 12.5

Plants in the 2 3-foot row sections 41 40

Plants in the 2 6-inch row sections 11 9

Nodes on the main stems of the plants 96 74

Lateral branches with blooms, dried flowers, or pods 5 2

Blooms, dried flowers, and pods 50 37

Pods with beans 0 0

Before gross yield is computed, a forecasting category is computed for each unit. In this 

example, both units would be category 2 (no pods with beans in the 6-inch section, fruit/nodes 

ratio between 0.20 and 1.75 inclusive).

To forecast plants per 18 square feet, the current number of plants is scaled to the standard 18 

square feet:

 (plants in the 3-foot and 6-inch sections)(18)
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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58

 X = ──────────────────────────────────────────────

 (3.5)(4-row space width)/(2)

Where 18 is standard area, (3.5) is the length of row counted, and (4-row space width)/(2) is the 

width of a 2-row unit. If the unit is broadcast, the 4-row space width is 6 feet.

The current plant count per 18 square feet for each unit in the example is:

Unit 1: (41+11)(18) 

 X = ──────────── = 41.8

 (3.5)(12.8)/(2)

Unit 2: (40+9)(18) 

 X = ──────────── = 40.3

(3.5)(12.5)/(2)

Suppose that the values for bo and b1 in the forecasting equation are 1.2 and 0.92, respectively. 

Then the forecasted number of plants per 18 square feet for each unit is:

Unit 1: P1= 1.2+(0.92)(41.8)=39.656

Unit 2: P2= 1.2+(0.92)(40.3)=38.276

To forecast pods with beans per plant, a two-variable regression model is used for forecasting 

category 2 (see previous table), containing the following variables:

V1 = current month's plant count expanded to 18 square feet (x)

V3 = lateral branches with blooms, dried flowers, or pods per plant for the 6-inch section

so, the model is:

Y = bo+b1V1+b3V3.

Given, the following forecast equation:

Y = 42.2 - (0.6) V1 + (4.8)V3,

the forecast of pods per plant for each unit is:

Unit 1: 42.2 - (0.6)(41.8) + (4.8)(5/11) = 19.30
CHAPTER 6 SOYBEAN OBJECTIVE YIELD METHODS

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59

Unit 2: 42.2 - (0.6)(40.3) + (4.8)(2/9) = 19.09

To forecast bean weight per pod, a 5-year historical average weight is used. Assume that the 5-

year historical average weight is 0.437 grams for the wide row samples for this State. The 

expression for each unit’s yield per acre is:

Unit 1: (39.656)(19.30)(.437)(43560) 

 Y1 = ──────────── = 29.74 bu/acre

 (18)(453.6)(60)

Unit 2: (38.276)(19.09)(.437)(43560) 

 Y2 = ──────────── = 28.39 bu/acre

 (18)(453.6)(60)

And the gross yield forecast for the sample is:

 (29.74+28.39)/2 = 29.06 bu/acre
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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60

CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

This chapter presents the procedures and formulae used to calculate cotton yield indications. The 

scope of the Cotton Objective Yield Survey, sample plots, and data collected are briefly 

described. More detail is given to the formulae that use the data to forecast and estimate yield.

Early in the growing season, some or all of the three components of net yield (number of bolls, 

average boll weight, and harvest loss) cannot be obtained directly and must be forecast. The 

procedures used to forecast these components are described in the following sections.

Sample Design

Cotton Objective Yield (CtOY) surveys are conducted in major cotton producing States:

Arkansas, Georgia, Mississippi, and Texas. As described in Chapter 2, NASS partitions each of 

these states’ land area into approximately one square mile pieces and calls the pieces segments. 

The resulting collection of segments is referred to as the “Area Frame”. This painstaking 

segmentation of land area into uniquely identifiable segments makes possible the selection of a 

probability-based sample of U.S. cotton acres. 

A probability-based survey requires the explicit identification and separation of all elements 

contained in the population of interest. NASS’s Area Frame is the vehicle for explicitly 

identifying and separating each acre of cotton produced in the U.S. Every year, during late 

spring, all four CtOY states screen a statistically selected sample of Area Frame segments for all 

agricultural activity, including cotton acreage planted. Each acre in every selected segment will 

be visually inspected and/or accounted-for by the owner/operator with respect to agricultural 

activity. In other words, every year a new listing of every cotton acre is constructed. This listing 

is the CtOY sample population. This listing is an important step towards employing probability 

theory to randomly select a sample of cotton acres from which inferences will be made about all 

cotton acres. The most important result of constructing a sample population is that any acre of 

cotton, planted in each state, has a chance to be selected for the CtOY survey. No other purveyor 

of U.S. cotton estimates can make an equivalent statement. 

Accurate inferences from a probability-based survey require the construction of a sampling 

population and, in addition, a means to select a representative sample from that population.

The statistical method used to select cotton acres to be included in CtOY is probability 

proportional to size (PPS). In statistics, this method ensures a representative sample is selected 

when sample elements vary in their size. During constructing of the cotton acres sample 

population, the explicit identification and separation of cotton acres, from other acres, is made 

according to fields. In agriculture a field is one, continuous acreage of land devoted to the same 

use. Since fields of cotton are the unit of selection for CtOY samples and because cotton fields

vary in acreage, probability proportional to size is ideally suited to selecting a sample that 

perfectly reflects the population characteristics of cotton. For example, employing PPS sampling 

implies a cotton field accounting for twice the percentage of total state cotton acres relative to a 
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

THE YIELD FORECASTING PROGRAM OF NASS

61

neighboring cotton field, will also carry twice the probability of selection as the neighbor. The 

representative acre selected from a sampled field is finally accomplished with simple random 

sampling. Since a selected acre is too large for complete enumeration, a selected sample will be 

enumerated and expanded up to the one-acre level.

In mid-July of each year, professional statisticians in the four CtOY states train field enumerators 

to properly identify and prepare selected samples for data collection. Generally, enumerators will 

have many years of experience in CtOY data collection and are well qualified to conduct their 

assignments. Practical field training is also available through relationships developed among 

individual enumerators and their supervisors. Overall, the preparation for data collection is 

rigorous and includes quality control processes that continue through the cotton growing season. 

Data are collected from each sample at monthly intervals starting in late July and continuing 

through December or until the sample has been harvested. Each month during the Objective 

Yield Survey, data collected from the sample fields are used to produce indications of planted 

acres (September only), acres for harvest, and yield.

A sample consists of two independently located units (or plots), each of which consists of two 

parallel 10-foot sections of row. An additional 3-foot section is appended to one row of each 

unit. This extra section is used when making detailed fruit counts. Field enumerators use a 

random number of rows along the edge of the field and a random number of paces into the field 

to locate each unit. At each visit, enumerators count all fruit and fruiting positions. Any mature 

bolls found in the 10-foot sections of the sample plots are picked and sent to a NASS lab where 

boll weight is determined. The count of bolls picked, and the weight of these bolls are 

accumulated through the season. Just before farmer harvest, all remaining open bolls are picked 

and weighed to establish gross yield. The yield is measured as pounds of lint per acre at 5 

percent moisture. Harvest loss is measured in separate units located near the monthly yield plots.

Data Collected

Field enumerators count and measure several items within or near the units. Data items are used 

to measure the size of the unit, number of bolls, weight per boll, and harvest loss. The following 

lists the data items collected and objective of these measurements:

Data items used to measure the size of each unit:

Distance between two rows (one row middle)

Distance between five rows (four row middles)

Data items used to forecast or estimate the number of bolls:

Number of plants in each row (all sections)

Number of squares (3-foot sections)

Number of small bolls and blooms (3-foot sections)

Number of large unopen bolls (10-foot sections)

Number of open bolls (10-foot sections)
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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Data items used to estimate weight per boll:

Weight of lint harvested by enumerators

Weight of lint dried to zero moisture

Data items used to estimate harvest loss:

Distance between two rows (one row middle)

Distance between five rows (four row middles)

Number of unopen bolls left in the field

Weight of lint gleaned from harvest loss units

Weight of dried lint

Maturity Categories

To forecast each sample’s yield per acre, regression models are developed by maturity category 

for each survey month. For cotton, the maturity categories are defined by the raw counts 

obtained in the sample. These categories are:

In 10-foot sections In 3-foot sections

1 No fruit present No fruit present

2 No fruit present Squares only

3 0 < RATIO < 0.5 Blooms or Bolls

4 0.5 < RATIO < 2.0 ----

5 2.0 < RATIO ----

6 Sample field has been harvested or harvest immanent. 

RATIO is the ratio of large bolls counted to plants counted in the 10-foot sections of the sample.

Large bolls include burrs, open bolls, partially open bolls, and large unopened bolls.

Sample Level Yield Forecasts

Forecasting the Number of Large Bolls

The expected number of large bolls for each sample is forecast using a regression model:

Ŷ

i = β0 + β1X1 + β2X2 + β3X3
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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63

where:

Ŷ

i = forecasted number of large bolls in ith unit

X1 = observed number of burrs, open bolls, partially open bolls, and large unopened 

bolls (40-foot equivalent) in ith unit

X2 = observed number of small bolls and blooms (40-foot equivalent) in ith unit

X3 = observed number of squares (40-foot equivalent) in ith unit

β0 − β3 = least squares regression coefficients

Small bolls are defined as boll less than one inch in diameter. Enumerators use a gauge with a 

one-inch hole to determine whether a boll is small or a large unopened boll. A square is an 

observable fruiting position that has not reached the bloom stage.

Forecast equations for each model are derived for each maturity category for each month for 

each district for each State. Not all possible independent variables are used in each model. For 

instance, for maturity category one only the intercept is fit. For later maturities and or months, 

squares and small bolls are excluded from the models. Data from the previous 5 years are used to 

estimate the regression coefficients. If a unique set of coefficients cannot be determined for a 

given class (due to insufficient data), the previous month's coefficients are used.

The actual count of large bolls is used for any sample in maturity category six in any month, and 

for all samples in December and later months. All samples in maturity category one use a 5-year 

historical average.

Analysis of Raw Data

The regression equations are derived from the previous 5 years' survey data using multiple 

regression techniques. Certain influential data points (i.e., "outliers") are excluded from the 

dataset prior to deriving the coefficients. These influential data points are identified using a 

"deleted residual" analysis or the "Cook's D" statistic (Belsley, Kuh, and Welsch, [4]). There is 

usually very little change in the regression equations from year-to-year because roughly 80 

percent of the data for each class were used in the analysis the previous year. Classes that do 

change significantly from one year to the next are usually those with very few observations. If a 

class has little data and a plausible forecast equation cannot be derived, the equation from the 

previous year is used.

Forecasting Boll Weight

Early in the season, until 20 percent of the projected number of large bolls have been picked and 

weighed by the enumerator, a 5-year historical average is used. When 20 to 85 percent of the 

projected number of large bolls has been picked, one model is used to forecast boll weight for all 

maturity categories in a district in a State:
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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64

Ŵsd = wsd(β0 + β1Xsd)

where:

Ŵsd = forecast boll weight for the s

th State and dth district

wsd = observed boll weight

Xsd = ratio of bolls picked and weighed to large bolls forecasted

β0 − β1 = regression coefficients

When more than 85 percent of the projected number of large bolls has been picked and weighed 

by the enumerator, actual boll weight is used.

The following table shows the independent and dependent variables for the State level indication 

models used during the 1996 growing season.

Dependent variable Independent variable

Official Final Yield Average estimated net yield per acre over all 

samples

Final Number of Bolls August - Average small bolls and blooms per acre 

over all samples

September - Average small bolls and blooms plus 

cumulative large bolls per acre over all samples

October - January - Average cumulative large 

bolls per acre 

Final boll weight August - September - Weight derived from 

average estimated final gross yield and average 

estimated final large bolls per acre

October - January - average cumulative net 

weight per boll 

Final Harvest Loss August - November - average of previous 5 years 

harvest loss

December - January - OY B Harvest Loss for 

current year
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

THE YIELD FORECASTING PROGRAM OF NASS 65

Cotton Objective Yield Models

Sample Level Models

models based on previous 5 years

Forecast Category

1

no fruit

present

2

squares

present

3

ratio

0 to 0.5

4

ratio

0.5 to 2.0

5

ratio

2.0+

6

harvested or soon 

to be harvested

Number of 

Bolls

August 5-year 

average

squares

cumulative large bolls

small bolls & blooms

squares

cumulative large 

bolls

September 5-year 

average

squares

cumulative large bolls

small bolls & blooms

squares

October cumulative large bolls

small bolls & blooms

November cumulative large bolls

December cumulative large bolls

Weight

per boll

<20%

picked 5-year average

20-85% 

picked cumulative net weight x smoothing parameter

>85% 

picked cumulative net weight

ratio = cumulative large bolls / plants in 10-foot units

large bolls = burrs + large opened bolls + large partially opened bolls + large unopened bolls

smoothing parameter = value <1 that approaches 1 as percent picked approaches 85 percent
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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Forecasting Directly to State Level

The discussion in the previous sections centers on processing data at the sample level. Modeling 

and yield calculations are done at the sample level and averaging is done as the last step.

Additionally, averages of the raw counts and component forecasts can be computed for 

supporting analysis.

A second approach to forecasting State yield, using the same data, can be applied by doing the 

averaging first and the modeling last. Averages per acre at the State level can be calculated for 

each of the count variables (plants, squares, small bolls and blooms, large unopen bolls, and open 

bolls. Average weight per boll can also be calculated, weighting the average weight per boll in 

each sample by the number of bolls in that sample. This process creates State level independent 

variables and leads to State and regional level models. The State and regional level independent 

variables can be regressed to final official yield, final bolls per acre, and final weight per boll.

The distinction is State and regional averages are used as independent variables in regression 

models that predict State and regional level final yields, bolls per acre, and weight per boll. In 

these models, one year and month represents one observation, so instead of partitioning 

thousands of sample level points into forecasting categories, we have one data point per month 

per year. A 15-year dataset is used for these models. The models are simple one variable 

regression models and are called the State level models, referring to the fact that they are State 

and regional level models, not sample level models as described in the previous sections.

Gross Yield

The estimate of final gross yield is computed by multiplying the forecasted number of large bolls 

at harvest by the forecasted average weight per boll, expanding to a per acre basis, and 

converting to a standard unit. The standard unit for cotton is pounds of lint at 5 percent moisture.

Production is reported in 480-pound bales.

The formula for computing gross yield is:

Gi

̂ =

(2.401)ZBiWi

Ri

where

Gi

̂ = estimated gross yield (lbs. of lint per acre) for sample i

Z = lint/seed ratio (3-year average)

Bi = number of large bolls at harvest in 40 feet for sample i

Wi = average boll weight for sample i (grams at 5 percent moisture, gin equivalent)

Ri = average row spacing for sample i

2.401 = 43,560 / (40 * 453.59) = which converts grams of seed cotton per 40 feet of row 
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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to pounds of seed cotton per acre.

The Objective Yield samples are selected in such a way that each acre has equal probability of 

selection within districts. Therefore, the average of the sample level yields across all samples in a 

district provides a forecast of mean gross yield per acre for the district. 

Mean Gross Yield for State

The sample level gross yield forecasts (estimates) are averaged to the State level. Since the 

sample is self-weighting, the simple mean of the sample forecasts (estimates) is an unbiased 

estimate of the State gross yield. Therefore,

G̅=

1

NG

∑Gi

NG

i

where

G̅ = State mean gross yield

NG = number of samples with gross yield forecasts (estimates)

Gi = gross yield for sample i

The standard error of the estimate is:

SG̅= √∑

(Gi − G̅)

2

NG(NG − 1)

NG

i

Gross Yield for Units with Incomplete Data

Gross yield is forecasted or estimated from the current month's survey data. In some cases, 

current data are unavailable and data from a previous month may be used to compute gross yield, 

or no gross yield may be computed for the unit. The different cases are discussed below.

Refusals

If the farmer refuses permission to enter the field, the sample is lost for the season. In this case 

the yield for this sample is left missing. Consequently, the refused sample contributes nothing to 

the State-level average yield. Stated another way, the assumption is made that if the sample had 

not been a refusal, its gross yield would have been equal to the State's average gross yield.

Inaccessible Samples and Units
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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68

Occasionally, some or both units are inaccessible due to scheduling or field conditions. If data 

from a previous visit are available, the previous forecast is carried forward. Otherwise, the 

sample is excluded from gross yield calculations. The sample must still be intended for harvest 

as cotton.

Early Farmer Harvest

If a previously laid out unit is harvested by the farmer before current data can be collected, the 

previous month's predicted yield is brought forward.

Lost, Abandoned, Destroyed Units

If a unit is lost, abandoned, destroyed, and so forth, no gross yield is computed for the unit. The 

unit contributes nothing to the sample-level yield indication.

Harvest Loss

The harvest loss is computed from gleanings obtained from one quarter of the samples. The 

sample level harvest loss is found by determining the total weight of seed cotton gleaned, 

expanding to a "per acre" basis, and converting to standard units. 

The formula for harvest loss is:

Li =

(2.401)WiZ

Ri

where

Li = harvest loss (lbs. of lint per acre) for the ith sample

Wi = weight of cotton left in units for sample i which is computed as: (partially opened 

and large unopened bolls left in the units) * (average net weight per boll) + 

(weight of cotton gleaned adjusted to 5 percent moisture)

Z = lint/seed ratio (3-year average)

Ri = row space measurement for sample i

2.401 = conversion factor (defined above)

For each month, if fewer than 10 harvest loss samples have been completed within a district, a 5-

year average harvest loss is used as an estimate.

These sample-level harvest loss estimates are averaged to the State level, with mean:
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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69

L̅ =

1

NL

∑Li

NL

i

where

L̅ = State level mean harvest loss

Li = harvest loss in sample i

NL = number of samples with Form E data

The standard error of the estimate is:

SL̅ = √∑

(Li − L̅)

2

NL(NL − 1)

NL

i

Net Yield for the State

Net yield for the State is computed by subtracting the estimated State-level harvest loss from the 

mean of all sample-level gross yield forecasts and estimates. Thus, estimated average net yield 

is:

Ŷ = G̅− L̅

where

Ŷ= estimated average State net yield

G̅= State mean gross yield

L̅ = State level mean harvest loss

The standard error of the estimate is:

SŶ = √SG̅

2 + SL̅

2 −

2

NG

COV(G, L)

where

SG̅and SL̅ were previously defined, and
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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COV(G, L) = ∑

(Gi − G̅)(Li − L̅)

NL − 1

NL

i

When less than 10 gleanings are completed, and historical average loss is used, the standard error 

is:

SY̅ = SG̅

Production for the State

Production for the State is the product of estimated State-level net yield and acres harvested:

P = ŶA

where

P = State production

Ŷ= State level net yield

A = acres harvested

with standard error:

SP = √A2SŶ

2 + Ŷ 2SA

2 + SŶ

2

SA

2

Removing Bias from State Level Calculations

Forecasts of State level yields are inherently subject to differ from the final, administrativelydetermined, yield. The difference is due to the three possible reasons: weather and crop 

conditions yet to be encountered at the time the forecast is produced, the difference between 

weather and crop conditions in the current year and the historic weather and crop conditions 

utilized to predict current yields, or systematic non-sampling errors which contribute to forecast 

error. NASS makes every attempt to minimize the impact of these three sources of error by 

means of administratively determine final values. These final, sometimes referred to as official,

values are used as dependent variables to estimate an ordinary least squares equation with the 

averages calculated from objective yield samples as the independent variable. For example, each 

state will have an administratively-determined, official cotton yield for all previous years. To 

forecast the official cotton yield for the current year, NASS regresses the objectively determined 

State level average cotton yields from previous years to the corresponding official cotton yields. 

This process provides a historical context for weather, biases, and non-sampling errors. 

The regression equation is:
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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71

yi = β0 + β1xi + εi

where

yi = Official state yield

xi = calculated State average net yield

β0 and β1 = ordinary least squares estimates

εi=random departure from the relationship

Computational Yield Example

Yield (computed for a single sample)

 September 1 Data

8-row space measurement 25.8

Counts Within 10-foot Units

Number of plants (4 rows) 87

Number of burrs (2 units) 113

Total open bolls (4 rows) 130

Weight of seed cotton picked (2 units) 650

Number of partially open bolls (4 rows) 48

Number of large unopened bolls (4 rows) 121

3-foot Tag Section Beyond Unit 1

Number of plants 11

Number of burrs and open bolls 33

Number of large unopened bolls 14

Number of small bolls and blooms 4

Number of squares 2

3-foot Count Section Beyond Unit 2

Number of plants 8

Number of burrs and open bolls 27

Number of large unopened bolls 11

Number of small bolls and blooms 6

Number of squares 1
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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72

Current Month Lab Form

Weight of seed cotton before drying 56

Weight of seed cotton after drying 52

 Previous Months= Data Brought Forward

Accumulated burrs within unit 20

Accumulated bolls picked within unit 50

Accumulated adjusted weight seed cotton 257

Maturity Category Determination

ratio =

(Bc + Ba) + (Tc + Xa) + Vc + Uc

Pc

where

B c= current burrs within 10-foot units

B a= accumulated burrs within 10-foot units

Tc = current total open bolls within 10-foot units

Xa = accumulated bolls picked within unit

Vc = current partially open bolls in 10 foot-units

Uc = current large unopened bolls within 10-foot units 

Pc = current number of plants within 10-foot units

Using the example data ratio =

(113+20)+(130+50)+48+121

87

= 5.54. The ratio is greater than 2.0, 

thus the maturity category is 5.

Forecast Number of Large Bolls

Multiple Regression Model

Ŷ = β0 + β1X1 + β2X2 + β3X3

Where

Ŷ = forecasted number of large bolls

X1 = number of burrs, open bolls, partially open bolls, and large unopened bolls (40-

foot equivalent)

X2 = number of small bolls and blooms (40-foot equivalent)
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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73

X3 = number of squares (40-foot equivalent)

β0 − β3 = least squares regression coefficients derived from the previous 5 years of 

sample level data

The multiple regression model uses 40-foot equivalents for the number of bolls. Each boll 

measurement must first be converted to this standard. 

Burrs and open bolls, partially open bolls, and large unopened bolls are counted in a total of 46 

feet of row (four 10-foot units and two 3-foot units). 

X1 =

40

46

[(Bc + Ba) + (Tc + Xa) + Vc + Uc + (C1 + U1) + (C2 + U2)]

where

X1 = number of burrs, open bolls, partially open bolls, and large unopened bolls (40-foot 

equivalent)

B c= current burrs within 10-foot units

B a= accumulated burrs within 10-foot units

Tc = current total open bolls within 10-foot units

Xa = accumulated bolls picked within unit

Vc = current partially open bolls in 10 foot-units

Uc = current large unopened bolls within 10-foot units

C1 = burrs and open bolls within 3-foot Unit 1

U1 = large unopened bolls within 3-foot Unit 1

C2 = burrs and open bolls within 3-foot Unit 2

U2 = large unopened bolls within 3-foot Unit 2

Using the example data:

X1 = ⌊(113 + 20) + (130 + 50) + 48 + 121 + (33 + 14) + (27 + 11)⌋ = 493.043

Small bolls and blooms are counted in six feet of row (both 3-foot units)

X2 =

40

6

(D1 + D2)

where

X2 = number of small bolls and blooms (40-foot equivalent

D1 = small bolls and blooms within 3-foot Unit 1

D2 = small bolls and blooms within 3-foot Unit 2

Using the example data: X2 =

40

6

(4 + 6) = 66.667
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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74

Squares are counted in six feet of row (both 3-foot units)

X3 =

40

6

(Q1 + Q2)

where

X3 = number of squares (40-foot equivalent)

Q1 = squares within 3-foot Unit 1

Q2 = squares within 3-foot Unit 2

Using example data: X3 =

40

6

(2 + 1) = 20.000

Least squares regression coefficients (β0 − β3 ) are derived from the previous 5 years of sample 

level data, for this example let:

β0 = 14

β1 = 0.933

β2 = 0.300

β3 = 0.110

The estimate of number of bolls using the regression model for this sample is:

Ŷ = 14 + (0.933 ∗ 493.043) + (0.300 ∗ 66.667) + (0.110 ∗ 20.000) = 496.209

Forecast Boll Weight

Ŵ = w(β0 + β1X)

where:

Ŵ = forecast boll weight

w = observed boll weight at 5% moisture (gin equivalent)

X = ratio of bolls picked and weighed to large bolls forecasted

β0 − β1 = regression coefficients

Determine the observed boll weight at 5% moisture:

w =

[r (

ja

jb

) (1.0526) + Ka]

(Xa + Tc)
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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75

where

w = observed boll weights at 5% moisture (gin equivalent)

r = weight of seed cotton picked in 10-foot section

ja = weight of seed cotton after drying

jb = weight of seed cotton before drying 

1.0526 = conversion factor to 5% moisture (gin equivalent)

Ka = accumulated adjusted weight of seed cotton

Xa = accumulated bolls picked within unit

Tc = current total open bolls within 10-foot units

Using the example data: 

w =

[650 (

52

56) (1.0526) + 257]

(50 + 130)

= 4.957

Determine the ratio of picked to forecasted large bolls:

X =

(Tc + Xa)

Ŷ

where

X = ratio of bolls picked and weighed to large bolls forecasted

Tc = current total open bolls within 10-foot units

Xa = accumulated bolls picked within unit

Ŷ = forecasted number of large bolls

Using the example data:

X =

(130 + 50)

496.209 = 0.363

For this example, let:

β0 = 0.882

β1 = 0.131

The forecasted boll weight using the calculated inputs: 

Ŵ = 4.957(0.882 + 0.131 ∗ 0.363) = 4.608 grams per boll

Forecast Gross Yield per Acre

The estimated gross yield for this example sample is:
CHAPTER 7 COTTON OBJECTIVE YIELD METHODS

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76

Ĝ =

(2.401)ZBW

R

where

Ĝ = estimated gross yield (lbs. of lint per acre)

Z = lint/seed ratio (3-year average)

B = number of large bolls at harvest in 40 feet

W = average boll weight (grams at 5 percent moisture, gin equivalent)

R = average row spacing

2.401 = 43,560 / (40 * 453.59)

which converts grams of seed cotton per 40 feet of row to pounds of seed cotton 

per acre.

For this example, let:

Z = 0.368

Ĝ =

(2.401) ∗ 0.368 ∗ 496.209 ∗ 4.608

(25.8⁄8)

= 626.45 pounds of lint per acre
CHAPTER 8 WHEAT OBJECTIVE YIELD METHODS

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77

CHAPTER 8 WHEAT OBJECTIVE YIELD METHODS

This chapter presents basic sampling, data collection, and mathematical methods utilized to 

estimate U.S. winter wheat yield and production. The sampling review will emphasize the 

technical differences in winter wheat sampling relative to techniques employed for corn, 

soybeans, or cotton. Data collection will focus on the variety of data collected and how data 

collection changes as the wheat crop matures. The mathematical methods review will center on 

mathematical/statistical estimation of final winter wheat yields utilizing measurable plant 

characteristics observed at specific points during the growing season. The end results of careful 

sampling, data collection, and mathematical methods are numeric indications suitable to 

establishment, and/or revision, of U.S. wheat acreage, yield, and production.

Sample Design

Wheat Objective Yield (WOY) surveys are conducted in the 10 major winter wheat producing 

States: Colorado, Illinois, Kansas, Missouri, Montana, Nebraska, Ohio, Oklahoma, Texas, and 

Washington. These ten states, on average over the last three years, have accounted for more than 

65 percent of U.S. production. A sample of wheat producers to be included in WOY is selected 

each year from among all producers with positive wheat acreage reported during the March 

Agricultural survey. Thus, the major sampling difference in WOY compared to other crops is 

that producers are the sample element for WOY, whereas fields are the sample element for corn, 

cotton, and soybeans. The difference is necessary since Area Frame records are unavailable for 

the current years’ winter wheat plantings. In the past, NASS sampled and enumerated segments 

from the Area Frame during late November to early December specifically for winter wheat 

plantings but discontinued the practice for budgetary reasons. A reasonable alternative to Area 

Frame records for winter wheat yield sampling are the Multiple Frame records collected during 

the March Agricultural survey. The Multiple Frame combines an exhaustive listing of 

agricultural producers, called the List Frame, with producers identified by the Area Frame in a 

manner that producer duplication is minimized, and producer omission is satisfactorily resolved. 

The resulting Multiple Frame is a satisfactory sampling frame for winter wheat yield forecasting. 

Accurate inferences from a probability-based survey require the construction of a sampling 

population and, in addition, a means to select a representative sample from that population. The 

statistical method used to select wheat acres to be included in WOY is probability proportional to 

size (PPS). In statistics, this method ensures a representative sample is selected when sample 

elements vary in their size. The wheat acres sample population is constructed by explicitly 

identifying and separating producers with winter wheat plantings and noting their whole farm 

wheat plantings. Based on this producer record, PPS sample selection assigns higher 

probabilities to producers with a larger percentage of the state’s total wheat plantings. Recall the 

sample design for WOY selects the producer first whereas, for corn, soybeans, and cotton the 

field is selected first. Then for each selected producer, a listing of wheat fields is constructed 

from which the representative field is selected and finally the representative acre is selected by 
CHAPTER 8 WHEAT OBJECTIVE YIELD METHODS

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78

simple random sampling. Since a selected acre is too large for complete enumeration, a selected 

sample will be enumerated and expanded up to the one-acre level.

In mid-April of each year, professional statisticians in the ten WOY states train field enumerators 

to properly identify and prepare selected samples for data collection. Generally, enumerators will 

have many years of experience in WOY data collection and are well qualified to conduct their 

assignments. Practical field training is also available through relationships developed among 

individual enumerators and their supervisors. Overall, the preparation for data collection is 

rigorous and includes quality control processes that continue through the wheat growing season. 

In late April field enumerators will begin visiting and enumerating samples and will continue 

personal visits at monthly intervals throughout the season until final harvest. 

Each sample consists of two units (or plots) to be utilized in forecasting final net yield per acre. 

Each unit consists of three parallel 21.6-inch sections of row. During each visit, enumerators 

count or measure each required plant characteristic, the required characteristics being determined 

according to the units’ maturity level. For example, at early maturities enumerators will count 

plants and measure row spacing. At later maturities, head weights are measured and recorded. 

After each data collection period, a forecast of each unit’s final net yield is constructed. 

Essentially forecasts of wheat yields depend on two items: 1. the current year’s measurable plant 

characteristics and, 2. the historic relationship between plant characteristics measured in previous 

years, at the same level of maturity, and final net yield. Each item is needed to forecast a samples 

final net yield per acre. In cases where the historic relationship is missing, a five-year average of 

the final plant characteristic is substituted. During some early forecasts there may be no plant 

characteristic that NASS measures that can be related to the final net yield. Head weight is the 

prime example. In these cases, historic averages are used to forecast final net yield. 

Data Collected

Field enumerators count and measure several items within or near the units. Data items are used 

to measure the size of the unit, number of heads, weight per head, and harvest loss. The 

following lists the data items collected and objective of these measurements.

Data items used to measure the size of each unit:

Distance between two rows (one row middle)

Distance between five rows (four row middles)

Data items used to forecast or estimate the number of heads:

Number of stalks in each row

Number of late boot heads in each row

Number of emerged heads in each row
CHAPTER 8 WHEAT OBJECTIVE YIELD METHODS

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79

Data items used to forecast or estimate grain weight per head:

Number of fertile spikelets on 10 heads

Number of grains on 10 heads

Weight of mature heads (before threshing) and weight of late boot heads

Weight of grain threshed from mature heads

Moisture content of the threshed grain

Data items used to estimate harvest loss:

Distance between two rows (one row middle)

Distance between five rows (four row middles)

Grain weight of heads between Row 1 and Row 4

Grain weight of loose kernels between Row 1 and Row 4.

Maturity Categories

At each visit, the enumerator makes maturity assessments within the units and a maturity 

category is established for the sample. Forecast equations are estimated using data collected 

during the previous five years, by month, and by maturity classification. The maturity 

definitions used by the enumerators are:

Maturity Definition

1 - Pre-Flag There is no swelling in the stalks and no flag leaf is present.

2 - Flag or early boot A flag leaf is present, and the collar of the flag leaf has emerged 

above the top foliage leaf. The enclosed head is located below the 

collar of the top foliage leaf.

3 - Late boot or Flower The wheat is in the late boot stage from the point where the 

swelling has occurred above the top foliage leaf until the head has 

emerged and will show a water clear liquid turning milky white.

4 - Milk The kernels are soft, moist, and filled with a milky liquid.

5 - Soft dough The contents of the kernels are soft and can be kneaded like dough.

6 - Hard dough The grain is firm and can be dented with the thumbnail, but not 

easily crushed.

7 - Ripe The grain is hard and breaks into fragments when crushed.
CHAPTER 8 WHEAT OBJECTIVE YIELD METHODS

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80

Forecasting and Estimating Number of Heads and Grain Weight per Head for Sample Fields

Wheat is no exception to the general rule of objective yield surveying, i.e., successfully 

forecasting fruit weight is more difficult than forecasting fruit count. Therefore, it should be no 

surprise that over the course of time and program development, one model has been deemed 

sufficient for predicting number of heads whereas two are employed to forecast final weight. The 

regression equations for all three models are developed at the sample level by relating counts and 

measurements of plant characteristics made during the growing season to actual counts, 

measurements, or weights made at harvest time. For example, the April stalk count of a sample 

may be easily related to the number of heads recorded just before farmer harvest in July. Many 

relationships like this are developed for forecasting and each relationship is estimated from the 

most recent five years of data.

The major early season independent variable used to forecast the final number of heads (used for 

pre-flag and flag or early boot maturities) is the observed stalk count. At this stage of 

development there are very few observable plant characteristics that are associated with final 

weight per head. Consequently, to forecast a yield, it is necessary to rely on the historical head 

weight (5-year average) as the forecast of end-of-season head weight.

As the crop develops toward mid-season, more plant characteristics appear that can be accurately 

defined, measured, and related to final yield. It is in this period of early head development (late 

boot or flower) that the plant enters a transition stage. The plant shifts from development of 

vegetative growth to grain development. At this time, it is possible to accurately forecast final 

head numbers. The maximum fruit load has been or is nearly set. The number of emerged and 

late boot heads are used to forecast the final number of heads. It is also possible to make the first 

forecast of head weight based on observable and measurable plant characteristics. Wheat heads 

have spikelets which are clearly distinguishable when the stalk reaches the boot stage. Within 

most of these spikelets one to three grains will form. Therefore, using the number of spikelets in 

a regression equation provides the first current indication of the end of season head weight. 

When the wheat plant reaches the late stages of development (milk and soft dough), the 

physiological processes of the wheat plant are directed totally toward kernel development. Head 

development has also reached the point where kernels are filling and can be accurately identified 

and counted. The observed number of grains per head and the observed clip unit green weight 

per head of emerged and late boot heads are weighted together by their R-square values and used 

at this stage for predicting the final head weight. At this time, forecasts become more precise 

since the effect of unfavorable weather or environmental conditions on final biological yield is 

reduced considerably. 

When a field reaches the hard dough or ripe stage (maturity codes 6 and 7), the sample units are 

harvested. Number of heads, average grain weight per head, and the moisture content of the 
CHAPTER 8 WHEAT OBJECTIVE YIELD METHODS

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81

grain are determined for each sample. The number of heads in the sample units is expanded to 

heads per acre and grain weight per head is adjusted to industry standard moisture of 12 percent. 

These actual yield components are used to compute the final sample gross yield per acre.

Table 1 illustrates the independent variables used to forecast the final number of heads and the 

grain weight per head over all maturity classes.

Table 1. Variables Used to Forecast the Components of Final Yield

Maturity

 Category

Final Number of Heads Final Weight per Head

Independent Variable Independent Variable(s)

Pre-Flag Number of stalks Historical Average

Flag or Early Boot Number of stalks Historical Average

Late Boot or Flower Emerged heads plus

heads in late boot

1. Fertile spikelets per 

head, and

2. Historical Average

Milk Emerged heads plus

heads in late boot

1. Grains per head, and

2. Clip Unit Green 

Weight per head

Soft Dough Emerged heads plus

heads in late boot

1. Grains per head, and 

2. Clip Unit Green 

Weight per head

Hard Dough and Ripe Actual count of emerged 

heads, detached heads, and 

heads in late boot

Actual threshed weight per 

head adjusted to standard 

moisture determined from the 

laboratory work.

The forecast model for final heads per sample has the following form for each maturity class:

yi = a + bxi + εi

where xi is the number of stalks in sample i if maturity is 1 or 2, and a combination of emerged 

heads and late boot heads in higher maturity classes, yi is the number of heads for sample i, and 

εi’s are random departures from the relationship. The historic coefficients a and b are estimated 

by ordinary least squares from data collected during the previous five years. This model 

produces R2’s between 50 and 80 percent for maturity class 1 and 2, in the 80’s and 90’s for class 

3, and in the 90’s to high 90’s for classes 4 and 5. 
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The forecast models for final weight per head are a weighted combination of two regressions for 

each maturity except maturity class 1 and 2 which rely solely on historic weights. The form for 

each model is:

Model 1: wyi = a + bxi + εi

Model 2: wyi = c + dzi + εi

where xi is one plant measure such as the number of fertile spikelets, or the number of grains per 

head, or the weight of harvested green heads, and zi is the other; yi is the final weight of heads 

for sample i, and εi and εi are random departures from the relationship and there is no 

specification for the relationship between εi and εi. The coefficients (i.e., a, b, c, and d) are 

estimated by ordinary least squares from data collected during the previous five years. Table 1 

highlights the variables used for estimating Model 1 and Model 2 for each maturity. Generally 

speaking, Model 1 and Model 2 have poor diagnostics, the R2values begin at 0 percent for 

maturity class 3 and neither model is regularly above 50 percent even for maturity class 5. Since 

Model 1 and Model 2 sometimes lead to performance ambiguity, a composite is constructed for 

each maturity class as follows:

WŶi =

R1

2

(wŷi1) + R2

2

(wŷi2)

R1

2 + R22

where, WŶ iis the weighted forecast of grain weight per head for sample i from Model 1 and 2, 

and R1

2 and R22

 are the multiple correlation coefficients for Model 1 and 2 respectively. In class 

3, the 5-year historic grain weight per head is manually assigned an R2 of .2. 

Forecasting Yield for Sample Fields

GŶi = (ŷi

) ∗ (WŶ i) ∗

CFi

RSi

where, RSi is the row spacing measurement across eight rows and CFi is a conversion factor 

defined as [ (43560)(8)(12) ] / [ (6)(60)(453.58)(21.6) ] = 1.186 adjusts for area measured and 

weight changes from metric to English. The parts are as follows:

43,560 is the number of square feet per acre, 

8 adjusts for measuring across 8 row spaces, 

12 converts inches to feet, 
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6 is rows counted in the sample units, 

60 converts pounds to bushels, 

453.58 converts grams to pounds and 

21.6 is the width of the wheat frame in inches.

State Average Forecasts and Estimates

In each month, the sample level gross yield forecasts are averaged to the State level. Since the 

sample is self-weighting, the simple mean of the sample forecasts is an unbiased estimate of the 

State gross yield. Therefore,

G̅=

1

NG

∑Gi

NG

i

Where G̅represents the mean gross yield for each state,

and the standard error of the estimate is:

SG̅= √∑

(Gi − G̅)

2

NG(NG − 1)

NG

i

Simple means are also calculated for most all independent variables and harvest loss measures. 

These calculations are used to support analysis of the State level gross, or net, yield. Notably, the 

State average grain weight per head is calculated using a weighted mean. The weighting variable 

is the sample’s Heads per Square Foot.

State Average Grain Wt. per Head = ∑(Sample Field Grain Wt. per Head * Sample Field Heads 

per Sq. Ft) / ∑(Sample Field Heads per Sq. Ft)

Harvest Loss

State level harvest loss is forecasted as the mean of all sample level harvest losses.

L̅ =

1

NL

∑Li

NL

i
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where Li is the harvest loss in sample i and NL = number of samples with gleaning data.

SL̅ = √∑

(Li − L̅)

2

NL(NL − 1)

NL

i

State Level Net Yield

Net Yield is a direct extension of the State level aggregates.
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 NY̅̅̅̅ = G̅- L̅

And the standard error of the State level net yield :

SNY̅̅̅̅ = √SG̅

2 + SL̅

2 −

2

NG

COV(G, L)

Where

COV (G,L) = 

N

L



1

(Gi- G )(Li- L )

NL-1

Production for the State

Production, P, for the State is the product of estimated State-level net yield and acres to be 

harvested for grain

P = (Aharv) ( NY̅̅̅̅),

And a standard error of:

SP = √(Aharv

2

)(SNY̅̅̅̅

2

) + (NY̅̅̅̅2)(SAharv

2

) + (SNY̅̅̅̅

2

)(SAharv

2

)

Gross Yield for Samples with Incomplete Data

Gross yield is forecasted or estimated from the current month's survey data. In some cases, 

current data are unavailable and data from a previous month may be used to compute gross yield, 

or no gross yield may be computed for the sample. The different cases are discussed below.

Refusals

If the farmer refuses permission to enter the field, the sample is lost for the season. In this case 

the yield for this sample is left missing. Consequently, the refused sample contributes no new 

information to the state level average yield. The sample, and the acreage represented by it, is 

assumed to be the state’s average gross yield.
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Inaccessible Samples

Occasionally, some samples are inaccessible due to scheduling or field conditions. If data from a 

previous visit are available, the previous forecast is carried forward. Otherwise, the sample is 

excluded from gross yield calculations. The sample must still be intended for harvest as grain.

Early Farmer Harvest

If a previously laid out sample is harvested by the farmer before current data can be collected, 

the previous month's predicted yield is brought forward. 

Lost, Abandoned, Destroyed Samples

If a sample is lost, abandoned, destroyed, and so forth, no gross yield is computed for the sample. 

The sample contributes nothing to the sample-level yield indication.

Removing Bias from State Level Calculations

Forecasts of State level yields are inherently subject to differ from the final, administrativelydetermined, yield. The difference is due to weather and crop conditions yet to be encountered at 

the time the forecast is produced, the difference between weather and crop conditions in the 

current year and the historic weather and crop conditions utilized to predict current yields, and 

systematic non-sampling errors which contribute to forecast error. NASS makes every attempt to 

minimize the impact of these three sources of error by means of administratively determine final 

values. These final, sometimes referred to as official values are used as dependent variables to 

estimate an ordinary least squares equation with the averages calculated from objective yield 

samples as the independent variable. For example, each state will have an administrativelydetermined, official wheat yield for all previous years. To forecast the official wheat yield for the 

current year, NASS regresses the objectively determined State level average wheat yields from 

previous years to the corresponding official wheat yields. This process provides a historical 

context for weather, biases, and non-sampling errors. 

The regression equation is:

yt = a + bx̅t + εt

where yt is the Official state yield in time period t, x̅tis the calculated State average net yield in 

time period t, a and b are ordinary least squares estimates, and εtis a random departure from the 

relationship.
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Computational Examples

Yield

Yield indications are derived by initially calculating the two yield components, number of heads, 

and weight per head. These components are forecasted by applying linear regression models to 

sample data. The models used by a State vary by class of wheat, geographic district, and 

maturity category. The parameters for these regression models are computed from the 5 most 

recent years of historical sample data for that State.

The following pages will demonstrate, by example, how models are used to forecast yield in the 

various sample maturity categories.

Maturity Category 1, pre-flag:

For samples in the pre-flag maturity category, the sample variable used to forecast number of 

heads is number of stalks. The variable to forecast the weight per head is the historical average 

weight per head.

Suppose the appropriate regression models are:

Number of heads = 180 + .2 * (total number of stalks),

and

Weight per head = .64

If the sample has 920 stalks, then the forecasted number of heads = 180 + .2 * (920) = 364.

Therefore, the forecast of gross yield per acre from a sample with an 8-row width of 6.4 would 

be: 

Gross yield = [(number of heads)(weight per head)(conversion factor)] / (8-row width)

= [ (364)(.64) (1.186) ] / 6.4 = 43.17.

Maturity Category 2, flag or early boot:

For samples in the flag or early boot maturity category, the sample variable to forecast number of 

heads is number of stalks. The variable to forecast the weight per head is the historical average 

weight per head.
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Suppose the appropriate regression models are:

Number of heads = 90 + .4 * (total number of stalks)

and

Weight per head = .64

If the sample unit has 650 stalks, then the number of heads = 90 + .4 * (650) = 350.

Therefore, the forecast of gross yield per acre from a sample with an 8-row width of 6.4 would 

be:

Gross yield = [(number of heads)(weight per head)(conversion factor)] / 8-row width

= [ (350)(.64) (1.186) ] / 6.4 = 41.51

Maturity Category 3, late boot or flower:

For samples in the late boot or flower maturity category, the variable to forecast number of heads 

is the sum of emerged heads and heads in late boot. Two models are used to forecast weight per 

head. The first model uses the number of fertile spikelets per head and the second model uses 

the historical average head weight. These are weighted together using R-square of the first 

model and a weight of 0.2 for the second.

Suppose the appropriate regression models are:

number of heads = 23 + .9 * (total number of emerged heads + heads in late boot)

weight per head (Model 1) = .12 + .04 * (number of fertile spikelets), with an R-square 

of .31

weight per head (Model 2) = .64

If the sampled unit has a total of 336 emerged heads and heads in late boot, and 15 fertile 

spikelets per head, 

then, 

number of heads = 23 + .9 * (336) = 325, 
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and weight per head (Model 1) = .12 + .4 * (15) = .72

The composite weight per head forecast is:

 weight of heads = R

2 Model 1(wt per head Model 1) + R2 Model 2(wt per head Model 2)

R

2 Model 1 + R2 Model 2

so that in this example:

weight per head = [.31(.72) + .20 (.64) ] / [ .31 + .20 ] = .69

Therefore, with 8-row width of 6.4,

Gross Yield per Acre = [ (number of heads)(wt per head)(conversion factor) ] / 8-row 

width

= [ (325)(.69)(1.186) ] / 6.4

= 41.56

Maturity Category 4, milk:

For samples in the milk maturity category, the variable to forecast number of heads is the sum of 

emerged heads and heads in late boot. Two models are used to forecast weight per head. The 

first model uses the number of grains per head and the second model uses the clip unit green 

weight per head. There are weighted together using the R-squares of the models.

Suppose the appropriate regression models are:

number of heads = 6 + 1.0 * (total number of emerged heads + heads in late boot),

weight per head (Model 1) = .59 + .003 * (number of grains per head), with an R-square 

of .95, 

and

weight per head (Model 2) = .5 + .16 * (clip unit head weight), with an R-square of .97

If the sampled unit has a total of 331 emerged heads and heads in late boot, 18 grains per head, 

and a clip unit green weight of .74, 

then
CHAPTER 8 WHEAT OBJECTIVE YIELD METHODS

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90

number of heads = 6 + 1.0 * (331) = 337,

weight per head (Model 1) = .59 + .003 * (18) = .64, 

and

weight per head (Model 2) = .5 + .16 * (.74) = .62

The composite weight per head forecast is

wt per head = R

2 model 1(wt per head Model 1 )+R2 Model 2(wt per head Model 2)

R

2 Model 1 + R2

 Model 2

so that in our example

weight per head = [ .95 (.64) + .97 (.62) ] / [ .95 + .97 ] = .63

Therefore, with 8-row width of 6.4,

Gross yield per acre = [ (number of heads)(wt per head)(conversion factor) ] / 8-row 

width

= [ (337) (.63) (1.186) ] / .64 = 39.34

Maturity Category 5, soft dough:

For samples in the soft dough maturity category, the variable to forecast number of heads is the 

sum of emerged heads and heads in late boot. Two models are used to forecast weight per head, 

one using the number of grains per head and the other using the clip unit green weight per head. 

These are weighted together using the R-squares of the models. 

Suppose the appropriate regression models are:

number of heads = 7 + 1.0 * (number of emerged heads + head in late boot),

weight per head (Model 1) = .33 + .02 * (number of grains per head), 

with an R-square of .98,

and

weight per head (Model 2) = .37 + .33 * (clip unit green wt.), 

with an R-square of .99.

If the sample unit has a total of 332 emerged heads and heads in late boot, 21 grains per head, 

and a clip unit head weight of .93, 
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91

then

number of heads = 7 + 1.0 * (332) = 339, 

weight per head (Model 1) = .33 + .02 * (21) = .75, 

and 

weight per head (Model 2) = .37 + .33 * (.93) = .68

The composite weight per head forecast is

wt per hd = R

2 model 1(wt per hd Model 1) + R2 Model 2(wt per hd Model 2)

 R

2 Model 1 + R2 Model 2

so that in the example

weight per head = [ .98 (.75) + .99 (.68) ] / [ .98 + .99 ]

= .71

Therefore, with an 8-row width of 6.4,

Gross Yield Per Acre = [ (number of heads)(wt per head)(conversion factor) ] / 8-row 

width

= [ (339) (.71) (1.186) ] / 6.4 = 44.60

Maturity Categories 6 and 7, hard dough and ripe:

Actual number of heads and actual head weight are used to calculate gross yield per acre. The 

following final lab data and gleaning counts and measurements are obtained for a sample:

number of emerged heads, detached heads, and heads in late boot = 350,

moisture content of enumerator harvested grain = 12%, 

number of heads threshed = 250, and 

threshed weight of grain = 180

weight of gleaned grain = 20 

moisture content of post-harvest gleaning grain = 14%

Calculate weight per head, gross yield per acre, harvest loss per acre, and net yield.

Wt. per Head = [(threshed wt of grain)(1.0 - moisture) ] / [ (number of heads threshed) 

(.880)]
CHAPTER 8 WHEAT OBJECTIVE YIELD METHODS

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92

= [ (180) (1.0-.12) ] / [ (250) (.880) ]

= .72

Assuming an 8-row width of 6.4,

Gross Yield Per Acre = [ (number of heads)(wt per head)(conversion factor) ] / [ 8-row 

width ]

= [ (350) (.72) (1.186) ] / 6.4

= 46.70

Harvest loss per acre = [(wt of threshed grain)(1.0-moisture content of grain) 

(conversion factor) ] / [(.880)(8-row width)]

= [ (20) (1-.14) (1.186) ] / [ (.880) 6.4 ]

= 3.62

Net Yield = Gross Yield - Harvest Loss

= 46.70 - 3.62

= 43.08
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CHAPTER 9 PREPARATION OF OFFICIAL STATISTICS

Overview

A fundamental principle behind the estimation process is that precision of the sample survey 

estimates is greatest at the aggregated regional and U.S. levels. The precision of a sample survey 

estimate is measured by the estimated sampling error. In theory, many independent sample 

surveys could be conducted simultaneously, each producing estimates of acreage, yield, or 

production. The extent to which these independent estimates would differ from each other is 

called the sampling error and can be estimated from each sample. For NASS surveys, the 

sampling error at the U.S. level for corn acres is about 1.0 percent, 2.3 percent in major States 

and 10-15 percent in other States.

The sample surveys are designed to produce State level estimates of acreage, expected yields, 

final yields, and total production. The surveys are conducted by each State, and the first level of 

analysis is done by each State. Each Regional Field Office does its independent appraisal of the 

relationships between the survey estimates and the final official statistics and forwards this 

information to Headquarters.

While each Regional Field Office is analyzing its survey data, statisticians in Headquarters are 

doing a parallel analysis of all survey data at the State, U.S., and regional levels. For the major 

field crops discussed in this paper, a formal Agricultural Statistics Board is convened to review 

regional indications and determine the official forecast or estimate. This Board is made up of 7 to 

10 statisticians representing different divisions of NASS. Each Board member evaluates the 

regional survey indications and supporting data and determines their forecast or estimate. Each 

member brings their individual perspective to the review which can result in different 

conclusions being drawn. Through review and discussion, the Board must collectively reach a 

consensus and establish the National number. The Board process ensures all perspectives are 

examined and the national or regional forecast or estimate is the result of a thorough analysis. 

The summation of the individual State estimates as prepared by each State is compared to the 

Board number. The Headquarters statisticians will re-examine all national and State data 

relationships and either adjust State estimates, so they sum to the U.S. or change the previously 

determined U.S. number.

Domestic supply is a key factor in the marketing of any commodity and affects the day-to-day

business decisions of the industry. As a result, crop production forecasts and estimates are 

extremely sensitive data. Premature or privileged disclosure of NASS numbers would give 

individuals or groups an unfair advantage in the marketplace. NASS must ensure that all official 

numbers are made available to everybody at the same time, making security a very big issue. All 

data, both individual and summary, are protected against disclosure at every step of the 

forecasting and estimating process. Data access must be always restricted in the Regional Field 
CHAPTER 9 PREPARATION OF OFFICIAL STATISTICS

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94

Offices and Headquarters. As data are summarized and aggregated to regional or national levels, 

the security is heightened. Yield forecasts and estimates from the largest producing States are 

encrypted before transmission to Headquarters. As data are received in Headquarters and 

commodity statisticians begin the review process, offices are designated as secure offices and 

visitors are denied access.

The formal meeting of the ASB to establish the final numbers and prepare the report is 

conducted under “lock up” conditions. Lock up begins with a complete isolation of all facilities 

required by the Board. All doors are locked, windows and elevators are covered and sealed, 

phones are disconnected, and the computer network inside “lock up” is isolated from the full 

network. Transmitters are not permitted, and the area is monitored for electronic signals. Highly 

speculative data are decrypted only after the area is secure. Only after all security is in place does 

the Board begin final deliberations. The area remains locked up until a prescribed release time 

(12:00 p.m. for Crop Production) at which time the report is disseminated in electronic and paper 

forms.

This chapter is devoted to describing the interpretation process followed by commodity 

statisticians to arrive at the best number. A brief discussion of acreage estimates is followed by a 

detailed explanation of forecasting yields. The last two parts address end of season estimates of 

acreage, yield, and production followed by an overview of how balance sheets are used as a 

check on the final estimates.

Acreage Estimates

The summary programs provide point estimates of acreage planted, called direct expansions, 

and measures of change from a previous estimate, called ratio estimates.

Direct expansions measure the level of the value of the item being estimated. For area frame 

surveys, every segment of land selected from the area frame has a known probability of 

selection. The inverse of the probability of selection for each sample unit (expansion factor) 

multiplied times the acres found in the segment are summed across the sample to determine a 

direct estimate of acres planted to each crop. List samples also have known probabilities of 

selection and their data can be similarly expanded to provide direct expansions in a multiple 

frame design.

Ratio estimates are used to measure change from a previous estimate of the same item 

(preliminary acres for harvest) or a related item (previous year’s planted acres). These types of 

ratios rely on matched reports from both surveys. The area frame sample is divided into five 

independent rotation groups with four groups carried over from one year to the next. The 

consecutive year’s data from these four rotation groups can be matched to provide a measure of 

the percent change in acres planted. The list sample can be similarly structured to provide survey 

to survey matched samples and ratios can be computed in the multiple frame design.
CHAPTER 9 PREPARATION OF OFFICIAL STATISTICS

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The determination of the official estimates of acres planted is based on an analysis of the 

historical and current direct expansions and ratio estimates as they compare to the final estimates 

of planted acres. The analysis is based on “difference” estimates which measure the average 

difference between the survey indications and the final estimates. This analysis is done at both 

the State and U.S. levels with any differences being reconciled in Headquarters.

The June Area Survey (JAS) and the June Agricultural Survey provide the benchmark estimates 

of acres planted. In some years, weather related problems delay planting activities which means 

farmers are reporting acres they still intend to plant. When this occurs, subsamples of farms 

included in the JAS are re-surveyed in July to determine the acres actually planted. These 

updated acreage estimates are reviewed similarly to the procedures followed in June. Yield 

surveys provide ratio indications which are used to monitor changes in acreages.

Acres harvested and to be harvested are key variables for deriving production forecasts and 

estimates, respectively. Direct expansion and ratio of change estimators are also used to estimate 

harvested acres. In addition, the ratio of harvested to planted acres as provided by the survey can 

be multiplied times planted acres for another indication of harvested acres. The “difference” 

analysis described above is also used to determine the official harvested acreage estimates.

Yield Forecasts

Arguably, the most watched publications of NASS are the Crop Production Reports containing 

the early season forecasts of production for the major field crops. Early season production 

forecasts are key pieces in the price discovery mechanism for these billion-dollar crops. This 

kind of scrutiny demands a review as comprehensive as the security provisions to ensure the best 

forecasts and estimates.

The yield surveys produce vast amounts of data for analysis. The modeling processes described 

in previous chapters produce multiple indications of net yield per harvested acre. The first 

monthly forecasts for a crop feature some key indications that include but not limited to average 

field level yield regressed to official estimates, average counts regressed to official estimates,

average projected yield reported by farmers in the Agricultural Yield (AY) Survey regressed to 

official estimates, and model-based indications. Once harvest begins, average realized farmer 

yields are regressed to official estimates. In addition to the point estimates, forecast errors of the 

regression equations and models are also computed. Adding and subtracting these forecast errors 

from the forecast value forms a forecast range for each indication. Usually, the ranges for these

indications overlap defining the range that simultaneously satisfies all forecasts. 

Merely selecting a yield from within the overlapping range is not the end of the process. 

Commodity statisticians must determine if all of the other pieces of available data support the 

“candidate” yield forecast. Some of the more important things to evaluate are:
CHAPTER 9 PREPARATION OF OFFICIAL STATISTICS

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96

1. Average maturity category - Enumerators determine the maturity category of each OY 

sample. The average maturity category helps commodity statisticians align the crop 

calendar with the monthly report calendar. This maturity should be consistent with 

weekly crop progress data. Extremely late (below average maturity) crops and extremely 

early (above average maturity) crops often produce data that lie in the fringes of the 

historical data and may result erratic forecasts due to extrapolating the forecast equations.

2. Forecasted fruit count - Even in the first survey month, plant counts are obtained for all 

OY samples and forecasts of the number of fruit per acre can be made every month for 

every crop regardless of maturity. As the fruit develop, counts of immature fruit are used 

to provide even more precise forecasts of fruit expected at harvest. Experience has shown 

that forecast equations for fruit count have very high R-square values and produce very 

accurate forecasts. In fact, the linear relationship is so strong these equations are robust 

against extrapolation.

3. Forecasted fruit weight - As easy as it is to forecast count, forecasting weight is equally 

difficult. In the early months, there is no measurable characteristic to use in a model and 

historical average fruit weights must be used. Even after the fruit set and measurements 

can be made, data are extremely variable, and correlations are not very high. Thus, fruit 

weight forecasts have much larger forecast errors than fruit count. Extreme maturities can 

significantly impact weight models. Fruit weight often becomes the key discussion factor 

in Board deliberations. 

4. Averages of the raw data - The raw counts are definitionally stable across years. As noted 

in earlier chapters, parameter estimates for the forecast equations are recomputed each 

year using a “rolling” dataset. Changes in forecasts from one year to the next are a 

combination of changes in the current raw counts and new equations. These changes are 

confounded in the forecast and isolating the changes in farmer practice from the 

differences in the crop season from the trends in yield is difficult. The raw counts give 

insight into true shifts in the components of yield like planting patterns and plant 

populations, fruit per plant, size of ears, etc. When the number of plants per acre is higher 

than ever recorded before, a record fruit count forecast and, possibly, a record yield 

should be no surprise.

5. Interaction of fruit count and fruit weight - Statisticians can obtain insight into yield 

levels by looking at the interaction of the two main components, count and weight. The 

final yield may be the same for 2 years, but they may be a result of different components. 

A simple scatterplot of count against weight with points labeled as to year clearly show 

how the current forecasts compare to the final estimates of previous years.
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6. Month to month shifts - Each of the five items discussed above can apply to a standalone, single month analysis. However, after the first forecast month, each can be applied 

in a month-to-month analysis. The second and third forecasts are measured against the 

previous forecast and the statistician must understand what is causing the indications to 

move up or down. Are the raw counts and measurements changing? Are the models 

forecasting the components at a different level? How are the farmer assessments of their 

yield prospects in the AY survey changing? What effect is final harvest data having on 

the indications?

This process is done independently in each State and at the combined level in Headquarters. 

Headquarters statisticians make the final determination, and, when necessary, will establish 

forecast or estimate that differs from the State(s) recommendations so the State numbers are 

additive to the U.S. level.

Final Estimates - Acres, Production, Stocks

Chapter 2 contains a discussion of the Agricultural Surveys and how they relate to yield surveys. 

The September and December Agricultural Surveys are the vehicles by which final acreage, 

yield, and production data are obtained. Final end-of-year estimates are prepared from these data. 

The September survey focuses on the small grains and is timed to be conducted as harvest is 

nearly complete. The December survey collects the row crops end of season data, and it is also 

timed to occur as harvest winds down. Respondents to these surveys report actual acres 

harvested and the actual yield or production realized from harvest. Grain in storage data are 

collected at this time and are used to estimate “carry out” stocks which are used in balance sheet 

reviews of the major crops. 

The OY sample plots are harvested at crop maturity. A sample of plots are gleaned for harvest 

loss after the sample fields are harvested. These crop cuttings form a secondary final yield 

indication, but, more importantly, they are used to compute parameter estimates in future years. 

The final OY observations serve as the values of the dependent variables of the regression 

models.

Balance Sheets

The end-of-season estimates of acres harvested, yield, production, and stocks are reviewed in 

combination using a balance sheet approach. Up to this point, the approach is to consider acres 

and yield independent of the supply and demand relationship. The balance sheet offers a more 

global look at how the estimates fit into the bigger picture. Using estimates from NASS surveys, 

and administrative data from outside sources, commodity statisticians can construct a balance 

sheet to see if the estimates reconcile with these sources. Using corn as an example, a December 

1 balance sheet analysis would look as follows:
CHAPTER 9 PREPARATION OF OFFICIAL STATISTICS

THE YIELD FORECASTING PROGRAM OF NASS

98

Quantity carried over from previous year (September 1 on-farm and off-farm stocks for 

corn and soybeans, June 1 for wheat)

Plus Imports since September 1

Current Production (NASS estimate)

Equals Beginning supply as of December 1

Minus Disappearance since September 1

Exports

Processing

Feed and seed

Balance Sheet Indication of December 1 stocks

Survey Indications of December 1 stocks (on farm and off farm)

Residual

The residual component of the balance sheet is the difference between the survey indicated 

stocks and the balance sheet stocks. Each survey component of the balance sheet contains 

sampling and non-sampling errors. The disappearance items such as exports and processing are 

based on administrative sources with varying levels of completeness. For these reasons, it is not 

reasonable to expect a zero residual; however, an unreasonable residual is cause for alarm and 

triggers a second review of the elements in the balance sheet. The objective is to have a 

reasonable balance and still have the estimates within the range indicated by the surveys.