Do Nof RemoVeFILE COpy -

United States

Department of

Agriculture

National

Agricultural

Statistics

Service

Research and

Applications

Division

SRB Staff Report

Numl>er SRB-90-0R

MA THEMA TICAL FORMULAE

FOR THE 1989 SURVEY

PROCESSING SYSTEM (SPS)

SUMMARY

May IYYO Phillip S. Kott
MATHEMATICAL FORMULAE FOR THE 1989 BURVEY PROCESSING

SYSTEM (SPS) SUMMARY, by Phillip S. Kott, Research

and Applications Division, National Agricultural

Statistics Service, U.S. Department of Agriculture,

Washington, DC 20250, May 1990. NASS Staff Report,

Number SRB-90-08.

ABSTRACT

The 1989 Survey Processing System (SPS) Summary was

designed to summarize the results of the six

agricultural surveys from June 1989 to March 1990,

the four labor surveys from July 1989 to April 1990,

and the August 1990 rice stocks survey. This report

is primarily an attempt to document statistical

formulae incorporated into the 1989 SPS Summary. The

focus is on providing equations for the expansions,

ratios, standard errors, and coefficients of

variation found in SPS Summary Tables 3 through 7.

Although the emphasis is on stating the formulae not

on justifying their use, informal arguments for

particular formulations will be given - especially

when there are no other readily available references.

ACKNOWLEDGMENTS

The report has had many drafts. In the course of

making the many refinements that ultimately lead to a

more accurate and (I hope) useful product, I have had

the help of very many talented and knowledgable

people. Among them were Huong Luong, Bill Iwig,

Martha Roehrenbeck, Mike Clark, Ned Jones, Bob Hale,

Jerry Thorson, Brad Pafford, Carol House, Dave

Dillard, Tim Placke, Rick Kestle, and Barry Ford. I

thank them all. In particular I would like to thank

Jack Nealon for his early and continuous support of

this endeavor. Jack reviewed about half of the 11

drafts and supplied the quote at the bottom of this

page. I apologize to all those I have missed.

May 1990

Washington, DC

"I don't believe in mathematics."

- ALbert Einstein

i
TABLE OF CONTENTS

AUTHOR'S FOREWORD iv

I.

II.

INTRODUCTION

OVERVIEW

Base and Follow-on Surveys

Multiple Frame Estimators

List Frame Estimators

Area Frame Estimators

Indications

The Labor Survey

1

2

2

2

3

4

5

5

III. MATHEMATICAL PRELIMINARIES

Reporting Units, Survey Items,

and List Adjustment Factors

Nonresponse Adjustments

Variances, Standard Errors, and CV's

7

7

8

9

IV. LIST EXPANSIONS 10

VI.

v.

Direct Expansion

Reweighting

Livestock Estimators

Variances

AREA EXPANSIONS

Direct Expansion - the Base Survey

Variances - the Base Survey

Direct Expansion - a Follow-on Survey

Variances - a Follow-on Survey

July Cattle and December Chicken

MULTIPLE FRAME EXPANSIONS

AND AGGREGATION

Direct Expansion

Variances

ii

10

11

12

13

15

15

17

17

19

22

24

24

25
a Base Survey

a Follow-on Survey

VII RATIO ESTIMATORS

Introduction

Item-to-Item

Item-to-Item

Base-to-Base

Survey-to-Survey

Digitized Land Expansions

26

26

27

29

30

33

36

VIII. AGRICULTURAL SERVICES 37

IX. YEARLY AGGREGATES 40

The

The

The

The

NOL Component of variance for July

NOL Component of Variance for October

List Component of Variance for July

List Component of Variance for October

41

42

42

45

X.

XI.

GLOSSARY OF TERMS

REFERENCES

iii

47

54
AUTHOR'S FOREWORD

When the Survey Processing System Summary team was

organized, I as the representative of the Survey

Research Branch (SRB) was given the task of making

sure the mathematical formulae incorporated into

the new Summary were correct. It seemed to me

that the best way to accomplish that task was to

create a report spelling out exactly what those

formulae were. Now over a year later the report

in ready for publication. It is being issued as

an SRB staff report bearing the year "1989" in its

title. It is my sincere hope that this report

will be updated every year, although whether that

task should remain the responsibility of the SRB

remains to be decided.

Phillip S. Kott

April 30, 1990

Washington, DC

iv
I. INTRODUCTION

The 1989 Survey Processing System (SPS) Summary

was designed (in principle) to summarize the

results of the six agricultural surveys from June

1989 to March 1990, the four labor surveys from

July 1989 to April 1990, and the August 1990

rice stocks survey. See [1] and [2] for more

information on 1989 agricultural and labor surveys

(note: "1989" refers to the year of the frame not

necessarily the year of the survey).

The SPS Summary is by its very nature dynamic. It

will change over the years as the National

Agricultural statistics Service (NASS) extends its

use to reimbursable surveys and employs more

sophisticated sampling and estimation strategies.

This report is primarily an attempt to document

statistical formulae incorporated into the 1989

SPS Summary. The focus is on providing equations

for the expansions, ratios, standard errors, and

coefficients of variation found in SPS Summary

Tables 3 through 7. Although the emphasis is on

stating the formulae not on justifying their use,

informal arguments for particular formulations

will be given - especially when there are no

readily available references.

The terminology used in this report does not

always conform to standard NASS practice, which is

constantly evolving and therefore the subject of

some confusion. A glossary of many of the

technical terms used here has been appended to the

report.

One particular note on terminology is in order at

this point. The text and glossary use tne word

"estimator" to refer to an estimation formula.

Following NASS practice, the word "indication" is

used in this report in place of "estimate" to

denote the result of applying an estimator to a

set of survey values.

More information on the SPS Summary, including

topics not discussed here (for example, Summary

Tables 1 and 2 and exact Table terminology) and

those covered only superficially (like unexpanded

counts), can be found in [3; section 8] and [4;

section 8].

1
II. OVERVIEW

Base and Follow-on Surveys

NASS uses multiple frame estimatior strategies to

calculate many of its indications. This is

because most of NASS's lists of potential farms

are incomplete, while estimates based purely on

area samples are often statistically inefficient.

The June Agricultural Survey is called the base

survey. The base survey is composed of a

(stratified) random sample of area seqments (see

[5J or [6] for a description of the selection

process) and a list sample of names associated

with potential farms. Sometimes the area segments

are used by themselves to make estimates for the

states (for numbers of farms, land in farms, and

crop acreages). More often they are combined with

estimates calculated from list fri.!J)les.

All other surveys covered by the 19S9 SPS Summary

employ multiple frame estimators

exclusively. These follow-on su:r_y.:~ys rely on

subsamples of tracts from the June area sample to

account for agriculture from farms not on NASS

list franC's.

Multiple Frame Estimators

As noted already, all follow-on surveys use

multiple frame (MF) estimators. ¥or the purpose

of the 1989 SPS Summary, they are all dual-frame

estimators (list frames coupled with area frames)

with the exception of the agricultural services

survey (a component of the labor ~urvey) in

California and Florida. The nature of that survey

will be explained briefly in a later section of

this chapter and with more detail in Chapter VIII.

There are five different types of MF estimators

used with the base survey (more (jet_ailson the

terms overlap, nonoverlap, extrene operator,

non-extreme operator, closed, open, and weighted

can be found in later sections and the glossary):

1. The overlap MF with closed nonoverlap (the

OL-MFjclosed) estimator -- for indications of crop

acreages.

2
2. The overlap MF with weighted nonoverlap (the

OL-MF/weighted) estimator -- for indications of

grain stocks, hogs, and cropland acreages in 10

states.

3. The extreme operator MF estimator with closed

non-extreme operators (the EO-MF/closed) estimator

for indications of hogs and (July) cattle.

4. The EO-MF with open non-extreme operators (the

EO-MF/open) -- for indications of hogs in 10

states.

5. The EO-MF with weighted non-extreme operators

(the EO-MF/weighted) estimator -- for indications

of hogs in 10 states.

The EO-MF/closed estimator for the JULY CATTLE

survey combines a July list sample with the June

area sample. All other follow-on agricultural

indications use the OL-MF/weighted estimator

exclusively, while labor indications use the

OL-MF/open estimator (heretofore unmentioned, but

self-explanatory).

List Frame Estimators

Each of the lower 49 states has at least three

list frames -- one for hogs, crops, stocks, and/or

chickens (called the hog/crops frame), one for

cattle/sheep/goats, and one for basic (or farm)

labor. Many states also have trout and/or catfish

list frames. For our purposes, the only other

frame of interest is the agricultural services

frame in California and Florida (there will be

more on this frame in a later section).

Each frame is a list of names (associated with

potential farms) organized into list strata. The

names in a particular stratum are believed to be

associated with farms having similar sizes with

respect to a relevant agricultural characteristic

(e.g., its peak number of cattle for the

cattle/sheep/goats frame).

Some of the strata in each hogs/crops and

cattle/sheep/goats frame are composed entirely of

(presumably) large farms called extreme operators

or EO's. Naturally enough, these strata are

3
called "EO strata."

NASS draws a without replacement simple random

sample of names from each stratum in a list frame

when that frame is relevant for a survey at hand;

for example, a stratified simple random sample is

drawn from a state's hogs/crops frame but not from

its basic labor frame for the base survey.

After the sampling units are contacted,

indications of list frame totals are calculated.

More on the mechanics of this is reserved for a

later section.

NASS is also interested in hog totals based on

hogs/crops EOls sampled in the base survey and

cattle totals based on cattle/sheep/goat EO's

sampled in the July agricultural survey. This 1S

for NASS's EO-MF estimators.

Area Frame Estimators

A random sample of area segments is selected as

part of the base survey. A tract is the land area

within a segment under one land operating

arrangement. Indications of number of farms, land

on farms, and crop acreages are computed using

information from the operators of these tracts

with the closed (land in farms, crop acreages),

open (number of farms, land in farms) and weighted

(number of farms, cropland acreages in 10 states)

estimators. Precise definitions of these three

estimators can be found in [5] or :6]. The

glossary may also be of some help.

Tracts that are contained in farms that are on a

particular list frame are called oyerlaps or OLls

(with respect to that frame). Conversely, tracts

not on farms on a list frame are called

nonoverlaps or NOLls. Similarly, tracts can be

EO's (extreme operators) or NEO's (non-extreme

operators) .

Multiple frame estimators combine estimators for a

list frame (or its EO's) with area frame

estimators. For the base survey, it is necessary

to set data values to zero for OL tracts when

employing an OL-MF estimator. Likewise, it is

necessary to zero out EO's when employing an EO-MF

4
estimator. For follow-on surveys, only NOL tracts

are subsampled, so nothing has to be zeroed out.

We will call the closed estimator that zeroes out

OL tracts "the NOL-closed estimator" since using

it can provide an indication for total values from

farms not in the list frame. The NOL-open,

NOL-weighted, NEO-closed, and NEO-weighted

estimators are defined in analogous manner.

Indications

This short section tries to map the estimators

discussed above with some of the indication

terminology commonly used by NASS.

As noted in the introduction, an estimator is

applied to survey data to get an indication.

Since there are no closed or weighted estimators

for hogs based purely on area frame data from the

base survey, NASS often calls indications

calculated from the EO-MFjclosed estimator for

hogs "closed indications." Likewise, the

EO-MFjopen and EO-MFjweighted estimator for hogs

are said to produce open and weighted indications,

respectively. In the same spirit, the combination

of EO's from the July cattle survey and the

NEO-closed cattle indication from the base survey

is called the "mid-year closed cattle indication."

Another name often used for a closed indication is

a "tract indication." An open indication

(produced from using the open estimator with area

frame data only) is also called a "farm

indication."

Finally, an indication from an OL-MF estimator is

often called simply an "MF indication," since

indications from EO-MF estimators are named after

their component NEO estimators; e.g., the closed

indication of hogs.

The Labor Survey

The labor survey has two parts: a basic (or farm)

labor survey and an agricultural (ag) services

survey. The basic labor survey is conducted in

all states, while the agricultural services survey

is conducted exclusively in California and

5
Florida. The former is a survey of list names (of

potential farms) and NOL tracts, thl~ latter a

survey of ag services - providers of laborrelated services that need not themselves be

farms.

In states other than California and Florida, the

reporting units of the basic labor survey also

provide information on labor provided to them by

ag services. A survey item that involves both

farm labor and ag services labor is called a total

labor item. In states other than California and

Florida, indications for ag services and total

labor items are derived in the same manner as farm

labor items.

In Chapters III through VII, referE~nces to the

labor survey apply specifically to the basic labor

survey. Chapter VIII discusses the ag services

survey in California and Florida. It also deals

with estimators of total labor items in those two

states. (Note: in states other than Cal ifornia

and Florida, total labor items are handled as

normal survey items of the basic labor survey.)

Another feature of the SPS Summary is the

computation of yearly aqqreqates for certain

labor survey items. This is discussed in Chapter

IX. It should also be noted that survey-to-survey

and base-to-base ratios (dealt with in Chapter V)

are not computed for any labor survey items.

6
III. MATHEMATICAL PRELIMINARIES

Reporting units, Survey Items, and List Adjustment

Factors

NASS draws a distinction between the names or

selected units on its list frames and the

reporting units or sub-tracts that actually

respond to its surveys. Each selected unit is

composed of at least one sub-tract. (NASS often

calls a reporting unit in the base survey from the

list frame a "tract" rather than a "sub-tract."

We will not follow that practice here.)

Area tracts are the reporting units for the area

frame portion of the base survey. For follow-on

surveys, however, it is possible for an area tract

(the selected unit) to subdivide into separately

reporting sub-tracts.

A survey item value is a quantitative answer to a

particular survey question or a function of those

answers. One such function is the sum of winter

wheat, durum wheat, and spring wheat from the June

Agriculture Survey. Two derived survey items

(i.e., functions of survey answers) merit

particular mention. A domain variable (used in

domain estimation) is a function of another survey

item value that equals that value only when the

respondent is within a certain domain; it is zero

otherwise (for example, a respondent's inventory

of hogs if he has 1 to 99 hogs, zero if he has no

hogs or more than 99 hogs). A count or count

variable is a survey item value that can only be

zero or one: 1 when a particular survey item

value is positive, 0 otherwise.

Let qis be a raw survey item value for sub-tract s

of selected unit i, and let

Yis = Lisqis' (1)

where Lis is the list adjustment factor (LAF) for

sub-tract s (see below).

An LAF is a scalar adjustment to item values

that accounts for more than one sub-tract being

associated with the same farming arrangement.

(Note: Lis is equal to 1 for an area tract in the

base survey.)

7
IN THIS REPORT, WE WILL REFER TO Yis (not qis) AS

THE SURVEY ITEM VALUE of s.

The survey item value for the selected unit 1 is

Yi = L: Yis ( 2 )

where the summation is over every sub-tract s

within selected unit i. (In Chapter V, selected

units for follow-on surveys are denoted with the

subscript rn rather than i.)

Nonresponse Adjustments

NASS has three methods of adjusting to nonresponse

caused by a reporting unit being either

inaccessible, refusing to participate in the

survey at all, failing to answer particular

questions, or giving obviously incorrect (i.e.,

edit failing) answers to particular questions.

These methods are hand imputation, machine

imputation, and reweiqhting.

Hand imputation is conducted by NASS usually in a

state office. This is the act of filling in an

unreported survey value or changing an obviously

incorrect value based usually on judgement but it

can also happen during the edit .l2..t_9gram (which

means it need not literally be done by hand) .

Hand imputation occurs before the SPS Summary

gets the data. Survey item values based entirely

on information provided either by a reporting unit

or by hand imputation (this includes LAF

information) are called usables. In contrast to

previous practice, usability is defined here on an

item by item basis. If a survey item is the sum

of other items, it is usable only when its

components aLe all usable.

Missing item values for CROPS and STOCKS (except

COUNTS) are machine imputated by the imputation

program described in detail in [7]. Missing LAF's

for crops, stocks, and TOTAL LAND expansions are

also imputed. SURVEY VALUES THAT ARE EVEN

PARTIALLY MACHINE IMPUTED (including the Lis from

equation (1)) ARE NOT CONSIDERED USABLES

Reweighting is a process of adjusting the

expansion factor in an estimator formula to

account for missing responses. The LABOR survey

8
uses reweighting both in its area frame and list

frame estimators. One LIVESTOCK estimator (called

the presence estimator) employs a more complicated

reweighting scheme on the list side only (all

missing livestock values on NOL tracts are hand

imputed). There is also direct expansion

livestock estimator that uses reweighting in a

straightforward manner, again, on the list side

only.

Reweighting is done as part of the SPS Summary.

Moreover, since variances can not be correctly

estimated in the conventional manner when there is

machine imputed data (see [8]), variances for

crops and stocks are conservatively estimated

using the formula based on reweighting (described

in the following chapters). Additional errors

caused by hand imputation are ignored by the SPS

Summary.

variances, standard Errors, and CV's

Suppose Z is an estimator used in the SPS Summary,

and V is the estimator for the variance of Z.

(When Z is an estimated total, it will be denoted

by Y. When Z is a ratio, by R.)

The estimator for the standard error of Z is

SE = jv,

while the estimator for the coefficient of

variation (CV) of Z (in percent terms) is

CV = (SEjZ) x 100.

(3)

(4)

This report contains formulas for estimators of

totals and ratios and for estimators of

variances. Equations (3) and (4) show how the

estimated standard errors and CV's displayed in

SPS Summary tables are derived from estimated

variances.

9
IV. LIST EXPANSIONS

In this chapter, we focus on estimators for the

total of a survey item in a list stratum in a

particular state. state, region, and U.S. level

aggregates will be addressed in Chapter VI.

A SELECTED UNIT VALUE FOR A SURVEY ITEM IS SAID TO

BE USABLE WHEN ALL ITS SUB-TRACT VALUES FOR THAT

ITEM ARE USABLE, which (again) can mean that they

have been hand imputed but does no~ allow for (any

part of) them to be machine imputed.

Direct Expansion

There is machine imputation for all nonusable CROP

and STOCK sub-tract values (except COUNTS). As a

result, both usable and nonusable item values are

employed in the estimator of a crop or stock list

stratum total. We begin with such an estimator.

The estimato~ for a crop or stock item total in

list stratum h is

Yh = eh ,L: Yi

l€Sh

= L Yie,

i€Sh

(5)

where eh

Yi

is the expansion factor for all

selected units in list stratum h,

is the set of all selected units in h

(L denotes the summation of all

i€Sh

selected units i in set Sh)'

is the item value for selected unit i

(which may involve MACHINE IMPUTATION

of sub-tract values), and

00. ehY i is the item eXI=>.swdedvalue for

selected unit i.

The expansion factor in this case is the inverse

of the selection probability of each name in list

stratum h; that is, eh = Nb/nh' where Nh is the

total number of names in llst stratum h (sampled

or not), and nh is the number of names sampled

from h.

10
Reweighting

The estimator for a item total in list stratum h

of a LABOR SURVEY (also a livestock item direct

expansion) is

eh

*

L Yi

i€Uh

= L Yir,

i€Uh

(6)

where Uh

and Yi is

is the set of selected units with usable

item values in stratum h,

is the reweighted expansion factor for

all selected units in list stratum h,

= eh*Yi is the reweighted item expanded

value for selected unit i,

as before.

The reweighted expansion factor is equal to Nh/uh'

where Nh is as before, and uh is the number of

selected units with usable item values (if uh is

zero, then Yhis undefined and remedial action

must be taken).

The theory behind reweighting is discussed

rigorously in [9]. Essentially, the set of

randomly chosen selected units from h with

usable item values is assumed to be equivalent to

a simple random sample of size uh.

The estimator in (6) is also applied to CROP and

STOCK items for CV estimation purposes, but the

resulting Yh's are not displayed in SPS Summary

tables.

EXPANDED COUNTS from agricultural surveys are also

computed using (6). These are the estimators of

the numbers of farms in particular domains (e.g.,

places having hogs). Expanded counts are item

totals for count variables. Unexpanded counts,

while included in SPS Summary tables, are not of

concern here. See [3; section 8] for more details

about them.

11
Livestock Estimators

NASS uses two estimators for livestock items

(including AQUACULTURE items, i.e'l catfish and

trout, but excluding all COUNTS): a direct

ex~ansion estimator which uses the formula in

equation (6) and a presence estimat.or described

below.

A distinction can be drawn between a nonusable

selected unit recorded as having (within at least

one of its sub-tracts) some quantity of a

particular livestock tyQg (such as hogs, cattle,

sheep, goats, or chickens) and one for which the

presence or absence of the livestock type is

unknown for everyone of its sub-tracts (note:

there is often no more than one sub-tract per

selected unit) .

Consider a survey item (e.g., market hogs) related

to a livestock type (hogs). IF A SELECTED UNIT

HAS A USABLE ITEM VALUE (i.e, if all of its subtracts have usable item values) AND ANY SUB-TRACT

IS RECORDED AS HAVING A POSITIVE QUANTITY FOR THE

TOTAL NUMBER OF THE LIVESTOCK TYPE, THEN THE

SELECTED UNIT IS A POSITIVE USABLE. Let uh+ be

the number of positive usables in stratum h, and

Uh+ denote the set of those usablcs in h.

IF A SELECTED UNIT DOES NOT HAVE A USABLE ITEM

VALUE BUT ONE OF ITS SUB-TRACTS HECORDED AS HAVING

A POSITIVE QUANTITY FOR THE TOTAL NUMBER OF THE

LIVESTOCK TYPE, IT IS A POSITIYJ;;tlONUSABLE. Let

~h+ be the number of positive nonusables in h.

Note that it is possible for a selected unit to be

a usable zero. This happens when all its

subtracts have usable item values of zero for

every it.em in the livestock type (or have LAF's of

zero) .

The PRESENCE estimator for an ite~ LIVESTOCK total

in list stratum h is (when uh+ is positive).

(7 )

12
where

xh(+) = ~ Yi/uh+'

i€Uh

and NO' Uh' and Yi are as before. (See [10] for

a justIfication of this estimator.)

When uh+ is zero and Ph is zero, then Yh is also

zero. Otherwise, when uh+ is zero, Yo is

undefined (and some sort of remedial actIon must

be taken).

variances

The variance estimator for the direct expansion

Yh in either (5) or (6) is

Vh = [(Nh - uh)/Nh] [uh/(uh - 1)] x

[~ (y.r)2 - (~ Yir)2/uh]

. I .

IEUhI€Uh

for uh > 1

(8)

otherwise, when Yhexists.

(It is undefined when Yh

does not exist.)

The first equality in (8) is unbiased for labor,

count, and livestock items when the assumption

underpinning reweighting is correct. Similarly,

this equality is conservative (biased upward) for

crop and stock items if NASS's machine imputation

program is more statistically efficient than

imputing missing item values with stratum means

(which is mathematically equivalent to

reweighting) .

The second equality in ~8) is based on the

realization that E[(Yh) ] = [E(yh)]2 + Var(Yh).

Since Var(Yh) is usually less than [E(Yh)]2,

(Yh)2/2 will most often be conservative as an

estimator of the variance of Yh.

13
+ (9)

when uh+ > 0

and nh' > 1

The variance estimator for Yh in (7) (the PRESENCE

estimator for LIVESTOCK) is given in [10]:

Vh = Nh2{[(Xh(+»2 - sh+2/Uh+] x

(1 - nh'/Nh)Ph(l-Ph)/(nh'-l)

Ph2(1 - Uh+/[PhNh])Sh+2/Uh+}'

otherwise

where

s +2 =

h

2

(Xh(+» /2

14

when uh+ = 1.
v. AREA EXPANSIONS

In this chapter, we focus on estimators for the

total of a survey item in the area frame of a

particular state. July cattle is somewhat special

and is treated in a separate section. It should

also be noted that, unlike its labor surveys,

there are no area expansions for Hawaii's two

agricultural surveys (December hogs and January

cattle). Moreover, there are no area expansions

for TROUT and CATFISH.

Direct Expansion - the Base Survey

As noted in Chapter II, a random sample of area

segments is selected as part of the base survey.

This sampling can be thought of here as a three

step process. First, the area segments of a state

are divided into land-use strata, such an

intensively cultivated, extensively cultivated,

range land, bodies of water, and non-agricultural.

Different states can have different land-use

strata definitions.

Second, the land-use strata are subdivided into

substrata based on geography and other

considerations (see [11] for more details) .

Finally, a (nearly) simple random sample of

segments are selected from each substratum ([11]

explains the need for the modifier "nearly").

Once a segment is sampled, the tracts within it

are enumerated so that they can be expanded in as

many as eight different ways (as discussed in

chapter II, these are the closed, open, weighted,

NOL-closed, NOL-weighted, NEO-closed, NEO-open, or

NEO-weighted estimators). The three CLOSED direct

expansion estimators for a land-use stratum total

of a survey item have the following form:

where h 1S the land-use stratum in question,

Bh is the set of all substrata in h,

Ghj is the set of all segments in

substratum j of land-use stratum h,

Thjk is the set of all tracts in segment k

of substratum j of land-use stratum h,

15
1S the expansion factor for all tracts

in segment Thjk'

is the survey value for tract m in

segment Thjk' which may (in principle)

be machine imputed, and

is an indicator variable, i.e., it

takes on either the value 0 or 1

depending on the estimator.

For the

For the

m is an

For the

m is an

the closed estimator whikm is always 1.

NOL-closed estimator, .Qhj~m is 1 if tract

NOL tract and zero if 1t 15 an OL tract.

NED-closed estimator, Whjkm is 1 if tract

NED tract and zero if it is an EO tract.

The two OPEN estimators (there is no NOL-open

estimator in the 1989 base survey) have a form

similar to (10):

where bhjkm

Yhjkm

is 1 if the farm headquarters for

tract m of segment Thik is within the

segment and zero otherwise,

is the entire farm value associated

with tract m, which may be machine

jmputed, and

all the other notation is as before.

The three WEIGHTED estimators have the form:

Yh = ~ ~ ehjk ~ WhjkmahjkmYhjkm' (12)

jEBh kEGhj mEThjk

where ahjkm is the weight used to prorate Yhjkm

(presently, the tract acres of m

divided by the farm acres of m; other

weights are under study), and

all the other notation is as before.

No matter which of the eight estimators is

employed to determine the land-use stratum totals,

the state total is

(13)

where ALIS the set of all land-usp strata in the

16
state.

variances - the Base Survey

Let the expanded item value for a tract be

Y

. e

hJkm for closed

estimators

for open

estimators

for weighted

estimators,

(14)

and nhj be the number of segments in Ghi. No

matter how Yhikme is defined, let the expanded

item value for a seqment be

Yhjk·e= ~ Yhjkme,

m€Thjk

A slightly conservative variance estimator of Yh

in (10), (11), or (12) is given in [12] (assuming,

incorrectly, that there is no additional variance

from using machine imputed data for stocks):

Vh =.~ [(nhj/[nhj -1]) x

J €Bh

{~ (Yhjk·e)2-

k€Ghj

(15)

(~ Yhjk·e)2/nhj}]·

k€Ghj

The variance estimator for YST in (13) is

(16)

Direct Expansion - a Follow-on Survey

For an area expansion of a follow-on survey, a

distinction must be drawn between selected units

(tracts) and sub-tracts (reporting units) I because

a tract in the base survey may subdivide into

different reporting units before the follow-on

survey is conducted.

Tracts are selected for the area frame (or NOL)

component of follow-on surveys in the following

17
manner. Those NOL tracts contacted for the base

survey are restratified based on their responses

to that survey and the equivalent of simple random

samples are chosen from what are called select

strata. For variance calculation purposes,

however, several select strata are often collapsed

into a single so-called summary stratum (see [13]

for a more detailed description of this process).

Let Yms denote an item value of interest for

sub-tract s of selected unit m (which may be hand

or machine imputed). For LABOR surveys this is

the full (open) farm value of the survey item; for

AGRICULTURAL surveys, it is the weiqhted farm

value. (In both cases, the raw survey values are

multiplied by LAF's; see equation (1).)

Let em be the expansion factor associated with

selected unit m. This is the product of the first

phase expansion factor from the base survey and

the second phase expansion factor from the

follow-on subsampling process (which itself has

two phases in both March and August; but that need

not concern us here; the second phase expansion

factor for the HAWAII LABOR survey is unity).

The direct expansion for summary stratum r of an

item from an AGRICULTURAL survey (except COUNTS)

is

(17)

where Rr is the set of all REPORTING UNITS in the

follow-on survey subsample that are

within summary stratum r (land-use

stratum in Hawaii) .

The direct expansion for summary stratum r of an

item from a lABOR survey (or a COUNT from an

agricultural survey) is

(18)

where Ur

d

1S the set of all reporting units in

Rr with USABLE item responses,

= emd is the reweighted expansion

factor for item t and sub-tract s, and

is the number of NOL reporting units in

the state divided by the number of NOL

18
reporting units in the state with usable

item responses.

What has been implicitly assumed is that each

NOL reporting unit is equally likely to provide

usable item values. If that assumption

is true, Yr* is an unbiased estimator.

Equation (18) is also applied to crop and stock

items for use in variance estimation. The set Dr

(and thus the denominator of d) includes only

those reporting units with non-machine imputed

values.

No matter whether (17) or (18) is used, the area

direct expansion for the state is

(19)

where AS is the set of all summary strata in the

state, and Yr(*) is either equal to Yr* (for labor

items and counts) or Yr(otherwise) depending on

which is appropriate.

variances - a Follow-on Survey

The theory behind variance estimation for the

NOL components of follow-on surveys is given in

(13]. In every state save Hawaii, there are (at

least) two phases of sampling for NOL tracts. As

a result, variance estimators for the NOL

component of a follow-on surveys have two

components. Only the sum of the two is displayed

in SPS Summary tables ~nd that only for YST in

(19). This is because there is no meaningful way

to estimate the portion of the first phase

variance that is attributable to a particular

summary stratum.

Second phase variance estimates for particular

summary strata may exist, but estimated second

phase standard errors and CV's are not displayed

in SPS Summary tables.

In this section, we will be dealing

values for selected units (tracts).

value of a selected unit is the sum

corresponding sub-tract values (the

or machine imputed sub-tract values

19

with item

The item

of its

Yms)' Missing

are treated
here as zeroes when determining sel~:;ted unit item

values. (This is because missing sub-tract values

are considered to be the result of another phase

of random sampling.)

Let m be a selected unit from summary stratum r,

Sr be the set of all such m in r, and Ym be the

item value m:

Ym = L: Yms' (20)

where the summation is over all the sub-tracts

within selected unit m (treating missing and

machine sub-tract values as zero). Further, let

fmbe the first phase expansion factor for the

area segment in which selected unit m is located.

The estimator for the second phase variance of Yr

in (17) is

V2r = [{ I: (em*/fm)2} - Nr]/(vr - 1) x

mESr

- (L: Zm)2/vr}

mfSr

(21 )

where Nr 1S the number of NOL tracts in summary

stratum r before subsampling,

vr1S the number of selected units in Sr

(after subsampl ing) , and

2m = fmym·

Note that for livestock items e~* is by definition

equal to e

W

' Furthermore, V2r is undefined when

vr < 2. Slnce there is no subsampling there, the

HAWAII LABOR SURVEY HAS NO SECOND PHASE VARIANCE.

The expression V2r can be biased, but the bias

will be small when d is close to 1. Moreover, the

bias is composed of two terms with opposite signs.

This (we hope) will have a cancelling effect. See

[14] for a fuller development.

Let Tik be the set of subsampled tracts in segment

k of substratum j from the base survey (note:

land-use strata play no active role in follow-on

survey estimators; also j denotes a "variance

stratum" in Hawaii). Further, let~

20
Yjko

=

when Tik has at least

one member

(22)

otherwise.

L: Yjk.

kEGj

where Gi is the set of all nj sampled segments in

substratum j.

Similarly, let

Yj.· = (23)

Suppose there are L substrata in the state (note:

substrata from different land-use strata are, by

our definition, different substrata). We can

define the following two variables:

L

v* = L: (n'/[n' -1]) ( L: Yjk. 2 - Yj ..2/nj )

j=1 J J

kEG'J

and

D* = L: {([ L: (em

/fm)2] - Nr)/[vr(vr - 1) ]

rEAS mERr

(24)

x

where Zjkr

(25)

L

[ L: (nJ'/[nJ'-1]) ([ L: ZJ'kr2] - zJ'.r2/nJ') - Zoor2]}

j=1 kEG,

J

is equal to L: z~, the summation

being over the lntersection of the

sets T'k and Sr (z'kr is zero when

the int~rsection ha~ no members) ,

= L: Zjkr' the summation of all

kEGj the Zjkr in substratum Gj,

L

and z..r =,L: Zj.r'

J=1

the summation of the

Zj.r over all L substrata

for a given summary stratum

r.

The variance estimator of YST in (19) suggested by

[13] is

21
V

ST V* + 0* when V* + 0* ~ ~ v2r

n:AS

V* when v* ~ ~ V2r > V* + D*

r€AS

when ~ V2r > V*.

r€As

(26)

In the 1989 version of the SPS Summary, the more

conservative v* from equation (24) is used in

variance estimation. For the HAWAIl LABOR survey,

which has no subsampling, V* would be an unbiased

variance estimator if it were not necessary to

collapse substrata into variance strata due to

sample size considerations.

The area expansions for both the MAHCH and AUGUST

Agricultural surveys (the latter is exclusively a

survey of rice stocks in six states) are based on

subsamples of NOL SELECTED units from the December

Agricultural Survey. (Note: the list and area

frames for the August 1990 rice stocks survey were

determined by the June 1989 base survey.) That is

to say, there is a three phase NOL sampling design

in those survey months. Nevertheless, v* in

equation (24) remains a conservative estimator of

the NOL variance.

Formally, there is a stage of sampling in all

follow-on surveys between the first and second

phases as described above. Approximately 60% of

the sampled June area segments are allocated for

agricultural survey subsamples and the remaining

segments for labor subsamples. This allocation

process can be thought of as part of the first

phase of sampling.

July Cattle and December Chicken

As mentioned previously, the July (or mid-year)

NEO-closed estimator for a cattle item is

calculated from the base (June) survey. There is

also a NOL-weighted estimator based strictly on a

July area subsample. This latter estimator is no

different from the area expansion for any followon survey; it uses equations (17) through (24).

The NEO-closed estimator for cattle is a more

complicated matter. Each cattle survey item in

22
the June area sample has two components. One

component covers cattle on Public Industrial

Grazing Association (PIGA) land and the other

cattle on non-PIGA land. For the NEO-closed

estimator, each thjkm in equation (10) is the sum

of the on-tract non-PIGA cattle value of interest

and ahjkm (from equation (12)) times the total

farm PIGA cattle value of interest. Variance

formulae for July cattle NEO-closed area

expansions follow equations (15) and (16).

The CHICKEN component of the December Agricultural

Survey is even more complicated than the PIGAeffected parts of the NEO-closed estimator for

cattle. As with the cattle estimator, the data

file inputed into the SPS Summary is such that the

appropriate equations for livestock surveys can be

applied in a straightforward manner.

23
VI. MULTIPLE FRAME EXPANSIONS AND .AGGREGATION

Direct Expansion

Equations (5), (6) and (7) provide estimators for

an item total in list stratum h, as described in

Chapter IV. (In this chapter, the LIVESTOCK

PRESENCE estimator is included in discussions of

direct expansion estimators.) If there are H list

strata in a state (h=l, 2, ... , H), then the

list direct expansion for the state is:

(27)

regardless of whether (5), (6), or (7) is used in

determining the Yh' (Note: if necessary, each

undefined Yh is changed to zero).

For the base survey, the state list direct

expansion in (27) can be added to the state area

direct expansion in (13) to form either the state

OL-MF/closed or OL-MF/weighted estimator,

presuming that the Yh in (13) are computed in the

appropriate manner (equation (10) is used for the

OL-MF/closed and (12) for the OL-MFjweighted

estimator with Whjkm =1 when m is an NOL tract and

o otherwise).

For a follow-on survey, YLin (27) is simply added

to YST in (19) to form the state direct expansion

estimator.

Returning to the list side, let h=l, ... , E be EO

strata, and let

(28)

For the base survey, YEin (28) can be added to

the state area direct expansion in (13) to form

either the state EO-MF/closed, EO-MF open, or

EO-MF/weighted estimator, presuming that the Yhln

(13) are computed in the appropriate manner

(equation (10) is used for the EO-MFjclosed, (11)

for the EO-MFjopen, and (12) for the

EO-MF/weighted estimator with Whjkm = 1 when m is

an NEO tract and 0 otherwise).

24
Regional or U.S. level direct expansions are

determined by simply adding together all the

component state direct expansions.

variances

The variance estimator for either Y~ or YE is

simply the sum of the variances of lts component

Yh: i.e,

(29)

while

(30)

where Vh is defined by either (8) or (9), as

described in Chapter IV. (Note: if necessary,

each undefined Vh is changed to zero.)

Likewise, the variance estimator for a state

direct expansion (list + area) is also the sum of

its component variance estimators. Finally, the

variance estimator of a regional or U.S. level

direct expansions is also equal to the sum of its

component variance estimators.

25
VII. RATIO ESTIMATORS

Introduction

The SPS Summary computes two types of ratios. One

type is the ratio of different survey items on the

same survey. For example, the ratio of wages paid

to labor hours on a labor surveyor the ratio of

corn production to harvested acres on an

agricultural survey. We call this an item-to-item

ratio.

The second type of ratio is of the same (or

similar) survey items on different surveys.

both surveys are base surveys, we call this

base-to-base ratio; otherwise, it :.scalled

survey-to-survey ratio.

When

a

a

The principle of ratio estimation is that all

respondents providing data (whether direct or

imputed) for the numerator of the ratio also

provide data for the denominator, and vice versa.

Ratio estimators take the following form in the

SPS Summary:

R = Y IIX I, (31 )

where yl and XI are estimators of the appropriate

totals based, in principle, only on data from

matched respondents.

The variance estimator for R generally has the

form (there is one exception which will be

addressed later):

Vyy

-----

(Y I) 2 ylXI

Vxx

+ ----- },

(X I ) 2

(32)

whe:e Vyy, V~x' and VyX are, respe~tively, ~he

varlanc~- estlmator fo~ YI, the varlance estlmator

for XI, and the covariance estimator for Y' and

X' .

Now YI and XI are always based on the same sample,

so Vyy, Vxx' and VyX have the same form. As a

result, only the estimator Vyx will be presented

in the text. It is a simple matter to derive Vyy

and V~x from Vyx (for example, one gets Vyy by

changlng all x-values in Vxy to y-values) .

26
The SPS Summary also calculates ratio expansions

from base-to-base and survey-to-survey ratio

estimators (and sometimes, but not often, from

item-to-item ratio estimators in the base survey;

see the section on "digitized land expansions").

A ratio expansion has the form:

YRE == XR, (33)

where X is an estimator for the same total as the

denominator of R, but is (usually) based on more

information than X'. We call X the root or root

estimator of the ratio expansion.

The variance of YRE is estimated in the SPS

Summary by

(34)

where var(X) is the variance estimator for X and

VRis defined in (32) (the derivation of VRE comes

from (A2) and (A3) of [14]). Except in degenerate

cases, equation (34) will provide a nearly

unbiased estimator for the variance (more

correctly, the mean squared error) of YRE when X

and R are independent (or at least uncorrelated) .

Unfortunately, this may not be the situation in

reality.

Item-to-Item - the Base Survey

The SPS Summary provides item-to-item ratios (such

as harvested to planted wheat acres) for

every list and land-use stratum in a state. FOR A

LAND-USE STRATUM, THESE ARE SIMPLY THE RATIOS OF

THE APPROPRIATE DIRECT EXPANSIONS (which may

involve machine imputed data) described in Chapter

V.

The situation is a bit more complicated for a list

stratum, say h, where an analogue of (6) is used

(when the set Mh is not empty):

and

Yh' eh' L; Yi

i€Mh

== L; y.r

1 '

i€Mh

27

(35)
where Mh

is the set of SELECTED UNITS with

both usable Yi and xi item values in

stratum h, and

= Nh/mh' where Nh is the total number

of names on the list frame in stratum

hand mh is the number of selected

units in Mh.

- ( L. y' r) ( L. xir)/mhJ

iEMh

1.

for mh > 1

(37)

for mh 1

When Mh is empty, Yh', Xh', and Rh = Yh'/Xo' are

undefined. (From now on, we will not provlde a

definition like Xh' in (35) when there is an

exactly parallel expression in y-values, in this

case Yh')'

The covariance estimator for Yh and Xo for a

LAND-USE STRATUM is analogous to equation (15)

(remember that Yh = Yh' in this case):

Vh.xy =.L. (nhj/[nhj -lJ) x

J EBh

{L. (Yhlk.e) (Xhjk.e) (36)

kEGhj -

(L. Yhjk.e) (L. Xhjk.e)/nhj}'

kEGhj kEGhj

where the notation is the same as in (15).

The covariance estimator of Yh' and Xh' for a LIST

STRATUM is analogous to (8) for count variables:

Vh'xy = [(Nh - mh)/NhJ[mh/(mh - l)J x

[ L. YirXir

iEMh

is undefined otherwise,

where Yir and xir are defined in (35).

WHEN mh=l, EQUATION (32) IS OVERRIDDEN, AND VR

(the variance estimator for Rh) IS UNDEFINED. The

28
second line of (37) is used for ratios that

involve aggregation across strata.

The covariance of a sum (across strata, states, or

regions) is the sum of the component covariances.

When aggregating across strata, all undefined Yhl,

Xh', Vh·yy' Vh·xx' and Vh.xy are changed to zero.

As an example of aggregation, the ratio estimator

for the list frame of a state is:

(38)

H

2:: Xh'

h=l

The variance estimator for RST is

+

(39)

2:: Vh.xx

-------- },

(2:: Xh I ) 2

where all the summations are from 1 to H.

Equations (38) and (39) are simply the

applications of (31) and (32) at the state list

frame level. Applications to other levels of

aggregation are straightforward.

Item-to-Item - a Follow-on Survey

Item-to-item ratios for list strata are handled

the same way on follow-on surveys as on the base

survey. Item-to-item ratios for NOLls are

calculated at the same levels of aggregation as

NOL direct expansions. For any item, we use an

analogue of (18):

(40)

where MRis the set of all REPORTING UNITS from

the NOL subsample for the state that

29
has both usable Yms and xms values,

em is the expansion factor for SELECTED

UNIT m,

and d' is the number of NOL reporting units in

the state divided by the number of

reporting units in MR'

In order to estimate the covariance of Y' in (40)

and its companion X', it is necessary to first

construct an analogue of Yjk' in equation (22).

This is simple enough to do_ Let

(41 )

where the summation is over all reporting units in

set MR and segment k of substratum (or variance

stratum) j. If there are no such reporting units,

set Yjk' I = Xjk- I = o. similarly, let

Y. I ""' y' I

J" =L., Jk-' (42)

where the summation is over all segments k in

substratum j.

The covariance estimator of Y'and XI in (40) is

then

L

L: (nj/[nj -1]) x

j=l (43)

(L: Yj k' I Xj k' I - Y j .. 'Xj .. '/nj) ,

kEGj

where n· is the number of segments sampled from

substratum j in the base survey, L the number of

substrata in the state, and Gj the the set of all

sampled segments in substratum j (as in (22)).

(We have dropped the analogue to D* in equation

(25); it is likely small and, if anything, has a

tendency to be negative.)

Base-to-Base

Base-to-Base ratio estimators involve only area

base survey samples. They compare June 1989

survey values with June 1988 survey values for the

area segments found in both base surveys. For

crop acreages, the closed approach is used (the

30
weighted approach is also used for cropland

acreages in 10 states); for land in farms, both

the closed and open approaches; for the number of

farms, the open and weighted approaches; for hogs,

the NEO-closed, NEO-open (for 10 states), and

NEo-weighted (for 10 states) approaches; and for

cattle, the NEO-closed approach.

Borrowing notation from Chapter V, let Yhjk.e be

the appropriate 1989 expanded value for segment k

in substratum j of land-use stratum h (see

equation (14), and let Xhjk.e be the matching

segment expanded value in 1988 (if one exists).

The ratio estimator for land use stratum his:

Xh'

,L (nhj/nhj') L Yhjk·e

J€Bh k€Ghj'

= ----------------------------

,L (nhj/nhj') L Xhjk.e

J€Bh k€Ghj'

L L Yhjk' '

j€Bh k€Ghj'

= ------------------ (44)

L L Xhj k' '

j€Bh k€Ghj'

where Ghj' is the set of all segments in

substratum j of land-use stratum h

in both the 1988 and 1989 area

samples (note: such segments have

a "comparability code" equal to 1 on

the edit master file),

nhj' is the number of segments in Ghj',

Yhjk' '= (nhj/nhj')Yhjk·e,

and all the other notation follows that of Chapter

V (nh' is as defined for the 1989 base survey).

For tho~e state with new frames in 1989 (Iowa, the

New England states, and West Virginia), Yh', Xh',

and Rh are undefined.

The covariance estimator for Yh' and Xh' is

31
{L: (Yhjko ')(xhjk.') (45)

kEGhj'

(L: Yhjko')( L: Xhjk.')/nhj'l,

kEGhj' kEGhj'

The real purpose behind base-to-base ratios is

ratio expansion (see equation (33»). Ratio

expansions can be determined for each land-use

stratum h by multiplying the 1988 land-use stratum

direct expansion, call it Xh' by Rh in (44).

To determine the variance estimator of Yh.RE

XhRh' the SPS Summary employs equation (34),

where the variance estimator for Xh is exactly

parallel to equation (15) but based on the 1988

sampled segments and their item values. (The SPS

Summary actually recalculates Xh and var(xh)

internally. )

The land-use stratum ratio expanSIons are

not summed to get the area frame ratio expansion

for a state. Rather,

(46)

where all the summations are over the land-use

strata in the state, is used. This ratio

expansion is in required YRE = XR form, and so

equation (34) is invoked to determine the variance

estimator for YST.RE.

The right hand side of equation (46) is also used

to calculate regional and U. S ° levE~l area frame

ratio expansions. The summations ~re redefined

appropriately.

Livestock ratio expansions based on (46) only

cover NEO tracts. To estimate the livestock

totals for a state, YST.RE in (46) is added to YE

from equation (28) (the July YE for cattle items).

The variance of this sum is the sum of the two

variances. The same thing is done for regional

and u.S. level livestock ratio expansions, an EO

total is added to the appropriate version of the

right hand side of (46). Variances are estimated

32
analogously to state variances (NEO variance plus

EO variance).

Survey-to-Survey

We are concerned in this section with the ratio of

the same item (or similar items) on two

agricultural surveys less than one full year

apart. These ratios are always in the form of

current to previous survey values.

Survey-to-survey ratio estimators for a LIST

STRATUM follow exactly the formula in equation

(35) (note: the Yi are determined using current

LAF's, while the Xi use the previous LAF's).

Likewise, equation (37) provides the needed

information for variance estimation.

There is one complication that needs to be

mentioned. Sometimes a selected unit contains

either more or less reporting units (sub-tracts)

in the current survey than in the previous survey.

Since equation (35) is a summation of selected

unit item values, this should not be a problem:

the current (previous) item value for a selected

unit is the sum of all its current (previous)

sub-tract values.

Unfortunately, when there are more sub-tracts for

a particular selected unit in June 1989 than in

December 1989, it is possible that not all of the

June sub-tracts appear in the December edited data

file (changes in the makeup of edited data files

prevent such phenonema from ocurring in March 1990

and afterwards). This can cause December-to-June

ratio estimators to be biased slightly upward

(remember, most selected units contain only a

single sub-tract in all survey months) .

The SPS Summary also calculates ratio expansions

from survey-to-survey ratios. It uses equation

(5) as the root estimator for CROP and STOCK items

and (7) as the root for livestock items. For the

variance of the root, it uses (8) and (9),

respectively. (As with base-to-base ratios,

the roots and their variance estimates are

recalculated internally.) Equation (34) is again

used as the variance estimator for the stratum

ratio expansion.

33
NOL survey-to-survey estimators are much

difficult since they depend on what two

agricultural surveys are being compared.

potential pairs of surveys fall into two

which are treated separately:

more

The

groups

Group 1: September to June, December to June,

March to December, August to March,

August to December.

Group 2: December to September, March to

September, January to July.

In the first group, the selected units of the

current survey are a subsample of the selected

units of the previous survey. In the second

group, the selected units of both surveys are

independently drawn from the sampled tracts of the

base survey.

For an NOL survey-to-survey ratio from Group 1 or

2, let Ym be the total item value for a selected

tract in the current survey (see equation (20)),

and xmbe the total item value for the tract in

the previous survey.

Item values on the tract or sub-tract level are

almost always weighted values (in the sense of the

weighted estimator). The one exception to this is

that CROP VALUES FOR THE BASE SURVEY ARE CLOSED.

The following is the estimator of Y' for a state

NOL survey-to-survey ratio from Group 1:

(47)

where MS

and d"

Y' = ~ emd' 'Yml

mEMS

is the set of all tracts from the

current NOL subsample for the state

that has both usable Ym and xm values

(a Ym value is said here to be usable

if all if its component Vms values are

usable; they can be neither missing nor

machine imputed),

is the expansion factor for tract m in

the CURRENT survey,

is the number of current NOL subsampled

tracts in the state divLded by the

number of tracts in MS'

34
(Note: as on the list side, the Ym are determined

using current LAF's, while the xm use previous

LAF 's.)

Paralleling (41), let

(48)

where the summation is over all sub-tracts in both

MS and segment k of substratum (or variance

stratum) j. If there are no such reporting units,

set Yjk.' = Xjk. I = o. Similarly, let

Yj ..1 = L; Yjk'"

where the summation is over all segments k in

substratum j.

(49 )

The covariance of Y' and X' is then expressed by

(43). Ratio expansions for the state NOL

component use (13) or (19) as their root,

depending on whether the previous survey was

conducted in June or December. Variance

estimators again are based on (34).

For area frame DECEMBER-TO-SEPTEMBER ratios,

equation (47) is again used but the numerator of

d" is now the number of tracts in both the

December and September samples, while

em = e~DemS/fm is the product of the base period

expans10n factor (fm in (21», the December

subsampling expansion factor (emD/fm, where em

D is

the DECEMBER expansion factor), and the September

subsampling expansion factor (emS/fm, where emS is

the SEPTEMBER factor). Equations (48) and

(49) follow. Area frame MARCH-TO-SEPTEMBER ratios

are analogous (e.g., em = emMemS/fm' where em

M is

the March expansion factor) as are area-frame

JANUARY-TO-JULY ratios.

To determine the survey-to-survey ratio for a

state, the SPS Summary follows the principle of

equation (38), adding the Yh' values from the list

strata ((35» to Y' from the NOL component «47»

in the numerator of the ratio and doing the same

with the Xh' and X' in the denominator. Ratio

expansions and variance estimation follow as

always.

35
Digitized Land Expansions

The SPS Summary produces another type of item-toitem ratio expansion for the base survey. The

root is total land area (for a state, region, or

the whole D.S) provided by statistical Abstracts

put out by the Bureau of Census. The numerator

values are CROP acreages by segment calculated

using equations (14) and (10) (the closed

estimator). The denominator values are digitized

acres for the segments. These are derived by the

Area Frame section using digitizing tablets to

electronically (and very accurately) measure the

area in each segment.

The ratio estimator for a land-use stratum itemto-item ratio in this case is equation (44) with

nhj = nhj'· As a result, Yhjk.' in (44) is

replaced by Yhjk.e in (14) (while the replacement

for Xhjk. I can be found in the input data set.)

Variance estimation (based on (45) with Yh'k.' set

equal to Yhjk.e) and aggregation to highe~ levels

are staightforward.

The variance of the root of one of the item-toitem ratio expansion under discussion is zero,

because the census land area data is considered

truth. As a result, the variance estimator of a

ratio expansion has the form

(50)

Equation (50) can be applied at any level of

aggregation in a straightforward manner.

36
VIII. AGRICULTURAL SERVICES

As noted in Chapter II, the agricultural services

survey is conducted in two states - California and

Florida. A survey item from this survey is often

paired with an item from the basic (or farm) labor

survey (in fact, they share the same "item code"

on the questionaire; for example, total workers is

item code 360 on both surveys). The SPS Summary

produces three types of expansions (or ratios)

from such paired survey items: farm labor, ag

services, and TOTAL LABOR (farm labor plus ag

services). This section treats the latter two

types of expansions for the California and Florida

labor surveys.

A sample is drawn from a supplemental list frame

of ag services (contractors) in California and

Florida. In addition to this, farms enumerated

for the basic labor survey report the ag services

firms they use. When these firms are not on the

list frame of ag services, NASS adds them to the

ag services survey. Their quantitative responses

are for all the labor services they provide.

Consequently, these responses must be divided by

the number of farms provided services by the firm.

This is handled (before the Summary) in the LAF.

The direct expansion estimator for a STRATUM OF AG

SERVICES uses the same formula as equation (6).

Its variance estimator is the same as equation

(8). Likewise, the direct expansion of the

numerator and denominator of an item-to-item ratio

is expressed by equation (35) with the variance of

the ratio following the same pattern as that of

any list stratum.

Let us now turn our attention to labor from ag

services firms not on the ag services list frame.

Suppose one of the sub-tracts of a selected unit

from either the basic labor list frame or the NOL

area subsample uses an ag services firm not on the

ag services list frame. That firm is added as g

sub-tract of the selected unit. ITS RAW SURVEY

ITEM VALUES ARE MULTIPLIED BY TWO LAF's -- one for

the ag services firm itself and one for the basic

list or NOL area reporting unit that originated it

(deemed to be the first sub-tract of the tract).

Since total labor survey items include both basic

labor and ag services items, it would be difficult

37
to handle non response simply by adjusting the

expansion factors. Instead, we employ these

variations to our usual procedures:

1) The value for an ag services survey item from

an added ag services sub-tract is modified to be

Yis = (g/g')Yis'

is undefined

when g' > a

(51 )

otherwise

(and remedial action

should be taken),

where Yis' lS the original survey item value

(including the two LAF's) when such

a valid value exists and ZERO

OTHERWISE,

g is the number of added ag services in

the state: contractors not on the ag

services list frame that were added

to the sample, and

g' is the number of those added ag

services with valid item responses

(for an item-to-item ratio, it is,

in principle, the number of added

ag services with valid item values

for both the numerator and the

denominator) .

(Note: The subscript "i" in (51) is replaced by

"m" for NOL area sub-tracts.)

2) All ag services survey item values for BASIC

LIST sub-tracts are (by definition) zero (they are

not defined for basic NOL sub-tracts) .

3) The survey value (ag services or total labor)

for a selected unit (tract) from a BASIC LIST

stratum is calculated using equation (2). The

resultant sum is deemed nonusable when and only

when one of the basic labor sub-tract fails to

provide a usable response for the paired farm

(basic) labor item. (IMPORTANT NOTE: Even when

part of S! nonusable tract, an M E;ervices subtract providing g valid res?onse ~ounts in

computinq g'. Conversely, even whE~n part of g

usable tract, an M services sub-tract not

providing g valid response does n(~t count in

computing g'.)

4) The NOL AREA direct expansion for an AG

SERVICES survey item uses equat.ion (18) with d

38
defined as the number of basic NOL reporting units

in the state divided by the number of those units

reporting the ag services they use (which can be

zero). For an item-to-item ratio, d' in (40)

equals d as described above. (This is because in

1989 surveys when any item response in a section

is not valid all item responses are deemed not

valid.)

5) The NOL AREA direct expansion for an TOTAL

LABOR survey item uses equation (18) with d

defined separately for ag services and basic labor

sub-tracts (the former as in point (4) above, the

latter as in the basic labor survey). The item-toitem ratio in (40) is handled analogously.

The variance estimator for a BASIC LIST stratum

direct expansion in (6) is equation (8) (this

estimator is biased when gig' is greater than one;

see the discussion of V2r in equation (21». The

variance estimator for an item-to-item ratio

follows equation (32) (as before) with equation

(37) serving as the formula for the stratum

covariance estimator.

The (conservative) variance estimator for the NOL

area direct expansion is equation (24). For an

item-to-item ratio, the key covariance estimator

is expressed by equation (43). NASS has no plans

to estimate second phase variances for ag services

and total labor items.

When aggregating, we once more change any

undefined expansion (and its variance estimator)

to zero. Expansions from all three frames must be

added together for state totals, separately in the

numerator and the denominator of item-to-item

ratios.

39
IX. YEARLY AGGREGATES

The SPS Summary has been equipped t.O provide

yearly estimates of some labor surVE'y items after

the July 1989 survey and again after the October

1989 survey.

Consider a particular labor survey item. Let t=1

denote October 1988, t=2 denote January 1989, t=]

denote April 1989, t=4 denote July 1989, and t=5

denote October 1989. Further, let Yt denote the

item direct expansion (at some level of

aggregation) for survey t calculated using the

formulae in Chapters III through VIII (Yt may also

be the numerator or denominator of an item-to-item

ratio) .

Each Ytis measured on a per-week basis. The

yearly aggregate of interest is also measured on a

per-year basis. Thus for an item requiring a

yearly direct expansion after the JULY survey, the

formula used is

Y

4

13 { L: Yt}.

t=l

(52)

(The SPS Summary actually resummarizes Y1, YZ' ,and

Y3 values to determine Y). For an item requlrlng

a yearly direct expansion after the OCTOBER

survey, the formula used is

Y

5

13{ L: Yt}.

t=2

(53)

(Again, the SPS Summary actually resummarizes Y2,

Y3, and Y4values to determine Y) .

The variance estimators for the Y in (52) and (53)

are not so straightforward. Their derivation

takes up tho remainder of the section. To this

end, the Yare be broken up into list and area

components. For ag services and total labor

items, the List component includes both the basic

and ag services list expansions.

40
The NOL component of variance for July

Let YAt be that part of Yt in (52) that comes

from the NOL subsample. The variance estimator

for YA = 13(YA1 + YA2 + YA3 + YA4) has the form:

(54)

where VA(1,2,3) is the variance estimator for

YA(1,2,3) = YA1 + YA2 + YA3. This is because the

July 1989 NOL subsample comes from the 1989 area

sample. As a result, it is assumed independent of

the three subsamples that come from the 1988 area

sample. (This assumption neglects the fact that,

in some states, only 20% of sampled area segments

were rotated out of the sample in June 1989. As a

result, the variance estimation described below

can be biased in those states.)

Paralleling equation (48), let

(55)

where Mjkt

3

Y'k·' = ~ ~ emdtYmst,

J t=l ms€Mjkt

is the set of all NOL sub-tracts in

segment k of substratum (or variance

stratum) j with usable item responses

in the survey for month t,

is the expansion factor for NOL tract

m,

dtis the number of NOL sub-tracts in the

state divided by those providing

usable item responses in the survey

for month t (with TOTAL LABOR items in

California and Florida, dtis defined

separately for ag services and basic

labor sub-tracts),

Ymst is the survey item value for sub-tract

ms and survey month t.

(Note: Variance strata are used in place of

substrata in Hawaii and in those states whose 1988

labor subsamples were not selected from the June

1988 area sample.)

Equations (49) and (43) follow immediately. The

latter (in Vyy form) providing a variance

estimator for YA(1,2,3) which can serve as

41
VA(l 2 3) in (54). , ,

The NOL Component of Variance for October

Let YAt be that part of Yt in (53) that comes

from the NOL subsample. The variance estimator

for YA = 13(YA2 + YA3 + YA4 + YA5) has the form:

VA = 169{VA(2,3) + VA(4,5)}' (56)

where VA(2,3) IS the variance estimator for

YA(2,3) = YA2 + YA3, and VA(4,5) is the variance

estimator for YA(4,5)

To calculate VA(2,3) and VA(4,S)' the principles

used in calculating VA(1,2,3) are again employed.

Now, however, the first summation in equation (55)

runs from 2 to 3 for VA(2,3) and from 4 to 5 for

VA(4,5) .

Again, equations (49) and (43) follow immediately.

The.latter (in Vyy form) providin9 d variance

estImators VA(2,3) and VA(4,5) WhL:h are plugged

into equation (56).

The List Component of Variance for July

Let Yht be that part of Yt in (52) (or (~i3))that

comes from stratum h of the list sample (h can

be a basic labor list stratum or an ag serVIces

list strat~llm). The variance estimator for

Yh = 13(Yh1 + Yh2 + Yh3 + Yh4) has the form:

(57)

where Vh(1,2,3) IS a variance estimator for

Yh(1,2,3) = Yh1 + Yh2 + Yh3· This is because the

July 1989 list sample is drawn independently of

the samples used for the other three surveys.

42
Unlike the NOL subsample, the list samples are not

the same in October 1988, January 1989, and April

1989. They are, however, highly correlated (and

all have the same size). Half of the selected

units from list stratum h in October and January

are the same. The other half of the January

sample corresponds to half of the April sample.

That part of the October sample that does not

correspond to the January sample is called

Replicate~. Replicate d is the overlapping

portions of the samples in October and January,

while Replicate ~ is the overlap in January and

April. Replicate ~ is that part of the April

sample that is not surveyed in January.

(Replicates 1 and 2 were also enumerated for the

July 1988 survey.)

To estimate the var1ance of Yh(1,2,3)' a selected

unit in Replicate 2 of the October survey is

matched to a selected unit in Replicate 4 (note:

all replicate mathching is done before the SPS

Summary). Likewise, a selected unit in Replicate

1 of the April survey is matched to one in

Replicate 3. The result is a "matched" sample of

selected units for the three surveys with the same

sample size as each of the surveys.

Paralleling equation (6), let

3

Yh(1,2,3)' = L L eh

*

Yit'

i€Uh t=l

= L Yir

i€Uh

is undefined otherwise,

(58)

where Uhis the set of all matched selected units

in list stratum h with usable item

values in all three surveys,

= Nh/uh'

is the total number of names in list

stratum h,

is the number of selected units in Uh'

is the month t survey 1tem values for

selected unit i,

= L eh*Yit, where the summation is

over t = 1, 2, and 3.

43
A conservative estimator for the variance of

Yh(1,2,3) is

- (,L: Yir)2/uh]

l€Uh

V h(1,2,3) = [Uh/(uh - 1)]

[.L: (Yir)2

l€Uh

2

{Yh(1,2,3)} /2

is undefined

x

when uh > 1

when uh < 2 and

Yh(1,2,3) exists

otherwise.

(59)

The first line of this estimator would be unbiased

if Yh(1,2,3) were equal to Yh(1,2,J)' and the

selected units for each replicate were drawn with

replacement. The replicates, however, were drawn

without replacement, which means that the with

replacement variance formula is conservative.

Moreover, Yh(1,2,3) (unlike Yh(1,2,3) ') can use

information from selected units that provide

usable data in one survey but not in another, so

it will often have less variance than Yh(1,2,3) '.

Equation (59) can be plugged into (57) which then

serves as a variance estimator for Yh.

Item-to-item ratio estimation follows along the

lines laid out in Chapter VII. Of course, Mjk in

equation (55) and Uhin (58) need be modified to

include only tracts or selected units with usable

item values in all three surveys for both the

numerator and the denominator. The covariance

analogue to (59) is

- (.L: Yir)(.L: xir)/uh]

l€UhlEUh

44

when uh > 1 (60)
= Yh(1,2,3)Xh(1,2,3)/2

when uh < 2 and both Yh(1,2,3)

and Xh(1,2,3) exist

is undefined otherwise.

Aggregation is fairly straightforward also. For

direct expansions, equation (52) holds at every

level of aggregation. The same applies to the

numerator and denominator of an item-to-item

ratio. For variance estimators, the rule that the

variance (or covariance) of a sum equals the sum

of the variances still applies. As long as the

component parts consist of state NOL variance

estimators (equation (54», list stratum variance

estimators (equation (57», or their sums.

The List Component of variance for October

The variance estimator for the list stratum total,

Yh = 13(Yh2 + Yh3 + Yh4 + Yh5), has the form:

( 61)

where Vh(2,3) is a variance estimator for Yh(2,3)'

and Vh(4,5) is a variance estimator for Yh(4,5).

The 1989 list sampling design follows the same

replicate pattern as the 1988 survey. Consequently, to estimate the variance of Yh(2,3)' a

selected unit in Replicate 3 of the January 1989

survey is matched (before the SPS Summary) to a

selected unit in Replicate 1 of the April survey

(both surveys enumerate Replicate 4). Likewise,

to estimate the variance of Yh(4,5)' a selected

unit in Replicate 1 of the July 1989 survey is

matched to a selected unit in Replicate 3 of the

October survey.

Paralleling equation (58), let

45
3

Yh(2,3)' ~ L L eh *Yit'

i(Uh t=2

= L Yir

i(Uh

is undefined otherwise,

(62)

where Uh

and Yir

is the set of all matched selected units

in list stratum h with usable item

responses in all both surveys (January

and April),

= Nh/uh'

is the total number of names in list

stratum h,

is the number of selected units in Uh,

is the month t survey itE!m values for

selected unit i,

= ~ eh*Yit, where the summation is

over t = 2 and 3.

A conservative estimator for the variance of

Yh(2,3) is

Vh(2,3) [uh/(uh - 1)]

[.z: (Yir)2

l(Uh

2

{Yh(2,3)} /2

x

when uh > 1

when uh < 2 and

Yh(2,3) exists

(63)

is undefined otherwise.

It is a straigtforward matter to modify equations

(62) and (63) to provide a variance estimator for

¥h(4,5) (the subscript (2,3) is everywhere

replaced by (4,5), Uh is concerned with usable

item values in July and October, and the summation

for Yir is over 4 and 5). Results from equation

(63) can then be plugged into (61) which then

serves as a variance estimator for Yh.

Extensions to item-to-item ratio estimation and

aggregation follow along the lines laid out in the

last section (with the subscript (1,2,3) in

equation (60) replaced by (2,3) and (4,5».

46
x. GLOSSARY OF TERMS

This glossary is not intended as a lexicon of

mathematical terms used in the text, rather it is

a listing of terminology that is somewhat distinct

to the surveys covered by the 1989 SPS Summary.

Terms

All terms in bold face that are not underlined are

contained in the alphabetical listing below.

Terms both bold faced and underlined are not in

the listing. These are either obvious or begin

with an acronym. There is an alphabetical listing

of acronyms in the following section.

Agricultural (Ag) Services survey - That component

of the Labor survey in California and Florida that

involves labor and wages from labor provided by

contractors that need not themselves be farms.

Ag services Item - A survey item related to labor

or wages from labor provided by contractors (note:

in states other than California and Florida, such

items come from the basic labor survey).

Agricultural survey - National multiple frame

survey conducted in June (the base survey), July,

August, September, January, and March of crops

(acreages, production, and planting intentions),

livestock, land in farms, number of farms, and

grain and rice stocks (not every question is asked

each month). Sometimes (incorrectly) called "the

Quarterly Agricultural Survey" or "QAS.II

Area Frame - The complete partition of a state

into nonoverlapping area segments. A stratified

sample of segments is drawn for use in the base

survey. A subsample of tracts contained within

those segments is drawn for each follow-on survey.

Area Frame Estimator - An estimator (usually a

direct expansion) either for the entire state or

for that part of the state not made up of overlap

farms or extreme operators. There are three types

of area frame estimators: closed estimators, open

estimators, and weighted estimators.

47
Area segment --See segment.

Base Survey - The June Agricultural survey.

Basic Labor Survey - A survey of po-tential farms

and area tracts concerning labor and wages from

labor. The basic labor survey is the only

component of the labor survey in states other than

California and Florida. Sometimes called the farm

labor survey.

Closed Estimator (also known as the closed-segment

estimator) - An area frame estimator used only for

the base survey that enumerates item values

contained on tracts identified to be within

sampled segments. The NOL-closed estimator enters

zeroes for item values on tracts that are part of

overlap farms. The NED-closed estimator enters

zeroes for item values on tracts that are part of

extreme operators.

Count (variable) - A binary variable determined

from survey responses that indicates when a

reporting unit is within a particular category;

e.g., whether it has hogs.

Direct Expansion - An estimate of a total

calculated by first multiplying survey values by

an expansion factor and then summing the results.

Expansion Factor - A number (which may be a

fraction) that in some sense refects how many

potential farm names (in a list frame estimator)

or tracts (in an area frame estimator) are being

represented by a survey value.

Expanded Count - The direct expansion of a count

variable.

Expanded Value - A survey value (sometimes called

"an unexpanded value") times its expansion factor

and its list adjustment factor.

Extreme Operator (EO) - A name on a list frame

associated with a presumably large farm in terms

of crops, livestock, or storage capacity. All

EO's are overlaps and are found within list strata

containing only EO's.

Farm Labor Item - A survey item from the basic

labor survey relating labor or wages from labor

48
employed directly by a farm. Sometimes called a

basic labor item.

Follow-on Survey - A labor survey, a reimbursable

surveyor an agricultural survey other than the

base survey. This multiple frame survey

enumerates a subsample of tracts contained in

those area segments sampled for the base survey as

well as a sample of names associated with

potential farms from the relevant list frame.

Hand Imputed - The act of filling in an unreported

survey value or changing an obviously incorrect

one (as determined by an edit program) based on

the judgement of some NASS employee or employees

(usually at a State office) or by the edit

program.

Imputed Value - A value determined by NASS that

replaces an unreported or obviously incorrect

survey value (see hand imputed and machine

imputed) .

Item - A survey question calling for a

quantitative response or a mathematical function

of such a response or responses (e.g., a count

variable). Also called a survey item.

Labor Survey - A quarterly (July, October, January

and April) fOllow-on survey of labor and wages

from labor on farms whether the labor is directly

employed or provided by agricultural services.

Land-Use Stratum - A collection of segments in the

area frame of a state that are thought to have

similar land-use characteristics (intensive

cultivation, range land, body of water, etc.).

List Adjustment Factor (LAF)- A scalar adjustment

to item values to account for more than one

sub-tract being associated with the same farming

arrangement.

List Frame - A list of names associated with

potential farms within a state that is eligible

for the list sample of a particular survey. Thus,

there are different list frames for different

surveys. Also known as a list universe. (NASS

sometimes refers to the collection of all the list

frames or universes in a state as the list frame

for that state. In this report, we always mean

49
the frame for a particular survey.)

List Frame Estimator - An estimator (usually a

direct expansion) for all farms associated with

names on a list frame. This estimator is based on

a stratified simple random sample of names drawn

from the list frame.

List stratum - A collection of names within a list

frame that are believed to be associated with

farms with similar characteristics.

Machine Imputed - The act of filling in an

unreported survey value or replacing an obviously

incorrect one (as determined by an edit program)

by means of an imputation progam.

Multiple Frame Estimator - An estimator combining

estimates for two (or more) frames. The component

frames need not be mutually exclusive but their

combination should exhaust the target population.

For the base survey, the OL-MF estimator combines

an estimator for the list frame with an NOL

(closed or weighted) estimator for the area frame.

Also for the base survey, the EO-MF estimator

combines an estimator for the extreme operators 1n

the list frame with an NEO (closed, open, or

weighted) estimator for the area frame.

Nonoverlap - Farms, or tracts on farms, that are

not associated with names on a particular list

frame. Follow-on surveys have nonoverlap strata

(see select and summary strata) made up of

nonoverlap tracts enumerated in the base survey.

Open Estimator (also known as the 9pen-seqment

estimator) - An area frame estimator used for the

base survey that enumerates whole farm values for

items when the farm operator lives on a tract

identified to be within a sampled segment - with

the following exception - the NEO-9pen estimator

records zeroes for item values on extreme

operators. A subsample of all non--overla\J (NOL)

farms where the farmer lives within a sampled

segment is used for the labor survey.

Overlap - A farm, or a tract on a farm, that is

associated with a name on a particular list

frame.

50
positive Nonusable - A survey item response that

is not valid but for which we have the following

information: the sampling unit is recorded as

having a positive quantity of the item or a

related item and a nonzero list adjustment factor

(e.g., a farmer may indicate that he has hogs but

refuse to give information on particular hog

questions like his number of market hogs). For

the purposes of this report, only a livestock item

response can be a positive nonusable.

Presence Estimator - A livestock estimator for a

list stratum composed of an estimator for the

fraction of sampled units with livestock of the

type in question times the estimated mean among

such units.

Ratio Expansion - An estimator for a current total

that is the product of, (a), a ratio estimator

containing direct expansions for the current total

in the numerator and the previous total in the

denominator, and, (b), an estimator for the

previous total (called the root).

Root (estimator) - That part of a ratio expansion

that is multiplied by the ratio estimator. The

root is an estimator for the denominator of the

ratio estimator that is not restricted to matched

respondents.

Reimbursable Survey - A follow-on survey conducted

by NASS for another agency or Congress. Such a

survey is often a one time event for which NASS

will be reimbursed.

Segment - A usually contiguous piece of land.

Each state is divided into segments (see area

frame and area frame estimator). Also known as an

area segment.

Select Stratum - A collection of NOL tracts

enumerated by the base survey with similar

characteristics. A simple random sample of tracts

from a select stratum is enumerated for a

follow-on survey. Also known as a NOL select

stratum.

Selected unit - A name from a list frame or an NOL

tract from a select stratum that has been sampled

for a survey.

51
Each

(NASS

frame

Substratum - A subdivision of a land-use stratum

used in selecting the sample or area segments for

the base survey. Every segment is in one and only

one substratum.

Sub-tract - A reporting unit for a survey.

selected unit has at least one sub-tract.

often calls a reporting unit from the list

in the base survey a "tract" rather than a

"sub-tract." We do not follow that. practice here.

There is no distinction between area tracts and

sub-tracts in the base survey).

Summary stratum - A collection of NOL tracts

enumerated by the base survey with similar

characteristics, usually made up of one or more

select strata. The sample for a follow-on survey

may only contain a single tract from a particular

select stratum, but there must be at least two

sampled tracts from each summary stratum. Also

known as a ~OL summary stratum.

Total Labor Item - The combination of a farm labor

and ag services survey item.

Tract - That part of an area segment that lS under

one land operating arrangement.

Usable (response) - A valid response for a survey

item. May be given by farmer (or agent),

hand-imputed by NASS (usually a state office), or

calculated from other usable items (as in the case

of a count variable). Note: On occasion a missing

or invalid response is treated as a usable zero

for estimation purposes.

variance stratum - The union of several similar

area substrata. It is treated as a single

substratum for variance estimation purposes.

Weighted Estimator (also known as the weightedseqrnent estimator) - An area frame estimator that

prorates whole farm values for tracts identified

to be within sampled segments (the area in the

tract divided by the area in the farm as reported

in the base survey is used for prorating). The

NOL-weighted estimator records zeroes for item

values on tracts that are part of overlap farms.

The NEO-weiqhted estimator records zeroes for item

values on tracts that are part of extreme

operators.

52
Yearly Aggregate - A statistic produced for the

labor survey (basic, ag services or total) that

combines survey values for the present and

previous three quarters.

Acronyms

The text uses many acronyms. The original form

of each survey related acronym is given below.

When that form can not be found in the previous

section of this glossary, direction to a related

term will be given.

EO - Extreme Operator; can be used along with a

MF (multiple frame) estimator, as in "EO-MF

estimator" (see multiple frame estimator)

MF - Multiple Frame

NEO - Not an extreme operator (see extreme

operator); can be used along with an area

frame estimator, as in NEO-closed

estimator (see area frame estimator,

closed estimator, open estimator, weighted

estimator)

NOL - Nonoverlap (or "not-on-the-list"); can be

used along with an area frame estimator, as

in NOL-closed estimator (see area frame

estimator, closed estimator, open estimator,

weighted estimator); can also be used along

with terms select and summary stratum, as in

NOL summary stratum.

OL - Overlap (or "on-the-list"); can be used

along with a MF (multiple frame) estimator,

as in OL-MF estimator (see multiple frame

estimator)

53
XI. REFERENCES

[1] SPECIFICATIONS -- Aqricultural Surveys: June

1989 - !,!arch1990, Estimates Division,

October 1988.

[2] Quarterly Labor Survey S?ecifications,

Estimates Division, August 1988.

[3] Aqricultural Surveys Supervising and Editinq

Manual, December 1989 - March 1990, Estimates

Division, 1989.

[4] Agricultural Labor Surveys Supervising and

Editing Manual, October 1989 - April 1990,

Estimates Division, 1990.

[5] Houseman, Earl E. Area Fram~ Samplinq in

Aqr~culture. SRS-20, 1975.

[6] Cotter, Jim & Nealon, Jack. Area Frame

Design for Aqricultural Survey§, Research and

Applications Division, August 1987.

[7] Atkinson, Dale. The Scope ang Eff~ct of

Imputation in Quarterly Aqricultural Surveys,

RAD staff Report No. SSB8804, February 1988.

[8] Herzog, Thomas & Rubin Donald B. "Using

Multiple Imputations to Handle Nonresponse

in Sample Surveys" in W. G. Madow, I. Olkin,

and D. B. Rubin, Eds., Incomplete Data in

Sam~le Surveys, Volume ~: Th~ory and

BiliQ9Iaphies. Academic Press, New York,

210-245, 1983.

[9] Oh, H. & Scheuren F. "Weighting Adjustment

for Unit Nonresponse" in W. G. Madow, I.

Olkin, and D. B. Rubin, Eds., Incomplete Data

in Sample Surveys, Volume .z.: Theory and

Biliographies. Academic Press, New York,

143-83, 1983.

[10] Kott, P. S. & Thorson, J. Improvinq Variance

Estimates for Livestock Surveys, RAD Staff

Report No. SRB-NERS-8901, February 1989.

54
[IIJ Geuder, Jeff. Paper stratification in SRS

Area Sampling Frames, SF & SRB Staff Report

No. 79, February 1984.

[12J Kott, P. S. Estimatinq Variances for the

June Enumerative Survey, RAD Staff Report

No. SRB-NERS-8806, May 1988.

[13J Kott, P. S. & Johnston R. Estimating the

Non-Overlap Variance Component for Multiple

Frame Aqricultural Surveys, RAD Staff Report

No. SRB-NERS-8805, May 1988.

[14J Kott, P. S. "Estimating Variances when the

First Phase Sample is Restratified," Survey

Methodology, forthcoming.

55

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