United States

Department of

Agriculture

National

Agricultural

Statistics

Service

Research and

Development Division

Washington DC 20250

RDD Research Report

RDD-07-01

March 2007

Supplemental

Samples for the 2007

Area Frame: A Design

for Estimating

Numbers of NML

Farms for the 2007

Census of Agriculture

Raj S. Chhikara

Floyd M. Spears

Charles R. Perry

Phillip S. Kott

This report was prepared for limited distribution to the research community outside the

United States Department of Agriculture. The views expressed herein are not necessarily

those of the National Agricultural Statistics Service or the United States Department of

Agriculture.
SUPPLEMENTAL SAMPLES FOR THE 2007 AREA FRAME: A DESIGN

FOR ESTIMATING NUMBERS OF NML FARMS FOR THE 2007 CENSUS

OF AGRICULTURE by Raj S. Chhikara1, Floyd M. Spears2, Charles R. Perry, and

Phillip S. Kott. Research and Development Division, National Agricultural Statistics Service,

United States Department of Agriculture, Washington, DC 20250-2000, March, 2007, NASS

Research Report No. RDD-07-01.

ABSTRACT

An area frame sample allocation is developed that will meet the survey cost and precision requirements of NASS in its estimation of the number of farms not on the mailing

list (NML) for the 2007 Census of Agriculture. Direct and model-predicted estimates of

the stratum standard deviations are obtained for 18 agricultural items (the 8 items used by

NASS for determining the area frame sample and 10 NML items) using the 2002 area frame

sample data, including the supplemental Agricultural Coverage Evaluation Survey (ACES)

segments. Standard deviation estimates of for these 18 agricultural items are considered as

input in the current NASS sample allocation procedure. Three different cases that utilize

these NML items are considered for determining sample allocations. In each case, the previously available 2007 sample allocation is combined with that obtained for the NML items

to determine a combined area frame sample allocation. The results from each case are compared to determine the ones that meet the NASS main objectives for the NML farm survey

in 2007. An area frame sample design that includes a supplemental sample of 3091 segments

is recommended.

KEY WORDS

NML Farm Items; Coefficient of Variation (CV); Stratum Standard Deviation; Model Fits;

Multivariate Allocation; Area Frame Sample Allocation; Stratum Groups

The views expressed herein are not necessarily those of NASS or USDA. This report was

prepared for limited distribution to the research community outside the U.S. Department

of Agriculture.

ACKNOWLEDGEMENTS

The authors would like to thank George Hanuschak and Roberta Pense for their keen

interest and support for the project. The authors would also like to thank Bill Wigton and

Herb Eldridge for their contribution and providing the SAS data file for this project.

1 Raj S. Chhikara is Professor, Division of Computing and Mathematics, University of Houston-Clear

Lake, Houston, TX.

2 Floyd M. Spears is Assistant Vice-President for Academic Affairs, Harding University, Searcy, AR.

i
Contents

GLOSSARY iv

EXECUTIVE SUMMARY v

1 INTRODUCTION 1

2 ESTIMATION OF STANDARD DEVIATION 1

3 SAMPLE ALLOCATIONS 3

4 2007 SAMPLE ALLOCATION AND SUPPLEMENTAL

SAMPLE 7

5 CONCLUSIONS 8

REFERENCES 11

APPENDIX A: 12

1 Chang and Kott (2004): NML Farm Modeling 12

2 Modeling Stratum Standard Deviation 13

APPENDIX B: Stratum Groups 15

APPENDIX C: Sample Allocation Tables 16

ii
List of Figures

1 Standard deviations of d-values versus p-values for the total number of NML

farms across all strata in the U.S. . . . . . . . . . . . . . . . . . . . . . . . . 3

List of Tables

1 Model Fits (No Intercept) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 U.S. sample allocations by stratum group for cases A, B and C using (a) dvalues, (b) p-values and (c) m-values to estimate standard deviations for NML

farm items. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 U.S. achievable target CV for NML items using (a) d-values, (b) p-values and

(c) m-values to estimate standard deviations for NML farm items. . . . . . . 6

4 Sample Design and Supplemental Samples by Stratum Group . . . . . . . . 8

5 Primary NML Items Causing Substantial Increases in Sample by State . . . 8

6 Strata with Substantial Supplemental Samples and their Causes . . . . . . . 9

B1 Stratum Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

C1 Recommended Supplemental Samples by State . . . . . . . . . . . . . . . . . 17

C2 Recommended Supplemental Samples by Strata within State . . . . . . . . . 19

iii
GLOSSARY

ACES - Agricultural Coverage Evaluation Survey segments

ASB Number - Agricultural Statistical Board Final Estimates (also known as Official

Statistics)

CV - the ratio of the standard error of an estimate to the ASB number for an item;

multiply the CV by 100 to convert to percentage

d-value - directly computed estimate of the stratum standard deviation from the 2002

area frame survey

JAS - June Area Survey

Multivariate Allocation - a nonlinear optimization convex programming procedure

used by NASS in determination of its sample allocation

m-value - estimated stratum standard deviation using the predicted value from modelfits as described in this report

NML Farm - a farm that is not on the census mailing list

NML Subdomains - sub-groups of NML farms that are minority-operated or specialty farms

p-value - estimated stratum standard deviation using the predicted value from the

empirical model for NML farms by Chang and Kott (2004)

R-square - measures the proportion of variability in the response data that is accounted for by the model

Sample Allocation - total number of sample segments at U.S. level and their allocation across land-use strata

Stratum - land-use stratum in NASS area frame

Stratum Group - group of land-use strata based on NASS categories of agriculture

intensity or location

iv
EXECUTIVE SUMMARY

One challenge in generating a reliable 2007 Census of Agriculture estimate is in determining that portion of the estimate represented by those farms not found on the Census mailing

list (NML). To estimate this portion, NASS will supplement the regular 2007 area segment

sample allocation with additional area segments. Estimates will be made for the total number

of NML farms and its sub-domains of Asian-operated, Black-operated, Hispanic-operated,

Native American-operated, female-operated, and vegetable, fruit, nursery and Christmas

tree farms. A target of approximately 3000 additional segments will be used for this supplemental sample. This will meet the Agency target CV of 0.5 percent at the national level

for the estimate of total number of NML farms and the Agency target CV of 5.0 percent for

each NML sub-domain, where the target CV is defined to be one hundred times the ratio of

standard error to the Agriculture Statistics Board (ASB) number for an item.

NASS uses a multivariate allocation procedure which requires stratum standard deviations for the agriculture items of interest as input to determine its sample allocation to

the land use strata. The annual area frame survey data collected in the 2002 Census year

included an additional 2429 Agricultural Coverage Evaluation Survey (ACES) segments.

These survey data were used in determining the stratum standard deviations for the NML

farm items. Three different stratum variances for each NML item were employed in this

study: (1) directly computed from the 2002 survey data, (2) Chang and Kott predicted

values based on logistic regression modeling of each NML item, and (3) determined from

the model-fit of directly computed versus Chang and Kott estimated stratum variance. This

third option was considered in an attempt to smooth the anomalies in stratum standard

deviation estimates that could skew the allocation for some strata. This is to safeguard

against the use of an unreliable stratum variance, particularly as a result of its estimation

based on small sample size.

The NASS allocation procedure was applied using each of the ten NML items separately,

and also in a multivariate approach using all ten NML items together. Another multivariate

approach was to consider all eighteen agricultural items, the eight regular items and the ten

NML items, together. In each case, the allocations were compared for all land strata with

the regular 2007 design sample, and the maximum was taken to be the stratum sample size.

The univariate NML allocations varied substantially for strata across various NML items,

whereas the allocation from the multivariate procedure with 10 NML items smoothed these

out and thus seemed more appropriate.

The optimum approach that met the target of adding approximately 3000 while having robust estimates of stratum standard deviations utilized the model-predicted stratum

standard deviations in a single multivariate allocation for the 10 NML items. The resulting

allocation was compared across land strata with the regular 2007 design sample, and the

maximum was taken to be the stratum sample size.

Five stratum groups are considered on the basis of land use as described in Appendix B.

These correspond to the land use strata numbered in 10’s, 20’s, 30’s, 40’s and 50’s. Stratum

v
groups 3 and 4 correspond to urban and low cultivation areas and are expected to have

relatively more NML farms than stratum groups 1 and 2 which correspond to high and

moderate cultivation areas, respectively. Stratum group 5 corresponds to non-agricultural

areas and is not expected to hae NML farms. The proposed sample allocation would require

a total of 3091 supplemental samples, of which 287 are in stratum group 1; 699 are in group

2; 381 are in group 3, 1724 are in group 4, and 0 in group 5. There is a more than 100

percent increase in stratum group 3, and nearly a 100 percent increase in stratum group 4

when compared to the regular 2007 sample design. The increases in sample size are much

smaller in stratum groups 1 and 2.

At the state level, there is a substantial increase in sample allocations in California

(additional 515 segments; an increase of 127 percent), Florida (additional 119 segments;

an increase of 119 percent), Michigan (additional 107 segments; an increase of 74 percent),

New Mexico (additional 105 segments; an increase of 85 percent), Oregon (additional 232

segments; an increase of 120 percent), and Texas (additional 625 segments; an increase of 56

percent). There are several strata in these states that have substantial supplemental samples

when compared to the regular 2007 design allocation.

The reason for the increase is determined by identifying the NML item for which the

univariate allocation in a stratum was substantially higher compared to the univariate allocation for any other NML item. The substantial increases for these states are due to one

or more NML items being predominant there. The primary NML item(s) for which reliable

estimation would require such an increase in sample allocation is listed in Tables 5 and 6.

Total NML farms is the primary cause of most increases, especially in stratum group 4.

A major exception is California, where Asian-operated farms are the cause of large increases

for several strata.

It should be noted that a slightly different allocation is being used operationally for

the 2007 ACES survey. The allocation takes advantage of targeted sampling in some

states/strata to reduce the number of samples needed, and yet achieve the target CV for

Black-operated and Asian-operated NML farms. It also takes into account the additional

goal of a state-level NML target CV of 6.5 percent for states or combined states in the case

of small states.

vi
1 INTRODUCTION

The NASS list of farms will be used to

mail for the 2007 Census of Agriculture.

However, since every list has incomplete coverage, a reliable estimate needs to be generated for those farms not on the mailing

list (NML). To accomplish this, supplemental area frame samples will be selected for the

2007 June Area Survey (JAS). From that expanded area frame, estimates will be generated for the NML farms and its sub-domains

for various minority operated and specialtytype farms. These sub-domains would include the following groups: Asian-operated,

Black-operated, Hispanic-operated, Native

American-operated, female-operated, and

vegetable, fruit, nursery and Christmas tree

farms. The NML farms are usually smaller

in size, operated by minorities or have

specialty-type farming.

For the annual agriculture survey, NASS

selects a stratified area frame sample specifically for that year based upon a multivariate

allocation procedure. To do this, the stratum standard deviations must be known for

eight primary agriculture items: corn, soybean, cotton, winter wheat, spring wheat,

durum wheat, number of farms and number

of cattle. To extend this allocation technique

to include the NML farm items for Census,

the stratum standard deviations for each of

the NML items would be required. Hence,

these are estimated for each NML item as

considered and described in Section 2.

Based on its experience from the 2002

Census of Agriculture (see the technical

memorandum of February 11, 2005 by

NML/ACES Sample Design Team), NASS

has decided to meet the following goals in

estimation of NML farm items from its 2007

area frame samples. The main objective is

to achieve a target CV of 0.5 percent at the

national level for the estimate of total number of farms, and a target CV of 5.0 percent

for each NML farm sub-domain. The target CV is defined to be 100 times the ratio

of standard error to the Agriculture Statistics Board (ASB) number for an item which

consists of its NML estimate plus the value

deteremined from the Census. Also, it is desired to have a target CV of 6.5 percent at

the state level. The exception would be for

small states where a target CV of 15 percent

is acceptable. Small states that are contiguous such as those in New England can be

combined to achieve the 6.5 percent target

CV.

Survey costs and timely acquisition of

data are major concerns for the agency.

NASS has set a target of approximately

3000 supplemental area segments in 2007

to achieve reliable estimates for the various

NML farm items. The focus of this research

was to develop a supplemental sample for the

2007 area frame design that would support

these NASS goals and objectives.

This report describes the approach taken

to estimate the stratum standard deviations

for the NML farm items and to determine

a robust and hence, a more stable sample

allocation. Section 3 describes different options considered for the sample allocation.

The various sample allocations obtained under these options are evaluated to determine

the one that is robust and most economical

to implement. The actual implementation,

of course, would require selection of supplemental samples, which is beyond the scope

of this research.

2 ESTIMATION OF

STANDARD DEVIATION

In 2002, NASS collected data on 2,429

additional area segments, besides its 11,075

June Area Survey (JAS) segments. These

1
supplemental samples were referred to as

the Agricultural Coverage Evaluation Survey or ACES. The JAS sample was primarily designed to estimate total farm counts,

major crop acreages, and livestock inventories. The ACES supplemental sample was

designed to improve the overall coverage of

the NML farms with a majority of these sample segments being allocated in low agricultural intensity strata. Thirty-three percent

of the ACES segments reported NML farms

as compared to 27 percent of the JAS segments. The ACES and JAS segments combined provided a much more useful data set

for the NML area survey, and hence are used

here for estimation of stratum standard deviations for the various NML farm items that

are considered in this study.

One set of stratum variances consisted of

directly computed survey values, called the

d-values. Another set of stratum variances

was made of those computed from the predicted values, called the p-values. These values were obtained from the empirically developed models for NML farms by Chang

and Kott (2004). They utilized the combined 2002 area frame survey data to model

the probability of an area frame farm not

being on the census mailing list and used a

host of covariates, including farm operator’s

gender, ethnicity and farm type, as outlined

briefly in Section 1 of Appendix A. A logistic regression methodology was the basis for

developing model-fits for the empirical NML

models. For full details, see Chang and Kott

(2004).

When the two estimates for stratum

standard deviation are compared, d-values

versus p-values, a strong linear relationship

was exhibited for each NML item. For example, depicted in Figure 1 is a plot of the

paired values for stratum standard deviation

of the total number of NML farms across

all land use strata. The d-values are on

the average varying more than the p-values.

This is an expected outcome since an NML

model-fit is likely to predict values that have

less variability than those directly computed

from the survey data.

When estimated based on a small sample size, the direct survey computed stratum standard deviation is not reliable and

needs to be improved upon. So we considered modeling the direct survey computed

values using the NML model predicted value

as a covariate. Since the covariate values

are more stable and less varying than the response values, this modeling of stratum standard deviation should smooth any anomalies

that exist in the directly computed survey

estimates. The model-fits should result in

more reliable predicted values for the stratum standard deviation. This in turn should

safeguard against the use of unreliable stratum standard deviations in the determination of sample allocation to strata.

Appendix A describes the modeling of direct survey computed stratum standard deviations as a function of that obtained from

the NML model predicted values.

Table 1 lists the model-fit characteristics, slope and R-square for each of the NML

items. It indicates a strong linear relationship with a correlation coefficient close to 1.

The model-fits are used to predict the

stratum standard deviations for the different NML items. These model-predicted

stratum standard deviations, called the mvalues, then provided a third set of stratum standard deviations for each NML item.

Thus three different stratum standard deviations were employed in this investigative

study of sample allocation. These three sets

of stratum standard deviation estimates are

referred to as follows:

2
Figure 1: Standard deviations of d-values versus p-values for the total number of NML farms

across all strata in the U.S.

01234567

0 1 2

3

4

5

6

7

P−Values

D−Values

a. d-values, which are directly computed

survey stratum standard deviations

b. p-values, which are estimated from

the empirical NML models developed

by Chang & Kott

c. m-values, which are estimated from

the model-fits of d-values and p-values

as described above.

3 SAMPLE ALLOCATIONS

The multivariate sample allocation for a

NASS area frame design is determined using

the stratum standard deviations computed

from prior year survey data for the regular

eight agriculture items. This multivariate allocation procedure can be carried out for any

one or more agriculture items of interest by

replacing one or more of the regular eight

items or by simply adding more items to it.

In this study, the allocation procedure considered each NML farm item individually, as

univariate case, as well as all 10 NML farm

items together as a single multivariate case.

Also considered is a single multivariate allocation for the eighteen agriculture items of

which eight are the regular items and ten are

the NML items. Since the 2007 area frame

design is for collection of survey data that

would support the annual JAS needs as well

3
Table 1: Model Fits (No Intercept)

NML Item Slope R-Square

Total 1.12 0.931

Asian 1.84 0.934

Black 1.44 0.983

Christmas Tree 1.47 0.973

Female 1.55 0.971

Fruit 1.74 0.969

Hispanic 1.57 0.939

Native American 1.54 0.919

Nursery 1.71 0.892

Vegetable 1.66 0.918

as reliable estimation of NML farm items,

the results of an allocation derived for the

NML items are then combined with the sample allocations obtained for the regular eight

items in order to determine a supplementary

sample.

The following three ways of sample allocation were considered for the NML farm

items to develop the final sample allocation.Table 2 lists the sample allocation by

stratum groups. There are five stratum

groups, which correspond to the land use

strata numbered in 10’s, 20’s, 30’s, 40’s and

50’s, as defined in Appendix B.

Case A: Univariate allocations for NML

items

1. Perform univariate NML allocations

for the 10 NML items.

2. Compare the univariate allocations

and take the maximum of these 10 allocations stratum by stratum to obtain

the combined univariate NML allocation. This corresponds to the column

labeled A1 in Table 4.

Case B: A single multivariate allocation

with 10 NML items. This corresponds to

the column labeled B1 in Table 4.

Case C: A single multivariate allocation

with the regular 8 agriculture items and the

10 NML items together. This corresponds to

the column labeled C1 in Table 4.

The final allocation was derived in each

case by taking the maximum stratum by

stratum of the regular 2007 NASS design allocation and the NML allocation. The resulting allocations for the three cases A, B

and C are given in columns labeled A2, B2

and C2, respectively, of Table 4.

In each of these cases, three sets of stratum standard deviations (d-values, p-values

and m-values, as discussed in Section 2) were

used to perform each of the three allocations

described above for the NML items. Table

2 lists the sample allocations obtained when

summed up at the stratum group level for

each of the cases A - C using (a) d-values,

(b) p-values, and (c) m-values for the NML

farm item stratum standard deviations.

Each of these allocations meets the goal

of an achievable target CV of 0.5 percent

at the national level for the total number of

NML farms and 5 percent or less at the national level for each of the NML sub-domains

with some exceptions. The Black-operated

farms and Christmas Tree farms have an

achievable CV slightly above 5 percent, and

the Asian-operated farms have the achievable CV close to 6 percent. Table 3 depicts

the achievable target CVs for all cases listed

in Table 2.

The NML sample allocations given in

columns A1, B1 and C1 of Table 2 show that

at the national level Case C has the largest

sample size, and that Case B has the smallest

sample size. The NML sample allocations

4
Table 2: U.S. sample allocations by stratum group for cases A, B and C using (a) d-values,

(b) p-values and (c) m-values to estimate standard deviations for NML farm items.

Case A Case B Case C

Combined Max of Multi- Max of Multi- Max of

Univariate NASS variate NASS variate NASS

for Design with 10 Design with Design

Stratum 10 NML’s & A1 NML’s & B1 18 Items & C1

Group (A1) (A2) (B1) (B2) (C1) (C2)

(a) Using d-values

10’s 3653 6545 3057 6339 6038 6630

20’s 3924 4294 3336 3872 3689 3883

30’s 767 844 616 700 554 634

40’s 4214 4431 3619 3922 3176 3435

50’s 96 104 96 104 96 104

Total 12,654 16,218 10,724 14,937 13,553 14,686

(b) Using p-values

10’s 1886 6067 1808 6041 6026 6575

20’s 2002 3010 1885 2987 2644 3076

30’s 440 521 391 472 355 436

40’s 2292 2701 2229 2664 1826 2261

50’s 96 104 96 104 96 104

Total 6716 12,403 6409 12,268 10,947 12,452

(c) Using m-values

10’s 2751 6314 2303 6192 6011 6559

20’s 3227 3815 2728 3474 3305 3580

30’s 767 834 651 728 608 687

40’s 3601 3879 3122 3491 2752 3036

50’s 96 104 96 104 96 104

Total 10,442 14,946 8900 13,989 12,772 13,966

5
Table 3: U.S. achievable target CV for NML items using (a) d-values, (b) p-values and (c)

m-values to estimate standard deviations for NML farm items.

Case A Case B Case C

Combined Max of Multi- Max of Multi- Max of

Univariate NASS variate NASS variate NASS

for Design with 10 Design with Design

Stratum 10 NML’s & A1 NML’s & B1 18 Items & C1

Group (A1) (A2) (B1) (B2) (C1) (C2)

a) Using d-values

Asian 5.63% 5.57% 5.81% 5.77% 5.79% 5.78%

Black 4.97% 4.83% 5.41% 5.19% 5.40% 5.35%

Ch. Tree 4.90% 4.88% 5.28% 5.24% 5.30% 5.29%

Female 1.73% 1.61% 1.86% 1.68% 1.83% 1.78%

Fruit 2.73% 2.64% 2.91% 2.78% 3.12% 3.08%

Hispanic 2.76% 2.57% 3.01% 2.73% 3.02% 2.96%

Nat. Amer. 4.13% 3.82% 4.96% 4.27% 4.96% 4.81%

Total 0.45% 0.41% 0.48% 0.44% 0.48% 0.47%

Nursery 3.77% 3.62% 4.63% 4.42% 4.85% 4.58%

Vegetable 3.29% 3.18% 3.61% 3.38% 3.68% 3.61%

b) Using p-values

Asian 5.68% 5.41% 6.55% 6.25% 6.43% 6.15%

Black 4.76% 4.25% 5.51% 4.38% 5.06% 4.51%

Ch. Tree 4.51% 4.14% 5.11% 4.55% 5.17% 4.68%

Female 1.43% 1.22% 1.46% 1.23% 1.42% 1.31%

Fruit 1.91% 1.83% 1.92% 1.84% 2.19% 2.13%

Hispanic 2.21% 1.90% 2.27% 1.95% 2.26% 2.16%

Nat. Amer. 3.22% 2.54% 3.52% 2.77% 3.18% 3.03%

Total 0.47% 0.40% 0.48% 0.41% 0.47% 0.44%

Nursery 3.10% 2.86% 3.59% 3.22% 3.44% 3.20%

Vegetable 2.56% 2.31% 2.66% 2.34% 2.64% 2.53%

c) Using m-values

Asian 5.96% 5.93% 6.11% 6.08% 6.10% 6.10%

Black 5.00% 4.81% 5.39% 5.12% 5.33% 5.24%

Ch. Tree 4.79% 4.72% 5.32% 5.21% 5.27% 5.20%

Female 1.84% 1.66% 1.98% 1.73% 1.95% 1.87%

Fruit 2.77% 2.69% 2.91% 2.80% 3.24% 3.22%

Hispanic 2.90% 2.59% 3.19% 2.79% 3.18% 3.10%

Nat. Amer. 3.91% 3.47% 4.95% 3.90% 4.12% 3.93%

Total 0.44% 0.40% 0.48% 0.42% 0.47% 0.46%

Nursery 3.79% 3.65% 5.21% 4.92% 4.68% 4.40%

Vegetable 3.39% 3.20% 3.80% 3.51% 3.90% 3.85%

6
using the p-values are substantially smaller

than those using the d-values or m-values.

The final allocations given in columns A2,

B2 and C2 show that case A has the largest

sample size, and cases B and C have approximately the same size, with some exception

when the p-values are used. However, more

samples are allocated to stratum groups 3

and 4 and fewer samples in stratum group 1

in Case B than Case C. Since it was preferred

to have more samples allocated in groups 3

and 4 than group 1, case B is viewed as optimal.

Compared to the univariate NML allocations in case A which vary substantially for

strata across various NML items, and their

maximization which leads to higher number

of samples, a single multivariate allocation

for the ten NML items in case B smoothes

these out and thus is a more stable allocation for the NML items considered together.

Furthermore, a single multivariate for the 18

items in Case C becomes more unstable because of the optimization process involved

in carrying out the sample allocation algorithm. Of the two, Case B is preferable

over Case C since it allocates more samples

to stratum groups 3 and 4, which are expected to have relatively more NML farms

than stratum groups 1 and 2 to which Case

C allocates more samples.

Next, the use of d-values in allocations

for the NML items leads to a higher sample

size then the survey cost would allow. The

sample size obtained from the use of p-values

turns out to be relatively low, especially for

stratum groups 3 and 4, and hence are less

likely to meet the NASS target CV requirements for the 2007 area frame survey.

It is noted that the achievable CV values

as given in Table 3 cannot be used to compare the three sets of stratum standard deviations (a) - (c) for their use in the allocation

procedure. When the achievable CV from

a sample allocation is computed using the

same stratum standard deviations as those

used in determining the sample allocation,

it will simply reproduce the input CV of the

allocation.

4 2007 SAMPLE

ALLOCATION AND

SUPPLEMENTAL

SAMPLE

The sample allocation obtained in Case

B above using the m-values is recommended

for the 2007 area frame sample design. This

meets the NASS goal of survey implementation cost of about 3000 additional segments

for its supplemental sample in support of

achieving reliable estimates for the various

NML items, as well as having a more stable stratum sample allocation. The following

method is therefore implemented for developing the new 2007 sample allocation:

i. For each new NML item, carry out

a model-fit of direct survey estimated

stratum standard deviation versus that

obtained using the NML model predicted values, and use the model-fit to

obtain the NML stratum standard deviations as described in Section 2.

ii. Determine a single multivariate allocation for the 10 NML items using the

stratum standard deviations obtained

from the model-fits described above.

iii. Finalize the allocation as outlined in

Case B by taking the stratum by stratum maximum of the regular 2007

NASS design allocation and the NML

multivariate allocation in (ii).

7
The regular NASS 2007 design allocation

and the proposed new 2007 design allocations are reported in Appendix C, by state

in Table C1 and by stratum within state in

Table C2. Also listed are the supplemental

samples obtained as the difference between

these two design allocations. The resulting

sample allocations are summarized by stratum group in Table 4.

Table 4: Sample Design and Supplemental

Samples by Stratum Group

Stratum 2007 Proposed Suppl.

Group Design 2007 Design Sample

10’s 5905 6192 287

20’s 2775 3474 699

30’s 347 728 381

40’s 1767 3491 1724

50’s 104 104 0

Totals: 10,898 13,989 3091

A total of 3091 supplemental samples are

required, of which 287 are in the stratum

group of 10’s; 699 are in the 20’s; 381 are in

the 30’s and 1724 are in the 40’s. There is

a 110 percent increase in stratum group 3,

and a 98 percent increase in stratum group

4 when compared to the regular 2007 sample

design.

5 CONCLUSIONS

Table 5 lists states that require substantial supplemental samples. It includes those

with at least 80 supplemental samples or

an increase of 100% or more over the regular 2007 sample design. The substantial increases in these states are due to one or more

NML items predominant there. Listed next

to each state is the primary NML item(s)

for which reliable estimation would require

such an increase in sample allocation. The

reason for the increase as stated herein is determined by identifying the NML items for

which the univariate allocations in a state

were substantially higher compared to the

univariate allocations for other NML items.

Table 5: Primary NML Items Causing Substantial Increases in Sample by State

State Increase (%) NML Items

AR 110 (34) Total, Asian,

Black

CA 515 (128) Asian

FL 119 (119) Total, Black,

Hispanic

GA 92 (32) Total, Black

MA 25 (208) Total, Nursery,

Chr. Tree

ME 31 (97) Total, Chr. Tree

MI 107 (74) Total

MS 97 (33) Black

NH 29 (290) Total, Vegetable

NM 105 (85) Total, Hispanic

NC 96 (30) Total, Asian,

Black

OH 88 (40) Total, Chr. Tree

OR 232 (120) Total, Asian,

Chr. Tree

SC 109 (92) Total, Black

TX 625 (56) Total, Black

VT 31 (148) Total, Hispanic

Total NML is a common cause for

increase in sample allocation in all but

two states. The predominance of Asianoperated farms in California and Blackoperated farms in Mississippi account for the

increase in those two states.

Listed in Table 6 are the specific strata

that have substantial supplemental samples

when compared to the regular 2007 design

allocation. Total NML is the primary cause

8
Table 6: Strata with Substantial Supplemental Samples and their Causes

Supplemental

State Stratum Samples Increase due to

Arkansas 21 67 Asian

42 43 Total, Indian

California 17 56 Asian

21 99 Asian

27 115 Asian

31 162 Asian

41 81 Asian

Florida 22 20 Total, Black

40 28 Total

42 32 Total

Georgia 40 92 Total, Black

Kentucky 40 24 Total

Louisiania 40 27 Total, Black, Vegetable

Maine 40 29 Christmas Tree

Massachusetts 40 25 Total, Christmas Tree, Nursery

Michigan 20 43 Total, Christmas Tree, Black, Indian

40 46 Total, Hispanic

Mississippi 20 46 Black

40 51 Total, Black

Missouri 40 75 Total

New Hampshire 40 29 Total, Vegetable

New Mexico 13 82 Total, Hispanic

New York 40 41 Total, Christmas Tree

North Carolina 40 88 Asian

Ohio 40 57 Total, Christmas Tree

Oklahoma 40 36 Total, Indian

Oregon 31 122 Asian

41 65 Total, Christmas Tree

South Carolina 40 83 Total, Black

Texas 26 34 Total

27 47 Total, Christmas Tree

42 482 Total, Black, Christmas Tree

Virginia 40 44 Total, Black, Christmas Tree

Vermont 40 31 Total, Hispanic

Washington 31 15 Total, Vegetable

Wisconsin 12 42 Christmas Tree

Wyoming 42 19 Total

44 11 Total

9
of many increases, especially in the 40’s stratum group. Asian-operated farms are the

cause of large increases in California for several strata.

It should be noted that the actual NASS

sample allocation to be used for the 2007

ACES samples takes into account targeted

sampling when a large increase in sample

size is needed to estimate Asian-operated or

Black-operated NML farms. The allocation

also looks more closely at state-level target

CV for NML farms. Thus the actual NASS

allocation varies slightly from the one given

here.

10
REFERENCES

Chang, Theodore, and Kott, Phillip S.

(2004). ”Modeling NML Using the Area

Frame Survey” Technical Manuscript.

August 27, 2004, USDA/NASS, Washington, D.C.

Chhikara, Raj S., Spears, Floyd M. and

Perry, Charles R. (2002). “Sample Allocation for Estimation of the Number

of ”Not on Mail List” (NML) Farms for

the 2002 Census of Agriculture,” USDANASS RDD Research Report No. RDD02-01, June, 2002.

Montgomery, Douglas C. and Peck, Elizabeth A. (1992). Introduction to Linear

Regression Analysis, second Edition, John

Wiley, New York.

NML/ACES Sample Design Team. ”Decision Memorandum for the 2007 Agriculture Coverage Evaluation Survey (ACES)

Sample Size”, Technical Memo, February 11, 2005, NASS/USDA, Washington,

D.C.

11
APPENDIX A:

1 Chang and Kott (2004): NML Farm Modeling

A farm not on the census mailing list (NML) is likely to be small in size, and has

certain characteristics as to its operation, farming, livestock or the amount of annual sales.

Thus, a measure of the NML farm likelihood may be modeled by taking farm characteristics

into account. If p denotes the probability of a farm being NML, then p may be expressed

mathematically as a function

p = f(x1, x2, ..., xp) (1)

where x1, x2, ..., xp denotes the covariates that quantify the farm characteristics and affect

the NML farm likelihood. A logistic regression model is used to specify the functional form:

ln p

1 − p = β0 + β1x1 + ... + βpxp (2)

A model-fit is carried out to estimate the unknown coefficients β0, β1, ..., βp for the model in

Equation (2).

Change and Kott (2004) conducted an extensive empirical study of modeling NML farm

using the data from the June 2002 Area Frame Survey, including ACES area segments. For

the covariates in the model, included were the farm sales and farm type variables, operator

characteristics, farm size and stratum, among others. A stepwise regression procedure was

utilized to select the variables for achieving optimal model-fit. The farm sale was found to

be the most important predictor of NML farm. Certain farm operation characteristics and

stratum were also significant predictors. Three population groups were determined appropriate to carry out the model-fits: (1) California, (2) Illinois, Indiana and Iowa combined

together, and (3) all 48 contiguous states. Alaska and Hawaii do not participate in the Area

Frame Survey.

Making use of a model-fit, an estimate of pi, the probability of farm i being NML, was

obtained from

ln pˆi

1 − pˆi

= βˆ0 + βˆ1x1 + ... + βˆkxk (3)

where x1, x2, ..., xk are the variables selected for model-fit.

NASS estimation procedure was applied to the model-fit determined probabilities ˆpi to

estimate the total number of NML farms and each of its subdomains. If the tracts in a

12
population area frame survey (AFS) are denoted by UA, then the AFS estimate of the total

number of farms in the population is given by

X

k∈UA

wkfkpˆk (4)

where wk is the sampling weight (expansion factor) and fk is the adjusted tract-to-farm

acreage ratio. For a subdomain, Equation (4) was applied using the ˆpk obtained for the subdomain item. A calibration process was involved in obtaining domain specific probabilities

since a binary variable was used in the model for each subdomain of NML farms.

For full details, refer to Chang and Kott (2004).

2 Modeling Stratum Standard Deviation

NASS direct survey computed stratum variance is an unbiased estimator of the population

variance for the stratum. However, we consider modeling the stratum standard deviation

due to a reduced amount of variability seen in model error.

Let s denote the population standard deviation for a stratum. Two estimates of s are

considered:

(a) y = direct survey computed standard deviation

(b) x = standard deviation obtained using predicated values from an NML model fit.

Both x and y are subject to sampling design variability. However, x is expected to be less

variable than y because x is obtained using the individual values that got smoothed by an

NML farm model fit described in Section 1 of Appendix B.

Considering the fact that sample standard deviation is a biased estimator of population

standard deviation, we consider its modeling with errors in both variables as follows:

yi = α + si + i (5)

and

xi = γ + φsi + δi (6)

where si is the stratum standard deviation, E[i] = 0 and E[δi] = 0 and Cov(i, δi)=0, i =

1, 2, ...n. Note that α and γ account for the bias in y and x, respectively. Further, 0 <φ< 1

since the NML model-smoothed value is expected to compress the actual stratum standard

deviation si, i = 1, 2, ..., n.

13
There are two possible ways of modeling here; either express y in terms of x or express

x in terms of y. However, there may be no difference between the two such modelings when

the paired data (xi, yi) are very close to a straight line, which in fact is the case as discussed

in Section 2. Thus, we consider y as the response and x as the regressor and write the model

that follows from Equation (5) and (6) as

yi = (α − γ

φ

) + 1

φ

xi + (i − δi

φ )

= β0 + β1xi + ei. (7)

where β1 = φ−1 > 1 and E[ei]=0, i = 1, 2, ..., n.

A no-intercept model is assumed. Its justification follows by recognizing that xi = 0

implies yi = 0. It could also be argued that β0 = (α − β1γ) ≈ 0 since both the xi and yi are

based on the same NASS estimation method, except the xi are computed using the NML

model-smoothed values and the yi are computed using the actual survey observed values.

The linear model in Equation (7) has error term ei that may be correlated with the

regression xi. If so

cov(xi, ei) = E[(xi − E(xi))(ei − β1δi)]

= E[δi(ei − β1δi)]

= −β1σ2

δ (8)

where E(δ2

i) = σ2δ . Since β1 > 1, there is negative correlation between the regressor value xi

and the error term ei. However, if σ2

δ is negligible, then the two are almost uncorrelated.

Table 1 on page 4 lists the model-fits obtained for various NML items. These model-fits

are made by applying the standard least square methods to the data. As expected, the

estimate slope βˆ1 > 1 in all cases. Since the error in xi is ignored in obtaining these modelfits, βˆ1 may not be unbiased. It follows that E[βˆi] = βi/(1 + θ), where θ = σ2

δ /σ2x and σ2x is

the variance between the xi in the data. However, if σ2

δ is negligible compared to σ2x, ˆ

β1 is

approximately an unbiased estimator of β1. The x values do vary considerably across strata,

as can be seen in Figure 1 in the case of total NML farms. On the other hand, it seems

the empirical NML model-fit developed by Change and Kott was fairly robust to have lead

to a biased yet efficient estimate of stratum standard deviation s, in which case σ2

δ may be

negligible.

14
APPENDIX B: Stratum Groups

NASS land use strata are grouped together by considering similarity in their major land

use, depending upon the agricultural intensity or the location. Table B1 lists the characteristics of the five groups of land use strata, the area level at which the sample allocations are

reported in Table 2 and discussed in the text.

Table B1: Stratum Groups

Strata Land-use Major

Group Strata Descriptor

1 10 - 19 Intense Cultivation

2 20 - 29 Moderate Cultivation

3 30 - 39 Urban Area

4 40 - 49 Low Cultivation

5 50 - 59 Non-Agricultural

15
APPENDIX C: Sample Allocation Tables

List of Tables

C1 Recommended Supplemental Samples by State . .. . .. .. . . . . . . .. .. . .. . . . . . . .. . 17

C2 Recommended Supplemental Samples by Strata within State .. .. . . . .. . . . . .. . 19

16
Table C1: Recommended Supplemental Samples by State

State State Regular Proposed Supplemental

FIPS Abbrev. 2007 Design 2007 Design Samples

1 AL 236 272 36

4 AZ 118 158 40

5 AR 328 438 110

6 CA 404 919 515

8 CO 267 291 24

9 CT 8 11 3

10 DE 23 29 6

12 FL 100 219 119

13 GA 290 382 92

16 ID 148 208 60

17 IL 401 401 0

18 IN 264 264 0

19 IA 452 452 0

20 KS 487 487 0

21 KY 189 227 38

22 LA 249 276 27

23 ME 32 63 31

24 MD 61 61 0

25 MA 12 37 25

26 MI 145 252 107

27 MN 393 419 26

28 MS 298 395 97

29 MO 383 458 75

30 MT 316 316 0

31 NE 473 473 0

32 NV 26 30 4

33 NH 10 39 29

34 NJ 48 59 11

35 NM 124 229 105

36 NY 96 143 47

37 NC 319 415 96

38 ND 420 420 0

39 OH 220 308 88

40 OK 335 371 36

41 OR 194 426 232

42 PA 179 225 46

44 RI 8 8 0

45 SC 119 228 109

46 SD 395 395 0

47 TN 334 334 0

Continued on next page

17
Table C1 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. 2007 Design 2007 Design Samples

48 TX 1120 1745 625

49 UT 69 102 33

50 VT 21 52 31

51 VA 179 223 44

53 WA 267 307 40

54 WV 66 77 11

55 WI 219 262 43

56 WY 53 83 30

Total US 10,898 13,989 3091

18
Table C2: Recommended Supplemental Samples by

Strata within State

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

1 AL 13 78 78 0

1 AL 20 90 90 0

1 AL 31 4 4 0

1 AL 32 2 2 0

1 AL 40 60 96 36

1 AL 50 2 2 0

4 AZ 13 52 83 31

4 AZ 14 8 8 0

4 AZ 20 12 12 0

4 AZ 21 2 2 0

4 AZ 31 4 12 8

4 AZ 32 2 2 0

4 AZ 41 23 23 0

4 AZ 44 2 2 0

4 AZ 45 2 2 0

4 AZ 46 2 2 0

4 AZ 47 2 2 0

4 AZ 48 3 3 0

4 AZ 49 2 3 1

4 AZ 50 2 2 0

5 AR 11 232 232 0

5 AR 21 32 99 67

5 AR 31 4 4 0

5 AR 32 2 2 0

5 AR 42 56 99 43

5 AR 50 2 2 0

6 CA 11 209 209 0

6 CA 17 20 76 56

6 CA 19 6 6 0

6 CA 21 63 162 99

6 CA 27 12 127 115

6 CA 31 16 178 162

6 CA 32 2 4 2

6 CA 41 54 135 81

6 CA 45 20 20 0

6 CA 50 2 2 0

8 CO 13 156 156 0

8 CO 15 6 6 0

8 CO 20 35 35 0

Continued on next page

19
Table C2 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

8 CO 24 3 3 0

8 CO 25 6 6 0

8 CO 31 3 10 7

8 CO 32 3 3 0

8 CO 34 12 12 0

8 CO 35 10 10 0

8 CO 40 3 3 0

8 CO 41 2 2 0

8 CO 42 3 9 6

8 CO 43 3 3 0

8 CO 44 3 11 8

8 CO 45 3 3 0

8 CO 47 10 13 3

8 CO 48 3 3 0

8 CO 50 3 3 0

9 CT 14 2 2 0

9 CT 31 2 2 0

9 CT 40 2 5 3

9 CT 50 2 2 0

10 DE 13 10 10 0

10 DE 20 5 11 6

10 DE 31 2 2 0

10 DE 32 2 2 0

10 DE 40 2 2 0

10 DE 50 2 2 0

12 FL 13 25 46 21

12 FL 17 6 10 4

12 FL 18 2 2 0

12 FL 21 15 18 3

12 FL 22 6 26 20

12 FL 27 6 17 11

12 FL 31 6 6 0

12 FL 32 2 2 0

12 FL 40 18 46 28

12 FL 42 12 44 32

12 FL 50 2 2 0

13 GA 13 91 91 0

13 GA 20 121 121 0

13 GA 31 2 2 0

13 GA 32 2 2 0

13 GA 40 72 164 92

Continued on next page

20
Table C2 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

13 GA 50 2 2 0

16 ID 10 30 30 0

16 ID 13 9 15 6

16 ID 15 48 68 20

16 ID 20 6 6 0

16 ID 22 16 16 0

16 ID 25 15 15 0

16 ID 31 3 21 18

16 ID 32 3 3 0

16 ID 40 3 18 15

16 ID 41 3 4 1

16 ID 42 3 3 0

16 ID 43 6 6 0

16 ID 50 3 3 0

17 IL 11 250 250 0

17 IL 12 70 70 0

17 IL 20 50 50 0

17 IL 31 10 10 0

17 IL 32 4 4 0

17 IL 40 15 15 0

17 IL 50 2 2 0

18 IN 11 125 125 0

18 IN 12 50 50 0

18 IN 20 55 55 0

18 IN 31 15 15 0

18 IN 32 2 2 0

18 IN 40 15 15 0

18 IN 50 2 2 0

19 IA 13 378 378 0

19 IA 20 66 66 0

19 IA 31 2 2 0

19 IA 32 2 2 0

19 IA 40 2 2 0

19 IA 50 2 2 0

20 KS 11 234 234 0

20 KS 12 112 112 0

20 KS 20 120 120 0

20 KS 31 3 3 0

20 KS 32 3 3 0

20 KS 40 12 12 0

20 KS 50 3 3 0

Continued on next page

21
Table C2 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

21 KY 13 80 80 0

21 KY 20 70 70 0

21 KY 31 5 19 14

21 KY 32 2 2 0

21 KY 40 30 54 24

21 KY 50 2 2 0

22 LA 13 187 187 0

22 LA 20 24 24 0

22 LA 31 4 4 0

22 LA 32 2 2 0

22 LA 40 30 57 27

22 LA 50 2 2 0

23 ME 14 12 14 2

23 ME 31 2 2 0

23 ME 40 16 45 29

23 ME 50 2 2 0

24 MD 13 15 15 0

24 MD 20 30 30 0

24 MD 31 2 2 0

24 MD 32 2 2 0

24 MD 40 10 10 0

24 MD 50 2 2 0

25 MA 14 2 2 0

25 MA 31 2 2 0

25 MA 32 2 2 0

25 MA 40 4 29 25

25 MA 50 2 2 0

26 MI 11 63 63 0

26 MI 12 24 42 18

26 MI 20 42 85 43

26 MI 31 2 2 0

26 MI 32 2 2 0

26 MI 40 10 56 46

26 MI 50 2 2 0

27 MN 11 210 210 0

27 MN 12 120 120 0

27 MN 20 35 35 0

27 MN 31 8 10 2

27 MN 32 2 2 0

27 MN 33 4 12 8

27 MN 40 12 28 16

Continued on next page

22
Table C2 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

27 MN 50 2 2 0

28 MS 11 95 95 0

28 MS 12 35 35 0

28 MS 20 80 126 46

28 MS 31 2 2 0

28 MS 32 2 2 0

28 MS 40 80 131 51

28 MS 42 2 2 0

28 MS 50 2 2 0

29 MO 11 195 195 0

29 MO 12 70 70 0

29 MO 20 70 70 0

29 MO 31 4 4 0

29 MO 32 2 2 0

29 MO 40 40 115 75

29 MO 50 2 2 0

30 MT 13 160 160 0

30 MT 20 75 75 0

30 MT 31 3 3 0

30 MT 32 3 3 0

30 MT 42 6 6 0

30 MT 43 48 48 0

30 MT 44 12 12 0

30 MT 45 3 3 0

30 MT 46 3 3 0

30 MT 50 3 3 0

31 NE 11 285 285 0

31 NE 12 77 77 0

31 NE 20 63 63 0

31 NE 31 4 4 0

31 NE 32 2 2 0

31 NE 40 40 40 0

31 NE 50 2 2 0

32 NV 13 4 4 0

32 NV 20 8 8 0

32 NV 31 2 6 4

32 NV 32 2 2 0

32 NV 41 2 2 0

32 NV 42 2 2 0

32 NV 43 2 2 0

32 NV 44 2 2 0

Continued on next page

23
Table C2 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

32 NV 50 2 2 0

33 NH 14 2 2 0

33 NH 31 2 2 0

33 NH 40 4 33 29

33 NH 50 2 2 0

34 NJ 13 5 5 0

34 NJ 20 30 30 0

34 NJ 31 5 5 0

34 NJ 32 2 2 0

34 NJ 40 2 13 11

34 NJ 42 2 2 0

34 NJ 50 2 2 0

35 NM 12 6 6 0

35 NM 13 32 114 82

35 NM 20 12 12 0

35 NM 31 2 13 11

35 NM 32 2 2 0

35 NM 40 5 8 3

35 NM 41 27 27 0

35 NM 42 10 19 9

35 NM 43 20 20 0

35 NM 44 2 2 0

35 NM 45 2 2 0

35 NM 46 2 2 0

35 NM 50 2 2 0

36 NY 13 25 25 0

36 NY 20 50 56 6

36 NY 31 3 3 0

36 NY 32 2 2 0

36 NY 40 12 53 41

36 NY 45 2 2 0

36 NY 50 2 2 0

37 NC 13 30 30 0

37 NC 20 200 200 0

37 NC 31 5 13 8

37 NC 32 2 2 0

37 NC 40 80 168 88

37 NC 50 2 2 0

38 ND 11 231 231 0

38 ND 12 90 90 0

38 ND 20 85 85 0

Continued on next page

24
Table C2 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

38 ND 31 2 2 0

38 ND 32 2 2 0

38 ND 33 2 2 0

38 ND 40 6 6 0

38 ND 50 2 2 0

39 OH 11 110 110 0

39 OH 12 35 35 0

39 OH 20 30 61 31

39 OH 31 15 15 0

39 OH 32 5 5 0

39 OH 40 20 77 57

39 OH 50 5 5 0

40 OK 11 120 120 0

40 OK 12 36 36 0

40 OK 20 80 80 0

40 OK 31 3 3 0

40 OK 32 3 3 0

40 OK 40 90 126 36

40 OK 50 3 3 0

41 OR 10 30 30 0

41 OR 13 40 40 0

41 OR 20 50 95 45

41 OR 31 2 124 122

41 OR 32 2 2 0

41 OR 41 8 73 65

41 OR 43 60 60 0

41 OR 50 2 2 0

42 PA 13 24 27 3

42 PA 20 98 121 23

42 PA 31 5 5 0

42 PA 32 2 2 0

42 PA 40 48 68 20

42 PA 50 2 2 0

44 RI 14 2 2 0

44 RI 31 2 2 0

44 RI 40 2 2 0

44 RI 50 2 2 0

45 SC 13 18 18 0

45 SC 20 60 86 26

45 SC 31 2 2 0

45 SC 32 2 2 0

Continued on next page

25
Table C2 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

45 SC 40 35 118 83

45 SC 50 2 2 0

46 SD 11 99 99 0

46 SD 12 130 130 0

46 SD 20 54 54 0

46 SD 31 2 2 0

46 SD 32 2 2 0

46 SD 33 2 2 0

46 SD 40 100 100 0

46 SD 44 4 4 0

46 SD 50 2 2 0

47 TN 13 100 100 0

47 TN 20 140 140 0

47 TN 31 10 10 0

47 TN 32 2 2 0

47 TN 40 80 80 0

47 TN 50 2 2 0

48 TX 10 88 88 0

48 TX 13 40 40 0

48 TX 14 273 273 0

48 TX 15 90 90 0

48 TX 16 16 16 0

48 TX 18 30 30 0

48 TX 20 64 64 0

48 TX 21 140 163 23

48 TX 24 70 70 0

48 TX 25 70 72 2

48 TX 26 4 38 34

48 TX 27 10 57 47

48 TX 28 25 30 5

48 TX 31 10 10 0

48 TX 32 5 5 0

48 TX 40 60 82 22

48 TX 41 49 52 3

48 TX 42 72 554 482

48 TX 43 2 9 7

48 TX 50 2 2 0

49 UT 13 28 30 2

49 UT 20 20 50 30

49 UT 31 4 4 0

49 UT 32 2 2 0

Continued on next page

26
Table C2 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

49 UT 41 5 5 0

49 UT 43 2 2 0

49 UT 44 2 2 0

49 UT 45 2 3 1

49 UT 46 2 2 0

49 UT 50 2 2 0

50 VT 14 12 12 0

50 VT 31 2 2 0

50 VT 40 5 36 31

50 VT 50 2 2 0

51 VA 13 15 15 0

51 VA 20 100 100 0

51 VA 31 10 10 0

51 VA 32 2 2 0

51 VA 40 50 94 44

51 VA 50 2 2 0

53 WA 10 119 119 0

53 WA 13 60 60 0

53 WA 20 48 64 16

53 WA 31 5 20 15

53 WA 32 2 2 0

53 WA 41 27 36 9

53 WA 44 2 2 0

53 WA 45 2 2 0

53 WA 50 2 2 0

54 WV 13 10 10 0

54 WV 20 14 14 0

54 WV 31 4 4 0

54 WV 32 2 2 0

54 WV 40 34 45 11

54 WV 50 2 2 0

55 WI 11 70 70 0

55 WI 12 30 72 42

55 WI 20 80 81 1

55 WI 31 5 5 0

55 WI 32 2 2 0

55 WI 40 30 30 0

55 WI 50 2 2 0

56 WY 11 8 8 0

56 WY 12 8 8 0

56 WY 20 8 8 0

Continued on next page

27
Table C2 (continued)

State State Regular Proposed Supplemental

FIPS Abbrev. Stratum 2007 Design 2007 Design Samples

56 WY 31 2 2 0

56 WY 32 2 2 0

56 WY 40 2 2 0

56 WY 42 5 24 19

56 WY 43 10 10 0

56 WY 44 2 13 11

56 WY 45 2 2 0

56 WY 46 2 2 0

56 WY 50 2 2 0

Total US All 10,898 13,989 3091

28