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BUREAU OF THE CENSUS STATISTICAL RESEARCH DIVISION REPORT SERIES

SRD Research Report Number: CENSUS/SRD/RR-87/08

SURVEY BASED ESTIMATES OF CENSUS ADJUSTMENT FACTORS AND ITS VARIANCES AND COVARIANCES - A MONTE CARLO STUDY

Elizabeth T. Huang Statistical Research Division

Bureau of the Census Room 3130, F.O.B. 84

Washington, D.C. 20233 U.S.A.

This series contains research reports, written by or in cooperation with staff members of the Statistical Research Division, whose content may be of interest to the general statistical research community. The views reflected in these reports are not necessarily those of the Census Bureau nor do they necessarily represent Census Bureau statistical policy or practice. Inquiries may be addressed to the author(s) or the SRD Report Series Coordinator, Statistical Research Division, Bureau of the Census, Washington, D.C. 20233.

Recommended: Nash M. Monsour

Report completed: February 26, 1987

Report issued: February 26, 1987

Survey Based Estimates of Census Adjustment Factor3 and Its Variance3 and Covariances - A Monte Carlo Study

Elizabeth T. Huang

I. Introduction

The Census Bureau is currently evaluating strategies for adjusting the

census count for small areas. One of the adjustment strategies being studied

is termed the statistical synthetic procedure. This procedure utilizes survey

- based estimates of total population by specified (non-administrative)

categories to construct census adjustment factors. As studied in Isaki,

Diffe:dal and Schultz (1986), the adjustment factors are applied to

Enumeration District (ED) counts of the appropriate category. Sever al

statistical synthetic procedures were constructed and evaluated using four

artificial population3 as proxies for the 1980 true population counts. The

adjustment factors for different synthetic estimators were calculated based on

the artificial population counts versus census counts for each category. The

census adjustments were at the ED level and the performances of the synthetic

estimators were evaluated at state or county level using several measures of

improvement.

In practice, the adjustment factor3 required for statistical synthetic

estimation must be estimated. For example, they can be estimated via a Post

Enumeration Survey (PES). In the following, it is assumed that the estimated

adjustment factors are consistent.

In this study, we try to simulate the effects of sampling on the

adjustment factors and the resulting statistical synthetic estimates.

Construction of a sample design using information from the available 1980

Census file will be described. The estimated censu3 adjustment factors from a

2

single replicated sample and a Monte Carlo based estimate of its variance and

.

covariance will be provided. The two purposes of the study are -

(1) The sample estimated adjustment factors can be used to obtain sample

based statistical synthetic estimates of the census population. We then

can evaluate the effect of sampling error on the adjusted census counts

based on the artificial populations.

(2) The variance and covariance of the estimated census adjustment factors

can be used for further smoothing of the adjustment factors through a

model1 ing approach. In addition, variances of the sample based

statistical synthetic estimators can be obtained. *

II. Data Files

The 1980 Census ED file used in the second annual research conference

paper (ARC II> (See Isaki, Diffendal and Schultz (1986) 1 was used as our

sampling frame. Based on the results of the ARC II paper, we considered two

of the four artificial populations - AP2, AP3 and two synthetic estimators -

syn DA, syn 2. AP2 and AP3 were formed so that these artificial population

counts by age-race-sex at the U.S. level equaled the comparable demographic

analysis counts. AP2 and AP3 differ on the basis of how the Hispanic (and

hence the Rest) artificial population data are derived. For AP2, it is

assumed that Hispanics are like the Nonblack population. For AP3, it is

assumed that Hispanics are similar to Blacks. The differences between syn DA

and syn 2 lay in the adjustment strata. It is assumed that the adjustment of

census undercount in small areas (EDs or blocks) is based on the construction

of strata of persons felt to possess similar undercount rates. Syn 2 uses

geographic division, size of place, and race as strata. (There are 96

strata); while syn DA uses age, race and sex as strata (there are 30

3

strata). In Isaki, et.al. (19861, it i 3 concluded that syn 2 is better than

the other synthetic estimates considered on the basis of the measures of

improvement used when estimating at the state and county level and when

adjustment factors are estimated without error.

Our objectives are to obtain sample replicates through a simple sampling

plan, to calculate replicate based adjustment factors of syn 2 and syn DA

using artificial populations AP2 and AP3 and to compute the variance and

covariance of the estimates. In the next section, a sample design and sample

f size allocation will be described.

III.*Sample Design and Allocation

A. Stratification of 1980 Census Enumeration District (ED) Files

The sampling frame for the study is the 1980 Census ED files. The

variables for each ED in the file are the geographic information (state,

county, SMSA, place size, etc. > and population tallies by age, race and sex

for 1980 census counts and census substitution counts. There are 289,237 EDs

in the 1980 Census ED files. The selected summary statistics for the ED files

by geographic divisions are tabulated in Table 1. Our objective is to obtain

a simple sample design in order to estimate the adjustment factors of

synthetic 2 estimator and its variance and covariance from fairly large

samples. For easy handling of such a big file - 1980 ED file, and to support

the estimation of syn 2 adjustment factors, we decided to use a stratified

sample design where the strata are similar to the adjustment strata

characterizing the synthetic 2 estimator. The adjustment strata of syn 2 were

defined on the basis of geographic divisions, size of place and race. Within

each geographic division, the population was divided by size of place and

race. The size of place categories generally were: central cities (CC> in a

4

SMSA with population 250,000 +; population in a SMSA but not in a central

city; population in cities 10,000 to 50,000 (not in SMSA), and rural areas

with population less than 10,000. In some geographic divisions, big cities

such as New York, Chicago, Detroit and Lo3 Angeles were formed as a separate

stratum; in other divisions, central cities in SMSA with population 50,000-

250,000 were formed as a separate stratum. The three race groups were Black,

Hispanic and Rest. In some geographic divisions, some races were collapsed

(see Appendix 1 for syn 2 adjustment strata). In calculating the adj us tment

factor, the unit in the adjustment strata is a person, while the sampling unit

for the study is an enumeration district (ED), which contains, on average,

approximately 775 persons or 200 households. There are sometimes persons of

several races in an ED. To stratify 1980 Census ED files we first used the

adjustment strata (geographic information only) of syn 2 to obtain an initial

stratification. We had 54 strata from this initial stratification by

geographic information. The summary statistics for each stratum of the 1st

stratification are tabulated in Table 3. We then used race variables as

defined in the adjustment strata of syn 2 to get the final stratification. We

defined a cutoff point such that the race proportion of each ED in the stratum

will be in a specified range. In a 1990 PES it will not be possible to define

ED strata in the manner used in this report. Such loss in efficiency could be

compensated by a more efficient block (rather than ED) unit sample design.

This is open to speculation. We did some collapsing or splitting if the

number of EDs in the stratum was too small or too large. For example, in most

geographic divisions, the number of EDs in a city with population between

10,000 and 50,000 is much smaller than the number of EDs in the rural area

with population of less than 10,000. We combined these two areas for most

di vi si ons . For division 8 - mountain area, the rural area with population of

5

less than 10,000 is split by race (white and nonwhite). After taking race

into account, we ended up with EDs stratified into 88 sampling strata. There

are 96 adjustment strata for syn 2. The summary statistics (no. of EDs, total

person3, variances, CVs for each race) for each stratum of the final

stratification (labeled stratification 2) is tabulated in Table 2. The

stratum code for the 1st stratification in the ED file is G2. The stratum

code for the final stratification in the ED files is G3. The correspondence

of these two codes are tabulated in Table 4.

Using race variables in the sampling stratification 2 minimizes zero

count cells in the syn 2 adjustment strata. Using sampling stratification 2

rather than 1 also increase3 the efficiency of the estimated totals for each

race either at the division or national level.

Let ;,Li’ be the estimated total of the ith race in the geographic

division or United States from a stratified random sample for i = 1, 2, 3

(Black, Hispanic and Rest).

A proportional sample allocation was used to determine the stratum sample

size. The population size is N ED’s. The sample size is n ED’s,. The stratum

sample size nh via proportional allocation is nh = Nhf, where Nh is the

population stratum size of stratum h, and f is the sampling fraction in each

stratum;

f = n/N.

A (i> The variance of the Y,~ is

= (1-f) f-l ZN S2 h h h

We have calculated the Z N S2 for each race i using the stratification 1 h h h

(geographic adjustment strata of synthetic 2 without using race), and the

6

stratification 2 (using stratification 1 and race variables). The

calculations showed that for the United States, the reductions in variance of

estimated total by using stratification 2 over stratification 1 are 265, 19%

and 2% for Black, Hispanic and Rest, respectively. The ratio of variances for

each division by using stratification 2 versus 1 is tabulated in the last

column of Table 2.

B. Sample Allocation

Two sampling schemes were originally suggested by Bob Fay. The first

- assumes a sample of ED’s that equal the anticipated 1990 PES sample size in

terms of total number of persons. The other is to translate the anticipated

sampl% size into blocks and use the number of blocks as the sample number for

ED’s. The first sampling scheme would represent an upper bound on sampling

error while the latter would represent an lower bound on the sampling error.

Assume that the 1990 PES will use l,OOO,OOO sample persons. Then the sample

size in our study for the 1st sampling scheme would be approximately 1440 EDs;

for the 2nd sampling scheme - approximately 10,000 EDs. It was decided to

draw 100 samples to do the Monte Carlo study to calculate the variances. With

computer limitation, timing and cost considerations, we were forced to reduce

the number of sample replicates to 90 and not to study the 10,000 ED sample.

The Monte Carlo study was first carried out for sample size of 1440 EDs. We

later repeated the study with sample size 721 to study the effect of sample

size on the variances of the adjustment factors.

Two sample allocations, Neyman allocation and proportional allocation,

were compared . (NJ For Neyman allocation, the stratum sample size, nh , in each

Stratum h is n NhSh (E N S )-‘, h h h

where Nh is the stratum size, Sh2 is the

stratum variance. For proportional allocation, the stratum sample size

(PI “h is nf, where f = NhN -1 . Geographic division 2’s data were used for the

7

comparison. The stratum sample sizes from both allocations using three race

stratum information were tabulated in Table 5.

Neyman allocations did give us better efficiency for estimating the three

race totals at the division level. However, the stratum sample size given by

the Neyman allocation using Hispanic or Black characteristic was 1 or 2 for

those strata with mainly “rest” race, and large stratum sample sizes were

allocated for those strata concentrated with Hispanic or Black. Since the

Rest group was also important, we decided to use proportional allocation.

. With a frame size of 289,237 EDs, and specified sample size of 1440 EDs,

the sampling rate is 0.00498 for each stratum or approximately one in 200 in

each*3 trat um. With the rounding errors of obtaining integer strata sizes, the

sampling strata weights varied about 200. The sample strata sizes are

tabulated in Table 6 with total sample sizes of 1440 and 721, respectively.

The ED3 of each geographic division were sorted by the sampling strata,

and the EDs within a sampling stratum were then sorted by the syn 2 adjustment

stratum according to the geographic area order. For easy operating and

economic reasons, a stratified equal probability systematic sampling procedure

was used.

IV. Estimation Procedure

The adjustment factors for syn DA and syn 2 using 2 artificial

populations, AP2 and AP3, were calculated for each of the selected samples as

f ollow3.

Let ^F (‘I J

be the estimated adjustment factor of the j-th adjustment

stratum by using sample 1, j = 1, . . . . J, 1 = 1, . . . . L, where J is the

number of strata, L is the number of samples.

8

(1) Let thij

be the number of true counts in the j-th adjustment stratum

from the 1-th sample of the i-th area (ED) within the h-th sampling

stratum;

(1) Let ‘hij

be the number of census counts in the j-th adjustment stratum

from the l-th sample of the i-th area (ED) within the h-th sampling

stratum;

Let Nhv nh be the number of population ED’s and selected sample ED’s in

the h-th stratum.

- The estimated true counts, census counts, and the adjustment factors of the

adjustment stratum j using sample 1 are: a

T(l) = 1 “h 1 t(l) j h “h I

hij

c(1) = z !I! 1 ,(l) j h “h i

hij

p j

= T(l) j ) J

(c(l) -1 1 = 1, . ..) L, j = 1, . . . . J.

The average of estimated adjustment factors from all samples is

L F = Z F.

j -(1),L

l=l J

The variance and covariance of sj can be computed by

cov (ii, A Fj) = k (i:l)-F,) (ij’)-Fj)/L, i=l, . . . . J, j=l, . . . ) J, except

A A l=l some cov (Fi,Fj)‘s of syn 2 are zeros by design. The sample ED’s are drawn

independently from each stratum, and the sampling strata are constructed

similarly as the adjustment strata. Hence, for example, the total sample

9

counts of White in central cities 50,000 + in the New England division come

from the selected ED’s from sampling strata 1 or 3 in the New England

division; they will not be located in the selected ED’s of Rural areas

(stratum 4) in the New England division or any selected places in other

geographic divisions. The variance and covariance matrix of %,‘3 for syn 2 is

a 96x96 block diagonal matrix I: with 9 block covariance matrices on the

diagonal, i.e., Z = diag (Z,), i=l, . . ., 9, where Zi is the covariance matrix A

of Fj3 for all js in the i-th geographic division. The variance and

covariance of ij3 for syn 2 is displayed by geographic division in Appendix 2.

In our study, we couldn't afford to draw all possible samples, so we used A

90 s%nples to compute Fj '3, and Cov (ii, A Fj)‘3 for syn DA and syn 2 synthetic

estimators. There are 88 sampling strata for each sample. For syn DA, there

are 30 (2x3~5) Sex x Race x Age adjustment strata. For syn 2, there are 96

adjustment strata by geographic division, size of place and race (see Appendix

1).

The mean and the standard deviation (SD) of Fj’s for syn DA and syn 2

using 2 artificial populations AP2 and AP3 are tabulated in tables 7 and 8,

respectively, for sample size 1440, and in tables 7-l and 8-1, respectively, A

for sample size 721. The variance and covariance matrices of Fjs for syn DA

using artificial populations AP2 and AP3 are tabulated in Tables 9 and 10,

respectively, for sample size 1440, and in Tables 9-l and 10-1, respectively,

for sample size 721. The block diagonal parts of the variance and covariance

matrices of ijs for syn 2 by geographic division using artificial populations

AP2 and AP3 are tabulated in Tables 11 and 12, respectively, for sample size

1440, and in Tables 11-l and 12-1, respectively, for sample size 721.

10

The variance of 3yn 2 or 3yn DA for a given area i can be calculated by

using the information of variance and covariance of the sample adjustment

factors. A J A

Recall the synthetic estimator for an area i is Yi = Z Fj c.. , where A j=l lJ Fj is the sample estimated adjustment factor from adjustment stratum j, and

‘ij is the census count of I-th area and j-th adjustment stratum. J is the

total number of adjustment strata. The variance of ii is

J * V(Yi) = z CT.

j-1 lJ V(Fj) + I: Cij cil Cov(i.,

j*l J +.

The variances of syn 2 estimates derived from one replicate at state

level are given in Tables 13 and 14 for artificial population AP2 and AP3 A A A

respectively; where the V(Fi) and Cov(F.,Fl) used are based on a Monte Carlo J

study of 90 replicates each with sample size of 1440. (See Tables 11 and 12).

V. Summary

The variance and covariance matrices of sample based syn 2 and syn DA

adjustment factors were obtained via a Monte Carlo study of 90 samples from 2

different sample sizes 1440 and 721, respectively. The CVs for sample based

syn DA adjustment factors ranged from 0.00002 to 0.0215 and 0.0003 to 0.0329

for AP2 and AP3, respectively, using sample size 1440. (See Table 7) ; from

0.00005 to 0.0288 and 0.0004 to 0.0465 for AP2 and AP3, respectively using

sample size 721. (See Table 7-l >. Since syn DA was categorized by race, age

and sex, the CVs of syn DA adjustment factors were varied by race, age and

sex. The Monte Carlo results showed that in the same age and sex group, the

CVs of the Black were bigger than the Hispanics, and the Hispanics were bigger

11

than the Rest; in the same age and race group, the male CV was bigger than the

female CV.

For sample based syn 2 adjustment factors, the CV3 ranged from 0.0018 to

0.0692 and 0.0011 to 0.1098 for AP2 and AP3, respectively, using sample size

1440. (See Table 8); from 0.0021 to 0.1235 and 0.0012 to 0.1231 for AP2 and

AP3, respectively, using sample size 721. (See Table 8-l 1. Syn 2 adjustment

factors were categorized by geographic division, size of place, and race. The

Monte Carlo results showed that in each geographic division, Black and

. Hispanics (Non white) had higher CVs than the Rest (White), the SMSA area had

higher CV than the Non SMSA area. *

The variances for sample based state syn 2 estimators were also obtained

using sample size 1440. The CV3 ranged from 0.0011 to 0.026 and 0.0011 to

0.0260 for AP2 and AP3, respectively. (See Tables 13 and 14).

VI. References

(1) Isaki, Diffendal and Schultz (1986). “Statistical Synthetic Estimates of

Under count for Small Area. 1( Appearing in the proceedings of the Second

Annual Research Conference. Bureau of the Census.

(2) Cochran, W.G. (1977). Sampling Techniques, John Wiley & Sons, N.Y.

12

Appendix 1

Adjustment Strata far Syn 2

Listed below are 96 strata used under strata formation 2. The strata

formation is based on three variable3 believed to highly influence the

undercount: &w@=pW, size of place and race. Separate adjustment strata

are formed within each of nine census divisions using size of place and race

(Black, Hispanic, Rest) where nonwhite is defined as Black or Hispanic. More

w emphasis is placed on geography and less on demographic variables than in

formation 1. For example, within a cen3us division, separate strata are *

formed for specific place sizes by race excluding sex and age.

Each race category listed on a separate line is a strata. For example,

for the New England division, the first stratum is white3 living in the

central city of 50,000 people or more. The second stratum is whites living in

a SMSA but not in a central city. The total number of strata is listed for

each geography grouping.

Tabulation Strata

1. New England - MA, ME, VT, NH, CT, RI

Total number of strata = 6

a> Central Cities 50,000 + White

b) In SMSA, not in Central City White

cl a and b Nonwhite

d) Cities 10,000 - 50,000 White

e> Rural 0 - 10,000 White

13

f) dande Nonwhite

2. NY, NJ, PA


a) New York City Black Hispanic Nonblack, Nonhispanic

b) Central Cities 250,000 + Black Nonblack, Nonhispanic

. cl Central Cities 50,000 - 250,000 Black Nonblack, Nonhispanic

*d) b and c Hispanic

e) In NY City SMSA, not in Central City Nonblack, Nonhispanic

f) In SMSA, not in Central City 250,000 + (except NY SMSA) Nonblack, Nonhispanic

g) eandf Black and Hispanic

h) In SMSA, not in Central City 50,000 - 250,000 Nonblack, Nonhispanic

j) Rural 0 -10,000 Nonblack, Nonhispanic

k) h,iandj Black and Hispanic

3. South - WV, VA, NC, SC, GA, FL, MD, DE, DC


a> Central Cities 250,000 + Black Nonblack, Nonhispanic

b) Central Cities 50,000 - 250,000 Black Nonblack, Nonhispanic

14

c> a and b Hispanic

d) In SMSA, not in Central City 250,000 + Black Nonblack, Nonhispanic

e) In SMSA, not in Central City 50,000 to 250,000 Black Nonblack, Nonhispanic

f) dande Hispanic

g) Cities 10,000 - 50,000 Black Nonblack, Nonhispanic

h) Rural 0 - 10,000 * Black

Nonblack, Nonhispanic

i) g and h Hispanic

4. KY, TN, AL, MS


a) Central Cities 250,000 + White

b) Central Cities 50,000 - 250,000 White

c> a and b Nonwhite

d) In SMSA, not in Central City White

e) Cities 10,000 - 50,000 White

f) Rural 0 - 10,000 White

g) d, e and f Nonwhite

15

5. MI, OH, IN, IL

Total number of Strata = 12

a> Chicago and Detroit Nonblack, Nonhispanic Black

b) Central Cities 250,000 + Nonblack, Nonhispanic Black

cl a and b Hispanic

d) Central Cities 50,000 - 250,000 White e

e) In SMSA, not in Central City 250,000 + White

*

f) In SMSA, not in Central City 50,000 -250,000 White

g> d,eandf Nonwhite

h) Cities 10,000 - 50,000 White

i> Rural 0 -10,000 White

j) handi Nonwhite

6. MN, WI, IA, MO, KS, NB, SD, ND


a) Central Cities 250,000 + White Nonwhite

b) Central Cities 50,000 - 250,000 White

cl In SMSA, not in Central City 250,000 + White

f> Cities 10,000 - 50,000 White

16

g) Rural 0 - 10,000 White

h) e,fandg Nonwhite

7. TX, OK, AR, LA


a) Houston and Dallas Black Hispanic Nonblack, Nonhispanic

b) Central Cities 250,000 + . Nonblack, Nonhispanic

c> Central Cities 50,000 - 250,000 * Nonblack, Nonhispanic

d) bandc Black Hispanic

e> In SMSA, not in Central City Nonblack, Nonhispanic

f> Cities 10,000 - 50,000 Nonblack, Nonhispanic

g) Rural 0 - 10,000 Nonblack, Nonhispanic

h) e,fandg Black and Hispanic

8. NM, CO, WY, MT, ID, UT, AZ, NV


a) Central Cities 250,000 + White

b) Central Cities 50,000 + White

c> a and b Nonwhite

d) In SMSA, not in Central City White

17

e> City 10,000 - 50,000 White

f) dande Nonwhite

g) Rural 0 - 10,000 All races

9. CA, OR, WA, AK, HI


a) Lo3 Angeles Black Hispanic

w Nonblack, Nonhispanic

b) Central Cities 250,000 + Nonblack, Nonhispanic *

c) Central Cities 50,000 - 250,000 Nonblack, Nonhispanic

d) bandc Black Hispanic

e) In SMSA, not in Central City 250,000 + Nonblack, Nonhispanic

f) In SMSA, not in Central City 50,000 - 250,000 Nonblack, Nonhispanic

g) eandf Black Hispanic

h) Cities 10,000 - 50,000 Nonblack, Nonhispanic

9 h and i Black and Hispanic

18

Appendix 2

Variance and Covariance Matrix of Estimated Adjustment Factors of Syn 2 for Each Geographic Division

1. Geographic division 1 - New England

Total number of adjustment strata = 6

Il=Diag(Zli),i = 1,2, where Xl1 is a 3x3 symmetric matrix of SMSA areas,

I12 is a 3x3 symmetric matrix of NSMSA areas.

2. Geographic division 2 - NY, NJ, PA

. Total number of adjustment strata = 15

a 3 = Diag(Z2i), i = 1, . . . . 4

where

I21 is a 3x3 symmetric matrix of N.Y. City areas

I22 is a 5x5 symmetric matrix of Central City areas

'23 is a 3x3 symmetric matrix of Noncentral Cities

(250,000+) in SMSA areas

'24 is a 4x4 symmetric matrix of Noncentral Cities

(50,000 - 250,000) and NSMSA area3

3. Geographic division 3 - South - WV, VA, NC, SC, GA, FL, MD, DE, DC.


"3 = Diag(Z3i), i=l, . . . . 3

where

"31 is a 5x5 symmetric matrix of Central Cities areas

'32 is a 5x5 symmetric matrix of Noncentral Cities areas

"33 is a 5x5 symmetric matrix of NSMSA area3

4. Geographic division 4 - KY, TN, AL, MS


z4 = Diag(Illi), 1=1,2

where

19

Z4, is a 3x3 symmetric matrix of Central Cities areas

242 is a 4x4 symmetric matrix of Noncentral Cities and NSMSA areas

5. Geographic division 5 - MI, OH, IN, IL


z5 = Diag(Zgi), i=l, . . . . 3

where

I51 is a 5x5 symmetric matrix of Chicago, Detroit and Central Cities

(250,000+)

'52 is a 4x4 symmetric matrix of Central Cities

(50,000-250,000) of Noncentral Cities

w I53 is a 3x3 symmetric matrix of NSMSA areas

6. Geographic division 6 - MN, WI, IA, MO, KS, NB, SD, ND

*Total number of adjustment strata = 9

‘6 = Diag(Z6i), i=l, . . . . 3

where

C61 is a 2x2 symmetric matrix of Central Cities 250,000 +

Z62 is a 3x3 symmetric matrix of Central Cities 50,000-250,000 in SMSA, not in Central Cities 250,000 +

‘63 is a 4x4 symmetric matrix of NSMSA areas

7. Geographic division 7 - TX, OK, AR, LA


“7 = Diag(Z7i), i=l, . . . . 3

where

"71 is a 3x3 symmetric matrix of Houston and Dallas areas

Z72 is a 4x4 symmetric matrix of Central Cities 50,000 +

I73 is a 4x4 symmetric matrix of area3 in SMSA,

not in Central Cities and NSMSA areas

8. Geographic division 8 - NM, CO, WY, MT, ID, UT, AZ, NV


z8= Diag(Zgi) g i=l, . . . . 3

where

20

Z81 is a 3x3 symmetric matrix of Central Cities 50,000 +

182 is a 3x3 symmetric matrix Of area3 in SMSA, not in Central Cities (lO,OOO-50,000)

‘83 is a scalar of areas in Rural 0 - 10,000

9. Geographic division 9 - CA, OR, WA, AK, HI


Zg = Diag(Igi), i=l, . . . . 4

where

Zg, is a 3x3 matrix of areas in Lo3 Angeles

I92 is a 4x4 matrix of areas in Central City 50,000 +

* Zg3 13 a 4x4 matrix of areas in SMSA, not in Central City 50,000 +

Zg4 is a 3x3 matrix of NSMSA areas

21

Table 1. The Summary Stati3tics for Each Geographic Division 1980 Census Eti File3

Geographic Division Total Avg. Persons # ED

Black Hispanic Rest Persons per ED

466,959 283,990 11,438,143

(0.038) (0.023) (0.938)

(1) New England-MA, ME, VT, NH,CT, RI 12,189,092 858 14,199

(2) Middle Atlantic-NY, NJ, PA 49306,760 2,159,031 29,903,591 (0.1184) (0.0594) (0.8222)

36,369,382 920 39,528

(3) South Atlantic-WV, VA, NC, SC, GA, 7,541,980 1,095,624 27,954,430 FL, MD, DE, DC (0.206) (0.030) to.7641

36,592,034 792 46,216

(4) East South Central-KY, TN, AL, MS 2,837,644 86,317 11,602,214

(0.195) (0.006) (0.799)

14,526,175 792 18,346

(5) East North Central-MI, OH, IN, IL 4,298,517 968,132 31,301,903 co.11751 (0.0265) (0.8560)

36,568,552 797 45,909

(6) West North Central-MN, WI, IA, MO, 953,745 261,357 20,355,355 KS, NB, SD, ND (0.0442) (0.0121) (0.9437)

21,570,457 557 38,749

(7) West South Central-TX, OK, AR, LA 3,472,915 3,102,122 16,898,468 (0.1480) (0.1322) to.71991

23,473,505 770 30,493

(8 > Mountain-NM, CO, WY, MT,ID, UT, AZ, NV 264,583 1,427,430 9,591,392 (0.0235) (0.1265) (0.8500)

11,283,405 591 19,084

(9) Pacific-CA, OR, WA, AK, HI 1,959,046 4,741,383 24,765,997 (0.0623) to.15071 (0.7871)

31,466,426 857 36,713

Total 26,102,149 14,125,386 183,811,493 224,039,028 775 289,237 (0.1165) (0.0630) (0.8204)

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Table 2. Continued Sampling Strata - Geographic Division 2

Race Prop. d Persons $'* cv sh2Nh

A

NY 1 #ED st2

103 v&&, 1

Geographic div. 2 - Middle Atlantic - NY, NJ, PA

Black 0.1184 41306,760 Hispanic 0.0594 2,159,031 Rest 0.8222 29,903,591 Total 36,369,382

No. of sampling strata = 14 l/

1) New York City, R-(Black) L R(Hispanic) and R(Black) L 0.10 (Black) Black 0.672 1,491,309 352,483 0.9288 Hispanic 0.135 300,598 38,374 1.5204 Rest 0.192 427,092 146,406 2.0901

2) New York City, R(Black) < R(Hispanic) and R(Hispanic) I 0.05 (Hispanic) Black 0.089 255,269 17,886 1.7352 Hispanic 0.331 954,287 88,563 1.0329 Rest 0.581 1,674,767 235,677 0.9601

3) New York City, R(Black) < 0.10 or R(Hispanic) < 0.05 (Rest) Black 0.011 21,008 582 2.2127 Hispanic 0.029 54,487 517 0.8041 Rest 0.960 1,822,180 357,251 0.6321

4) Central Cities 250,000 +, R(Black) L R(Hispanic) and R(Black) L 0.06 (Black) Black 0.715 987,050 160,518 0.7270 Hispanic 0.025 34,411 3,970 3.2792 Rest 0.260 358,211 86,988 1.4746

5) Central Cities 250,000 +, R(Black) < 0.06 or R(Hispanic) < 0.02 (Rest) Black 0.010 10,237 216 2.0294 Hispanic 0.007 7,891 0.9923 Rest 0.983 1,049,456

l23,5% 0.4737

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89,527 341,565

3,312 59,238

293,321 780,562

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Table 2. Continued

Race Prop. # Persons cv sh2Nh

103 #ED

Geographic div. 3 (cont.) 6) In SMSA, not in Central City 250,000+, R(Black) t R(Hispanic) and R(Black) L 0.04, (Black) 3,091

Black 0.303 995,049 184,999 1.3361 571,832 Hispanic 0.024 79,145 2,846 2.0837 8,799 Rest 0.673 2,213,252 506,435 0.9939 1,565,391

7) In SMSA, not in Central City 250,000+, R(Black) < 0.04, and R(Hispanic) < O.O2,(Rest) 3,925 Black 0.010 29,271 220 1.9911 865 Hispanic 0.009 27,254 102 1.4532 400 Rest 0.981 2,894,338 539,885 0.9964 2,,19,048

8) In SMSA, not in Central City 50,000-250,000, R(Black) L R(Hispanic) and R(Black) L 0.04, (Black) 4,477 Black 0.282 1,077,939 154,432 1.6322 691,392 Hispanic 0.014 52,981 2,249 4.0074 10,069 Rest 0.704 2,690,062 421,665 1.0807 1,887,795

9) In SMSA, not in Central City 50,000-250,000, R(Black) < 0.04 and R(Hispanic) < 0.02, (Rest) Black 0.009 34,512 139 2.3293 946 Hispanic 0.007 28,774 1.6853 344 Rest 0.984 3,939,604

399,8:: 1.0961 2,730,681

6,829

10) In SMSA, not in Central City 50,000+, R(Black) < R(Hispanic) and R(Hispanic) L 0.02, (Hispanic) 3,659 Black 0.018 60,624 2,415 2.9659 8,835 Hispanic 0.146 481,865 84,789 2.2111 310,243 Rest 0.836 2,767,941 496,520 0.9315 1,816,767

11) Cities & Rural, R(Black) L R(Hispanic) and R(Black) L 0.04, (Black) 7,604 Black 0.349 2,277,378 120,446 1.1588 915,873 Hispanic 0.006 41,018 801 5.2473 6,092 Rest 0.645 4,208,888 249,094 0.9017 1,894,110

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Table 2. Continued Sampling Strata -,Division 4

w; 1 Race Prop. # Persons

'h 2

cv sh2Nh

#ED st2

103

Geographic div. 4 - East South Central-KY, IN, AL, MS

Black 0.195 2,837,644 Hispanic 0.006 86,317

Rest 0.799 11,602,214 Total 14,526,175

No. of sampling strata = 5

1,858,315 4,611

6,688,168

1) Central Cities 50,000 +, R(Black) + R(Hispanic) < 0.06 for Central Cities 250,000+, 0.07 for Central Cities 50,000+ (White)

Black 0.016 24,332 447 1.6994 874

Hispanic 0.007 10,090 45 1.2957 87

Rest 0.978 1,505,471 390,392 0.8118 763,607

2) Central Cities 50,000 +, R(Black) + R(Hispanic) L 0.06 for Central Cities 250.000+, 0.07 for Central Cities 50,00O+(Nonwhitej

Black 0.568

Hispanic 0.006 Rest 0.426

1,112,056 268,038

10,810 154 833,541 256,417

0.9856 567,437 2.4293 326 1.2861 542,835

3) In SMSA, not in Central City, R(Black) + R(Hispanic) < 0.05 (White) Black 0.008 21,063 153

Hispanic 0.005 14,022 29

Rest 0.987 2,586,278 424,874

4) Cities + Rural, R(Black) + R(Hispanic) < 0.04 (White) Black 0.006 20,380 88

Hispanic 0.006 20,385 36

Rest 0.988 3,321,843 349,652

5) Areas in (3) and (4), R(Black) + R(Hispanic) L 0.05 for areas in (3), 0.04 for areas in (4) (Nonwhite)

Black 0.329 1,659,813 135,503 Hispanic 0.006 31,010 662 Rest 0.665 3,355,081 330,398

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1.3140 802,858

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Table 2. Continued

Race Prop. t Persons St cv ShZNh 103

#ED

Geographic div. 5 (cont.) 6) Central cities 50,000-250,000, R(Black) + R(Hispanic) < 0.03 (White)

Black 0.008 9,489 62 1.4478 108 Hispanic 0.007 8,906

378,2:! 1.3921 88

Rest 0.985 1,239,384 0.8684 661,908

7) In SMSA, not in Central City 250,000 +, R(Black ,> + R(Hispanic) < 0.03 (White) Black 0.003 18,961 31 2.4318 257 Hispanic 0.009 67,549 125 1.3663 1,031 Rest 0.988 7,380,599 587,379 0.8576 4,851,160

8) In SMSA, not in Central City 50,000-250,000, R( B lack) + R(Hispanic) < 0.03 (White) Black 0.003 19,908 33 2.2941 263 Hispanic 0.007 39,076 54 1.4904 427 Rest 0.990 5,756,723 412,449 0.8857 3,274,43*

9) Geograpahic areas in (61, (71, (8), R(Black) + R(Hispanic) L 0.03 (Nonwhite) 8,097 - - Black Hispanic Rest

0.189 1,482,293 111,331 1.8226 901,443 0.039 306,045 6,548 2.1408 53,016 0.772 6,069,716 482,639 0.9268 3,907,925

10) Cities lO,OOO-50,000, R(Black :> + R(Hispanic > < 0.02 (White) Black 0.004 3,091 23 Hispanic 0.005 3,527 20 Rest 0.991 729,934 305,172

11) Rural O-10,000, R(Black) + R(Hispanic) < 0.02 (White) Black 0.001 6,634 6 Hispanic 0.004 22,107 18 Rest 0.994 4,919,361 238,793

12) Areas in (IO) and (111, R(Black) + R(Hispanic)L 0.02 (Nonwhite) Black 0.058 102,904 12,470 Hispanic 0.027 47,358 1,988 Rest 0.915 1,613,770 331,082

1.6416 24

1.3675 22 0.8075 325,618

3.1017 51 1.5812 148 0.8180 1,966,457

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Table 2. Continued

Sampling Strata - Div.(l 6 (continued)

Nh 6 vt; I Race Prop. # Persons cv. - #ED

St2

103 VGstl)

6) In SMSA, not in Central City, 50,000-250,000, R(Black) + R(Hispanic) < 0.02 (White) 3,751 4 3.6030 14

13 1.8688 50

246,002 1.0547 922,753

1,392 16 2.1897 23 25 1.2259 35

323,126 0.7456 449,792

Black 0.001 1,988

Hispanic 0.004 7,296

Rest 0.995 1,763,997

7) Cities lO,OOO-50,000, R(Black) + R(Hispanic) < 0.02 (White) Black 0.002 2,568

Hispanic 0.005 5,717 Rest 0.992 1,061,~ 92

8) Rural O-10,000, R(Black) + R(Hispanic) < 0.02 (White) Black 0.001 4,934 Hispanic 0.004 23,674 Rest 0.996 6,637,872

9) Areas in (61, (71, (8), R(B lack) + R(Hispanic) b 0.02 (Nonwh Black 0.049 94,258 Hispanic 0.033 64,192 Rest 0.918 1,775,099

18,205 2 4.8946 32 8 2.1438 141

132,400 0.9979 2,410,350

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vt; > Race Prop. B Persons

'h' cv

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103

Geographic div. 7 (continued) 6 > Central City 50,000 +, R(Black) L R(Hispanic), and R(Black >

R(Black) 5 0.06 for Central City 50,000-250,000 (Black) Black 0.545 1,061,253 Hispanic 0.039 76,765 Rest 0.415 807,847

1 0.05 for ED in Central City 250,000+, 2,121

259,407 1.0179 550,202 7,378 2.3733 15,649

222,336 1.2380 471,574

7) Central City 50,000 +, R(Black) < R(Hispanic), and R(Hispanic) L 0.05 for ED in Central City 250,000+,

R(Hispanic) L-O.06 for ED in Central City 50,000-250,000 (Hispanic) Black 0.035 92,001 7,065 2.1241 16,426 Hispanic 0.483 1,265,867 446,309 1.2270 1,037,669 Rest 0.482 1,261 ,296 261,636 0.9429 608,305

8) In SMSA, not in Central City, R(Black) < 0.03 or R(Hispanic) < 0.04 (Rest) Black 0.006 16,901 75 2.9630 432 Hispanic 0.017 50,307 280 1.9292 1,624 Rest 0.977 2,864,555 421,064 1.3141 2,442,592

9) Cities lO,OOO-50,000 and Rural O-10,000, R(Black) < 0.04 or R(Hispanic) < 0.03 (Rest) Black 0.007 16,645 68 2.4961 343 Hispanic 0.009 23,239 54 1.5850 270 Rest 0.984 2,499,013 217,710 0.9393 1,095,298

10) Areas in (8) and (9), R(Black) L R(Hispanic); R(Black) I 0.03 and 0.04 for EDs in Areas (8) and (9) respectively (Black)

Black 0.308 1,368,538 141,715 1.3930 717,644 Hispanic 0.026 114,764 4,964 3.1089 25,137 Rest 0.666 2,956,379 370,770 1.0430 1,877,580

11) Areas in (8) and (91, R(Black) < R(Hispanic); R(Hispanic) L 0.04 and 0.03 for EDs in Areas (8) and (9) respectively (Hispanic)

Black 0.024 105,319 2,717 2.6312 14,446 Hispanic 0.249 1,102,836 131,596 1.7486 699,565 Rest 0.727 3,219,752 410,657 1.0580 2,183,051

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9E

37

1


Race Prop. W Persons 'h'

cv 'h Nh

103 #ED

Geographic division 8 (continued) 6) Rural O-10,000, R(Black) + R(Hispanic) < 0.04

0.001 0.013 0.986

Black Hispanic Rest

7) Rural O-10,000, R(B Black Hispanic Rest

lack) + R (Hispanic) L 0.04 (Nonwhite) 2,926

0.008 11,357 719 6.9082 2,104

0.240 334,629 34,596 1.6264 101,227

0.751 1,045,457 178,622 1.1829 522,648

(White) 5,666

858 1 5.0065 3 20,751 59 2.0936 333

1,568,117 123,432 1.2694 699,365

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39

1

Table 2. Continued

Race Prop. 11 Persons cv Nh ':

103 #ED

Geographic div. 9 (continued) 6) Central Cities 50,000+, R(Black) L R(Hispanic) and R(Black) L 0.03 (Black)

Black 0.314 464,612 111,938 1.2062 187,497 Hispanic 0.075 110,282 12,109 1.6714 20,283

Rest 0.612 905,215 588,510 1.4195 985,754

7) Central Cities 50,000+, R(Black) < R(Hispanic) and R(Hispanic) h 0.05 (Hispanic) Black 0.041 158,721 5,369 1.7589 20,457 Hispanic 0.215 837,019 97,295 1.4198 370,694 Rest 0.745 *,903,163 345,875 0.7718 1,317,784

8) In SMSA, not in Central City 250,000+, R(Black) < 0.02 or R(Hispanic) <0.05 (Rest) Black 0.007 23,402 94 1.7811 403 Hispanic 0.025 83,686 561 1.2193 2,417 Rest 0.968 3,245,599 533,489 0.9695 2,298,271

9) In SMSA, not in Central City 50,000-250,000, R(Black) < 0.02 or R(Hispanic) < 0.05 (Rest) Black 0.004 8,288 38 2.4228 125 Hispanic 0.025 53,498 596 1.4773 1,929 Rest 0.971 2,054,182 534,659 1.1526 1,731,226

10) In SMSA, not in Central City 50,000+, R(Black) h R(Hispanic) and R(Black) L 0.02 (Black) Black 0.326 478,405 211,433 1.4014 308,269 Hispanic 0.094 137,639 24,640 1.6628 35,925 Rest 0.580 849,981 721,230 1.4568 1,051,553

11) In SMSA, not in Central City 5O,OOO+, R(Black) < R(Hispanic) and R(Hispanic) L 0.05 (Hispanic) Black 0.023 236,707 3,323 2.4285 33,138 Hispanic 0.229 2,367,095 113,091 1.4167 1,127,748 Rest 0.749 7,751,356 411,105 0.8249 4,099,538

1,675

3,810

4,308

3,238

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41

Table 3. The Stratum Statistics for Each Race - Stratification 1 1980 Census ED File;

2

Race Prop. d Persons ‘h

2 cv

Nh ‘h 103 t ED

New England division Black Hispanic Rest

1) Central Cities 50,000 + Black Hispanic Rest

2) In SMSA, not in Central City Black Hispanic Rest

3) Cities lO,OOO-50,000 Black Hispanic Rest

4) Rural O-10,000 Black Hispanic Rest

0.038 0.023

0.938

0.110 366,550 46,099 2.3143 182,136 0.058 194,440 11,569 2.1856 45,711 0.832 2,778,619 285,612 0.7599 1,128,455

0.013 76,684 1,820 3.5868 11,733 0.011 66,190 468 2.1070 3,016 0.975 5,856,608 424,650 0.7175 2,738,142

0.019 11,642 3,703 2.9113 2,062,452 0.015 9,526 1,168 1.9984 650,595 0.966 597,600 568,322 0.7027 316,555,577

0.005 12,083 647 6.8254 2,097,264 0.006 13,834 158 2.9427 511,018 0.988 2,205,316 290,351 0.7924 941,609,852

12,189,092 466,959 283,990

11,438,143

198,029 49,889

5,124,762

14,199

3,951

6,448

557

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43

Table 3. Continued m

Race Prop. # Persons Nh ';l

103 #ED

Geographic Div. 2 7) Cities lO,OOO-50,000

Black Hispanic Rest

8) Rural O-10,000 5,870 Black 0.010 36,108 824 4.6672 4,837 Hispanic 0.007 27,042 297 3.7395 1,743 Rest 0.983 3,674,289 273,582 0.8356 1,605,926

680 0.031 21,926 7,835 2.7452 5,328 0.015 10,299 1,705 2.7266 1,159 0.954 675,003 312,236 0.5629 212,320

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Race Prop. # Persons 'h

* (I cv Nh 'h

103 #ED

Div. 4 - East South Central - KY, TN, AL, MS Black 0.195 Hispanic 0.006 Rest 0.799

1) Central Cities 250,000+ Black 0.390 Hispanic 0.005 Rest 0.605

2) Central Cities 50,000-250,000 Black 0.266 Hispanic 0.007 Rest 0.727

3) In SMSA, not in Central City Black 0.102 Hispanic 0.006 Rest 0.892

4) Cities lO,OOO-50,000 Black 0.267 Hispanic 0.007 Rest 0.726

5) Rural O-10,000 Black 0.166 Hispanic 0.005 Rest 0.828

14,526,175

2,837,644 86,317

11,602,214

1,372,156 4,615

6,474,504

648,789 210,190 1.3702 407,558

7,625 34 1.4836 66 1,006,516 287,499 1.0329 557,460

487,599 195,340 1.934 416,857 13,275 160 2.0345 342

1,332,496 413,048 1.0293 881,445

411,421 46,549 2.9225 259,415 25,183 337 4.0651 1,880

3,600,144 418,094 1.0009 2,330,040

335,453 171,880 1.7377 241,663

9,045 1,345 5.7001 1,891 910,703 467,990 1.0562 657,994

954,382 73,049 2.0656 532,822 31,189 59 1.8009 433

4,752,355 310,012 0.8546 2,261,228

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Race Prop. % Persons s; 6 cv Nh 'h

103 #ED

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Black 0.044 71,656 Hispanic 0.016 26,088 Rest 0.940 1,521,701


0.007 40,973 0.008 46,904 0.985 5,741,364

1,931 10,535 2.7660 20,343 1,369 2.7388 2,644

345,386 0.7458 666,941

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Race Prop.

Table 3. Continued

Q Persons 'h2

cv #ED

Division 7 - TX, OK, AR, LA Black Hispanic Rest

1) Houston and Dallas Black Hispanic Rest

2) Central Cities 250,000+ Black Hispanic Rest

3) Central Cities 50,000-250,000 Black Hispanic Rest

4) In SMSA, not in Central City Black Hispanic Rest

5) Cities lO,OOO-50,000 Black Hispanic Rest


0.1480 0.1322

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23'+,473,505 3,472,915 3,102,122

16,898,468

2,594,921 2,499,518

11,439,181

0.276 789,714 268,504 1.7578 719,323 0.151 433,975 68,828 1.6195 184,391 0.573 1,641,159 623,878 1.2894 1,671,370

0.182 517,842 113,317 1.8754 326,920 0.273 779,063 271,524 1.9296 783,347 0.545 1,555,350 284,555 0.9895 820,942

0.192 657,956 152,241 2.2043 565,880 0.175 597,938 176,734 2.6133 656,921

0.633 2,162,260 367,046 1.0415 1,364,311

0.075 553,749 41,938 3.9774 451,039 0.094 700,498 44,815 3.2502 481,981 0.831 6,175,032 504,663 1.2373 5,427,656

0.161 253,606 109,635 2.2326 187,475 0.113 178,551 72,052 2.5707 123,208 0.726 1,144,260 318,889 0.8439 545,301

0.131 700,048 39,360 2.4789 344,284

0.077 412,097 30,830 3.7269 269,668 0.791 4,220,407 184,018 0.8891 1,609,602

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Race Prop.


d Persons 9 * cv Nh 'h

h 103

#ED

Div

1)

2)

3)

4)

5)

.sion 9 - CA, OR, WA, AK, HI Black Hispanic Rest

0.0623 1,959,046 0.1507 4,741,383 0.7871 24,765,997

Los Angeles Black Hispanic Rest

0.164 539,205 81,735 1.7879 0.259 852,543 109,010 1.3059 0.577 1,898,643 263,439 0.9116

Central Cities 250,000+ Black Hispanic Rest

0.116 464,292 44,787 2.0028 0.114 454,817 40,982 1.9558 0.770 3,068,927 412,382 0.9194

Central Cities 50,000-250,000 Black Hispanic Rest

0.050

0.153 0.797

In SMSA, not in Central City 250,000+ Black 0.057 Hispanic 0.162 Rest 0.781

In SMSA, not in Central City 50,000-250,000 Black 0.019 Hispanic 0.137 Rest 0.844

179,454 21,846 3.3983 546,210 69,043 1.9849

2,845,236 405,706 0.9237

627,884 37,076 3.4669 1,778,014 85,123 1.8551 8,593,057 477,527 0.9091

118,918 6,342 5.1371 863,904 52,948 2.0432

5,308,061 501,286 1.0232

36,713 1,035,114

*,*79,338 15,516,638

3,372 275,611

367,583 888,315

4,394 196,792 180,077

1,812,007

4,126

go,1 37 284,873

1,673,942

11,305 419,141

962,310 5,398,446

7,671 48,650

406,165

3,845,362

Zf 1‘S~tr‘ 1 9L1’6f ZCh3‘1

869 ‘tr

Ltrl‘l

Sftr‘ftrtr ~~1’6f Zf6 ‘1

fff 1’1 trfL ‘60f f66’90f ‘Z 9Gh8 ‘2 6ff ‘8 f9L‘OSL trZ99’9 tr6f zoo’tf 1

ZLG6'0 fro9 '98f 08O'GtrL lL8’0 LLZZ'Z Lf 1 ‘trf Zf 1’ 56 111’0 226 L’f g!x’z 16Z‘I; 1 8 10’0

ff6 l O 190 ‘0 900’0

wax DTuedsTH

we-CEl 000’01-0 TxJnkl CL

wax 3TuedsTH

ve10 ooo~o+ooo‘oi sacm (9

IH ‘YW ‘VM ‘HO ‘V3 - 6 ‘JOTsTATa

fol Y u zs N

A3 SUOSJQ # 'dOJd aaE'u

53

Table 4. The Correspondence of the Strata Code From Stratification 1 (G2,j and 2 (G3)

Geographic Division

1 G3 1

G2 1

2 G3 1

G2 1

3 G3 G2

4 G3 G2

5 G3 G2

6 G3 1 G2 1

7 G3 1 G2 1

8 G3 G2

9 G3 G2

1 1

1

1,*

1

192

1 1

2 2

2 1

2 1

2

192

2 1

2 1

2 1

2

192

2 1

3 192

3 1

3 3

3 4

3 3

3 3

3 1

3 4

3 1

4

4,5

4 4

5 4

4

3

5

193

4 5

5,6 4,5,6

4

3

4 4

4 4

4

5

4 4

5

1,3

5

394

5 5

5

495

5 5

8 9 10 8 6,7,8 10

8 9 8 6,798

8 9 10

4,5 4,5 8 9,lO 8,9,10 8,9,10

6 7 7 7

6 7 4,5 4,5

8 9 10 11 12 13 8 9 8,9 899 12,13 12,13

8 9 10 4.6 9 10

8 10

8 s' 698

11 12 13 14

9,lO 12 13,14 12,13,14

11 12 13 11,13 11,13 11,13

11 12 11 10,ll

11

.r

ul~

lv~

ww

w

woo

ulul

---

>^“

” 00

mw

w

0x00

- -

l-l--

w

~~

0000

w

w

w

IO

0000

0 0

0 I

ooxx

x 5%

lLru

++--u

i XW

-S a

- su

lul-

- A

AN

0 . 0

. “.

4 0 . 5:

AW

0

0 .

OE

is

. u

b

RN

m

0 . 0 c

0 . -

0 . s m

w

rvw

-m-w

ww

w

W

Y

,“2

P

0 . E

d N

-L

n -c

--a-w

ww

m

0 . s: .e

55

Table 6. Proportional Sample Allocation for Each Sampling Stratum (N = 289,237, n1 = 1440, nt = 721)

Strata

Division 1 1 2

3 4

Division 2 1 2

3 4

5 6

;

9 10 11 12

13 14

Division 3 1 2

3 4

5 6

i

9 10 11 12

Nh “lh “2h Nh "lh “2h Nh "lh “2h

14,199

2,368 6,030 2,001

3,800 39,528

2,333 3,312 1,927 1,791 1,414

1,009

1,103 1,128

1,289 5,727 1,862

7,731 6,049

2,853 46,216

2,588

1,071

2,832 2,281

1,271

3,091 3,925 4,477 6,829

3,659 7,604 5,478

71 12

30 10

19 197 12

17 10

9 7 5

65 6

29 9

38 30 14

230 13 6

14 11 6

15 20 22

34 18

38 27

36 6

15 5

10

98 6

9 5 4

3 2 2

3 3

15 5

19 15 7

115 6

3

ii

i 10 11

17 9

19

13

Division 3

13 1,110 Division 4 18,346

1 1,956 2 2,117

3 3,876 4 4,472 5 5,925

Division 5 45,909 1 692 2 2,694

3 1,359 4 1,615 5 2,137 6 1,750 7 8,259 8 7,939 9 8,097 10 1,067 11 8,235 12 2,065

Division 6 38,749 1 1,656 2 1,707

3 2,328 4 5,012 5 1,659 6 3,751 7 1,392 8 18,205

9 3,039 Division 7 30,493

1 989

6

91 10 11

19 22

29 228

3 13 7 8

11

9 41 40 40

5 41 IO

193 8 8

12

25 8

19 7

91 15

152 5

3 46

5 5

10 11

15 114

2

: 4

5 4

21 20 20 2

21

5 97 4 4 6

13 4

10

3 46

7 76 2

Division 7 2

3 4

5 6

7 8

9 10 11

Division 8 1 2

3 4

5 6

7 Division 9

2

3 4

5 6

ii

9 10 11 12

13

1,099 591

723 1,433 2,121

2,325 5,801

5,031 5,064

5,316 19,084

1,415

2,373 2,322

809

3,573 5,666 2,926

36,713 752

1,644

976 1,471 1,564 1,675 3,810 4,308 3,238 1,458 9,972 3,496 2,349

5

3 4

7 11 12

29 25 25 26

95 7

12 12 4

18 28 14

183 4

8

5

; 8

19 22 16

7 50 17 12

3 2 2 4

2

15 12 12

13 47 3 6 6 2

9 14

7 92 2 4

2 4 4 4

9 11 8 4

25 9 6

W

w

4

b

0 0 m

Z

57

TABLE 7-1 MEAN AND STANDARD DEVIATION OF THE ESTIMATED CENSUS ADJ&TWENT FACTOR FOR SYN DA

AGE 1: O-1Q

;; o-14 o-14

‘): O-14 5: O-14

;i 1;-;; 8: 15-27 ?: 15-29 10: 15-23 11: 15-29 12: 15-29 13: 30-44 1:+ : 33-44 15: 30-44 1s: 30-44 17: jO-44 18: 30-44 l?: 45-64 20: 45-64 21: 45-64 22: 45-64 23: 45-64 24: 45-64 25: 65+

F 8;: 2s: 65+ 29: 65+ 30: 65+

RACE BLACK BLACK HISPANIC HISPANIC REST REST BLACK BLACK HISPANIC HISPANIC REST REST BLACK BLACK HISPANIC HISPANIC REST REST BLACK BLACK HISPANIC HI??AtiIC REST REST BLACK BLACK HISPANIC !iISPANIC REST REST

SEX TIALE FEMALE MALE FEMALE HALE FEMALE HALE FEMALE MALE FEMALE MALE FEMALE WALE FEMALE MALE FEnALE MALE FEMALE WALE FEMALE MALE FENALE hALE FEMALE MALE FEMALE MALE FEMALE HALE FEMALE

MEAN 1.07030 1.06519 1.00673 1.00411 1.00316 1.00185 1.053?0 1;03047 1.02438 .?9?55

1.01307 .???82

1.20144 1.05c43 1.051?7 l.Ol'+CS 1.0274! l.JO719 1.14186 1.02856 1.03823 1.01615 1.02056 1.00844 .96601 .?8?8(1 .?a781

1.00546 .?9847

1.00942

SAMPLI SIZE

AP2 SD

16331350-003 :17271216-001 .23230?30-002 19018441-002

:57481833-003 .40181?71-003 .17613629-091 66231446-002

:82476854-002 36513858-003

:21702625-002 .4??21423-004 34544146-001

:?6514217-002 .16?17355-051 .37546858-002 .44789752-002 102?3960-002

:29570404-001 .65303951-002 13387638-001

:53654375-002 .39340240-002 . 13415041-002 11538888-001

:34962428-002 .27535328-002 .3?653673-002 64474570-003

:12594023-002

721

cv .Oi53

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.oc21

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: E%F .0037

:K .025? .0063 .0129 . 0053 .0039

:X .0035 .0028 .0039 .0006 .0013

AP3 MEAN SD

1.07030 1.06519 1.06249 1.05812

: ;:;;i

1.0539c 1.0301'7 1.07520 :.o‘zs~s 1.00889 .99782

1.20144 1.05043 1.17465 1.04106 1.02038 1.00330 1.14186 1.02856 1.11082 1.02253 1.01563 1.00825 .96601 .98?84 .a7160 .99420 99914 .**s

1.00473

.1633135C-301

.17271216-001 20252409-001

:1???2034-001 .49580432-003 .57213220-003 .17613629-001 . 66231446-902 .2574?838-301 .9188?597-002 14251259-002

:43?65588-003 .34544146-001 .96514217-032 .54563429-00 i . 13110716-001 .31756335-002 66561548-003

:29570404-O01 65303951-002

:40945764-001 .86525064-002 .3183971?-002 .126?5366-002 11538888-001

:34962428-002 16364865-001

: 454956?9-002 .46440610-003 . 13999111-002

.oF!3

.0162

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:;g; .0126 .0031 .0007 .0259 .0063 .0369 .0085 .0031 .oc13 .0119 -0035 .0168 .0046 .0005 .0014

6SOO’ ZOO-SL62106S 8lEOO'l 8600' 'ZOO-21986186 hLZ0’ 1 OO-OL6hf68’2 - OhLSO‘1

8h900’1 q1qIyI 01 9SZO’ LOO-Zfl6Sl9Z’

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9100’ ZOO-189b6E91 ’ 069hO.l

lSfOO’l 8200’ 1,

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:fh

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:lh qwm 2

6ZhO’ lOO-896CbZ9h’ SL6LO’l 6ZhO’ LOO-OShZSZ9h’ 698L.0’1 b : Oh

ElOO’ ZOO-OZlfLffL’ PW f

lZ900’1 EZLO’ :0

LOO-91f60hZl. 9010’

CC01 0’1 q:w LOO-06OZfL.01 ’

-c ZlhlO’l 0810’ LOO-S86f Lb81 ’

:;: 09fZO’l ?l!VP

- hL.80‘ 1-0-0=6-0s 9vx7sum0-Im - I :Lf

100 ‘ZLhLhZZ‘ Zl,LlO’l -Jrwe!H hZO0’ ZOO-lfZ96LfZ’ 82800’ 1 200~~96E060h’

s/ OhOO’

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6520’ 16flO’l HN ‘Gi”

LOO-h6hZLhLZ’ i?l

h6L90.1 6SZ0 ’ LOO-h6hZLhLZ’ :SE

h619O.L T”IB thO0’ ZOO-S8SSZ9L.h’

Cl ffS00’1 8L.00’ ZOO-6SfZL88L’ \lff ‘W

: hf

L9f 0’ LOO-6LZOl08f’ LL.800’1 ZI

L6hfO’l L9fO’ LOO-6LZOl08f’ :ff

LSSO’ 1 OO-86EhOZ09 ’ L6hfO’l TV10 1 ’

88'260'1 Zhl 0' LOO-SZl16Shl’ :Zf

8fOO’ I8hZO'l -J!UrJOH

ZOO-h096LE8E' Of

6L800'1 0900' :lE

'ZOO-OhOOfS09' OLhO'

bLhlO'1 iv\. 0 P LOO-E06h9llS’

b L.0880’1 3LhO’ 100~E06h911S’

: Of

LEOO’ LO880’1

ZOO-996fOhlf’ 8h800’1 -P/w

lSO0’ :0

ZOO-CZ6ZhhlS' 8LElO'l HF’B Iy 1’ hhS0’ 1 oo-OLSOOf 64 *

t’ Lh68O’L hhS0’ LOO-OLSOOf6S’

:;;

8601. OOOtl996L611 ’ lh680.1 vtw 9

hhl60’1 OEEO’ LOO-801926Ef’ : tz

6L9ZO’L 3:w- \I s LFOO’ ZOO-99ESl80f’ 1 h900’1 LSOO’ ZOO-CSCZESIS'

: 9z

lLh0' LOO-06llf6fh’ osolo’l

“&Y,:: v

Zl690’1 1lhO' LOO-06llf6fh’ :sz

ZSOO’ ZOO-h666hlZS’ Zl690’1 f‘

fS600’1 1800’ ZOO-OZh6h9Z8’ : hZ

L8hlO’l Hh ‘HP ECCO’ 1 OO-ZhZ0009f’

-c SSZ80’1 fEf0’ LOO-ZhZOOO9f’

:fZ -...- - SSZBO’L ‘Ql”l8

9 9 L--o---ro-F$-65-c?n~z~ I

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611 0’1 v -w 8200’ ZOO-8Z9SLl8Z’

5 I 8ShOO’1 ChOO’ ZOO-SllOfhfh’ 69LiO’1 HP’ off

:lZ fl

8200’ ZOO-8198Lh8Z’ 06ZOO’l 9hOO’ ZOO-SZZ66LSh’ : oz

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ZOO-l ChLOLL 1 * tl

Sff00’1 6100’ -1

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LOO-SS99ZlSZ’ Z06fO’l EZZO’ :81

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zoo-9LslLzlz’ I I

8SZOO’l ZEOO’ WE’ *51 :Ll

ZOO-1 88hZ9Zf’ LlOO’ ZOO-Sl890691’

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4 Zh901 ‘1 66hO’

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ZOO-hLOZ9 h9 h’ Z610’ LOO-fSZ60f02’

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LOO-SL16lOIZ' EfhL.0’1 q-%3 --TZTb’O~i;68 niCtr’F[ z 0 -

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8100’ ZOO-OZBSLf81 ELEOO-1 6200’ sl’Yv :9

ZOO-9Lf6688Z’ L6SOO’l -q 1 qm SZOO’

!i ZOO-hfL.OhLhZ’ 6hZOO.l OhOO’

:s ZOO-Zh88h66f’

69f 0’ 9OhOO’l F.j:Ym

LOO-98916f6f’ f

f6890.1 ZZEO’ :h

1 OO-Z6S998ff. 98lSO’l -J! )jr”“ff I 1100’ zoo-.L.88L8Lol’

t‘ hOfOO’1 8100’ :f ZOO-fhhfL.181’ h6hOO'1

9fOO' FJ!YF

ZOO-6h9ZSh9fe T

..9SSOO’l 2900’ :‘I

ZOO-61 8hLLZ9 * 806OO’L _ ~IW f :1 A 2 as - NV3W A3 as NV3W -T

3) Ifi1

TdV ZdV (‘0)-sz:OE:s1-;;.~~;/ZC-~iJP3-3[.d~:*~~ 3aow .\lw-avx.d

Ohhl 321s 3’ldCIYS 343asdi m:e -.-

2 u/es Jo4 sYro73ej ymu~snrpy snsuag pa7etuk3sj aq7 Jo u0LJeLAcy-j pJepue7s pue ueaw -8 alqel 3 2\

Table 8. 59

54:

:;;

57: 58: 50: 63: 61:

AP2 AP3

wh:t;c MEAN

x74 MEAN

- 1.00827 1,00493 . 6lcfO%3-002 ocoobl Ad 1.02037 whirs

:742&i-002 z l-00 I .?.Zas___l,O_ZSS,~.S~_sS~~O 1 '0206 . < __ -

1.00652 .39037217-002 .0039 1.00408 .24820712-002 .0025 JdvJ 1.06635 .63230961-001 .0593 I.07040 .63630672-001 .0594 White 1.00283 .23044844-002 .oozg 1.00169 13457455-002 .0013 Whs k 1.00468 .27019755-002 .0027 1.00269 :15202561-002 .0015

Md whit4 1.02352 1.00491 :10993?57-001 21342234-001 :8489 a 1.02783 1.00270 :5535110+002 21565981-001 .0210 .0055

wh; k 1.00304 .34185645-002 23977774-002 .0024 1.00340- :14578647-002 .0034 1.00180 21606452-002 :%i i,o218_1. 22179763-00.1 -.0237-

1.12440 .77867384-001 -0602 14845816-001 1.12440 611?9888-001 .0544

JR, till 1.01187 .88480372-002 1.00712 .45"2057?-002 : 1.01107 172382567-002 8E uve, titi 1.01135 11125539-001 .OllO 1.00674 .64608438-002 0064 Pladt 1.04970 :26870923-001 .0256 1.04970 26870923-001 :0256 Il;jfXlo;C 1.01218 .70481472-002 .0070 I.05127 :29855199-001 .0284 tit.5 , VII 1.01474 .76649836-002 0076 1.00826 .44169275-002 vn, AJIJ 1.01173 .23711991-001 :0234 1.00716 16108541-001 :X un. Uli 1.01382 54174349-002 .0053 1.00810 :30311845-002 .0030 !k?ik+%~$-$~~;;~

I:00633

%-+%84 ~!i511.o-t93!koo.l -0 23 a-

.46091927-002 .0046

if 3 1.02452 .2304472?-001

wh:trL 1.01049 69324065-002 .0225 1.06040 54405429-001 : 1.00376 -53878617-002 :"5::

4 1.00604 :41564257-002 0041 E whit, 1.00530 :57876254-002 :K 1.00330 35615956-002 :0035 b 25829?50-001 .0252 1.06293 :73753696-001 -0654 7 1 . Ol_3 19 . 2WXP.4-6~0_91~- 0198 I 1.05850 .32011104-001 .0302--

89 :

85: 85:

;;;

83: 7 00 : ?I: 02: Qj:

{q: 05:

1.01541 1.00788 1.01150 1.00775 1.06073 1.01496 1.00813 1.01120 1.04288 1.00910 1.00498 1.00890

19289808-001 137030803-002 .46068683-002 .32614599-002 .35506013-001 10470381-001

:51022408-002 .804552?2-002 53902491-001

:63832920-002 .46762447-002 .91837251-002

.Ol?O

.0037

.0046

.0032

: KG 0051

10080 .0517 .0063 .0047 .0091

1.06404 1.00504 1.00704 1.00450 1.06073 1.06270 1.00490 1.00668 1.04288 1.03865 1.00294 1.00550

.80653624-001

.23640053-002 27086733-002

:19441051-002 35506013-001

:4559?476-001 30026750-002

:48454879-002 53902491-001

:29011023-001 .26036669-002 .66315710-002

0758 :0024 .0027 0019

:0335 0429

:0030

: K87 .0279 0026

:0066 05: IQ 8, I-l 1.01137 .10026433-001 .0099 1.03772 -32298656-001 .0311

:fiy -1 : 06 --

Et!3 ED. NO CORPECTIONS APPLIED

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Table 8:1 61

59: II

--

hhirc

AP2 APS MEAN .SD

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2 12 1 7s 1s 57 Lf 72 fl 21 IL 01 27 9f ff OS 77 SE s2 f2 6

- 6 6 - 6

6 6 8

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a

99

Table 14. The Estimated State Adjustment Counts (Syn 2) and Its Variance n = 1440

ARTIFICIPl. PCPULhTION 3

DIVISION STATE STATE SUM STANOARO ERROR VARIANCE --w----w a---- --me- e-s -------- ----- -v-----v

1 1 1 1

1 1 2 2 2

5 3 3

. 3 3 3 3 3 4 4 4 4 5 5 5 5 6

.6 6 6 6 6 6 6 7 7 7 7 a a a 8 8 5 a a 3 9 9 9 9

9 23 25 33 44 50 34 36 42 10 11 12 13 24 37 45 51 .54 1

21 28 47 17

:"6 39 19

20 27 29 31 38 46 55 5

22 40 48 4 a

16 30 32 35 49 56 2 6

15 41 53

3065974. 1110298.

. 5661335. 911430. 934631. 505424.

7298695. 17337327. 11733360.

580086. 631103.

9660579. 5403291. 4172253. 5019228. 307G726. 5291757. 1935011. 3059996. 3622843. 2497274. 4546062.

11298524. 5123734. 9162057.

10678877. 2366593.

2326706. 4312230. 4s57*01. 1546360. 54244C. 679030.

4639417. 2259264. 415915L. 2984579.

i40702oa. 2699724. 2862337. 935683. 773046. 795150.

1295683. 1451438. Lb5374. 399686.

23416743. 958906.

2604853. 4086238.

.13595156+OOS

.14052772+004

.15332154+005

.1174a3s9+oo4

.22156547+004

.74267034+003

.29570496+005

.58090476+005

.46463200+005

.27874223+004

.164026Ob+OOS

.62305862+005

.26403687+005

.32175147+005

.26580071+005

.22470520+005

.22877002+005

.40822455+OC4

.22464876+005

.92095492+004

.14123334+005

.27031637+005

.61465357+005

.13572510+005

.34669334+005

.33129633+005

.32075424+004

.39221930*004

.49754614*004

.22585344+005

.3iaa9ci3+co4

.71C43E34+oC3

.75170104+003

.12219833+005

.1~0034967+005 26756745+005

:9X34468+004 .10393063+006 .24089599+005 . 21764691+005 . 10653220+005 .0?059a06+004 .59907354+oC4 . 18819488*005 .74979307+004 . 52100066+004

.13614998+004

.13423?47+006

.25438432*004

.58008859+004

. 85258503+004

:la482827*009 .1974aC40+007 .23507496*009 .13802395+007 .49091257+007 .55155924+006 .87441424+009 .33745034+010 .21588290+010 .77697229+007 .26904549+009 .388202os+oio .69715470*009 .10352401+0,10 .70650016+009 .50492464+009 .52335721+009 .16664729+3Ca .50467064+009 .84797379+030 .19946b55+009 .73070940+009 .37779901+010 .1842132S+OO9 .12019627+010 .90779480+009 .10288328+008 .15?93598+008 .24785277+008 .51009775+OQ9 .lC1693&5+CO8 .50472263*306

.56505446+006

.14932432+909

.10070057+009

.71592341+i'O9

.85256540+008

.108014S2+011

.53330679+009

.473?0178+009

. 11349109+009

.75794099+008

.35~89510+008

.35417312+009

. S6218965*005

.27144169+ooa 13536618+007

:10019698+Cll .64711384+007 .33650277+008 . 74405293+008

cv

--

.44342046-002

.12656757-002

.27002224-002

.12890029-002

.23706197-002

.14694006-CO2

.40514772-CO2

.33506016-002 39599229-002

:47398208-002 .25990379-001 .64494957-002 .43065936-002 .77116961-002 .45676283-002 .72703074-002 43231391-002

:21096756-CO2 . 58193220-002 25418G19-002

:S6555002-002 .59461655-002

.54399783-002

.25000982-002

. 37940120-002

.2!!214234-002

.11189389-002

.16657273-302 12408265-002

: 46494C86-002 20622242-C32

:11058439-CC2 . 11070218-002 26339157-002

:44416375-002

. 64332182-002

. 3093&074-002

.73a65315-002 89229859-002

:76038135-002 . 11385501-001 . 11139545-001 .,75341576-002 14524762-001

:51659704-002 .11195311-001 . 34064236-CC2 .57325423-002 -26528599-002 . 22269533-002 .21109515-002

survey based estimates of census adjustment factors and it's … · 1998-11-17 · srd...

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