Adjusting Establishment Selection Probabilities and

Number of Occupational Selections to Reduce Variances

in BLS Compensation Surveys

Authors: Steven P. Paben and Lawrence R. Ernst

Date: May 29, 1997
1

INTRODUCTION

The National Compensation Survey (NCS) is both a replacement for the

Occupational Compensation Survey Program (OCSP), which measures employee

wages by skill level, and also a program that integrates this new survey with two

existing BLS compensation surveys, the Employment Cost Index (ECI), and the

Employee Benefits Survey (EBS). NCS uses a rotating panel design with three

stages of selection used in selecting each panel: geographic area PSUs;

establishments selected from industry strata; and occupations selected separately

from each sample establishment. The establishments are selected with probability

proportional to size (pps), with total employment the measure of size. For each

selected establishment the number of sampled occupations are a nondecreasing

function of employment size, with the occupations selected pps.

This study of the sample design has two purposes. First, to determine whether

differential sampling intervals for establishments in different size classes would be

more effective for the purpose of variance minimization than sampling of

establishments by direct pps. Second, to determine whether a different allocation

than the current allocation of the number of occupation selections within an

establishment by size class can reduce variances without increasing the total

number of occupational selections across all sample establishments.

SAMPLE DESIGN

Much of the focus in NCS, including all the analysis in this paper, is on the

production of locality estimates, that is estimates for individual PSUs, particularly

certainty PSUs, for which the first stage of sampling is not an issue. Consequently,

this stage of sampling is not addressed here. In the second stage of sampling,

establishments are selected pps from industry strata, with total employment the

measure of size. The sampling frame from which the establishments are selected is

constructed primarily from the unemployment insurance universe.

In the third stage of sampling, occupations are selected separately from each

establishment. Typically, the occupational selections are done from a complete list

of in scope employees for the establishment obtained from the respondent.

(Certain cases of employees, such as those who set their own pay are out of

scope). A systematic equal probability sample of employees is selected. Then, for

each selected employee, wage data is obtained for all employees with the same

detailed job as the selected employee within the particular establishment. For

example, if one of the employees selected is a full time, grade 9, non-union,

accountant, whose earnings are time based (as opposed to incentive based), then

data is collected for all employees satisfying these criteria for that establishment.

Consequently the equal probability selection of employees is equivalent to a pps

selection of detailed jobs. The number of occupational selections in each

establishment is dependent upon the size of the establishment. For each of the
2

surveys that we studied the number of occupational selections was determined by

the following schedule:

Table 1.

Number of Employees Number of Selected Occupations

0 - 49 4

 50 - 99 8

 100 - 249 10

 250 - 499 12

 500 - 999 16

 1000 + 20

The weight for each employee in a selected job is obtained by taking the product of

the reciprocal of the probability of selecting the establishment, the reciprocal of the

probability of selecting the job given that the establishment is selected, and

nonresponse adjustment factors for establishment and occupational nonresponse.

METHODS

In order to determine an optimal allocation, the NCS test variance program and

procedures were used. We used data from five of the six Statistical Metropolitan

Areas covered by this 1996 test survey program. One of the test surveys was not

used due to some outliers in the original variance calculation. The optimization

was based on the variance for weekly mean wage.

The variance to be minimized has a between and a within establishment

component. The number of establishments sampled affects both components. The

number of occupational selections affects only the within establishment component

of the variance. Since our sample has multiple stages of selection, this problem

could have been treated as a nonlinear optimization problem. However, we

concluded it was somewhat simpler to view the problem as two Neyman

allocations and that this approach would produce similar results, as we establish at

the end of this section.

The first allocation to optimize is the number of establishments. We actually are

trying to find an optimal allocation for differential sampling intervals based on the

size classes shown in Table 1. The sampling interval for the i-th size class is

obtained by dividing the overall sampling interval by a factor, f

i

, and thus the

problem is reduced to finding an optimal set of f

i

’s. This factor increases or

decreases the allocation depending on whether it is greater or less than one. The

constraint on this optimization is that the total number of establishments summed

over the five test surveys and six size classes must remain the same.

The second allocation to optimize is the number of occupational selections within
3

each sampled establishment. The current allocation uses the schedule defined in

Table 1. We want to optimize this allocation using the same size classes. The

constraint for this allocation is that the total number of occupational selections

must remain the same.

The following method is similar for both allocations. We start with the optimal

allocation for the differential sampling intervals. The objective function is

g$

Bij

i i j

f

2

1

2

1

6

= =

∑∑ , (1)

whereg$

Bij

2

is the between establishment component of the estimated relative

variance for the ith size class and jth industry stratum summed over the five areas,

using the original allocation of establishments. Only two industry strata were used

in the test surveys, namely the government (state and local) and private sectors.

Thus, it is not actually a single variance that we are minimizing but a sum of

relative variances.

The relative variance is the variance divided by the mean wage squared. The

between establishment component of the relative variance is the between

establishment component of the variance divided by the mean squared, with an

analogous definition for the within establishment component of the relative

variance. The between establishment component of the relative variance was used

since this component is not affected by the allocation of occupations. The effect of

minimizing the between establishment component in this optimization will be seen

at the end of this section.

The following optimization method is similar to the one due to Neyman described

in Cochran (1977) for finding an optimum allocation in a stratified random sample.

The linear objective function (1) subject to the constraint

f

in n

i

i

=

∑ =

1

6

, (2)

on the total number of noncertainty establishments is minimized by

f f

i

Bi

Bi

i

=

∑

$

$

g

g

, (3)

where,
4

f

n n

n

Bi i

Bi i

=

∑

∑

$

$

g

g

, (4)

ni

 is the number of noncertainty establishments in each size class over all

areas and strata, and n is the total number of noncertainty establishments.

We use a similar process in finding the optimal allocation for the number of

occupational selections. Here, we use the optimal allocation of establishments

obtained by the procedure just described and for this establishment allocation

determine the occupational allocation that minimizes the within component of the

relative variance. Both noncertainty and certainty establishments are used since

they both contribute to this component of the relative variance. The linear

objective function in this case is

$

*

g Wij

ij i j

i

i

f

m

m

2

1

2

1

6

= =

∑∑ ⋅ , (5)

where g$Wij

2

is the estimated within component of the relative variance for the ith

size class and jth stratum summed over the five areas for the actual allocation of

establishments and occupational selections used in the test surveys. (Actually this

component of the relative variance contains a finite population correction term

which is omitted from g$Wij

2

since it is not a function of the number of occupational

selections and hence does not effect the optimization.) f f

ij = i

 for noncertainty

units and f

ij = 1 for certainty units, where f

i

 are now constants obtained from the

first optimization. f

ij is present in (5) since the original number of noncertainty

establishments in size class i has been multiplied by f

i

. miis the actual number of

occupational selections in each size class. mi

*

is the optimal allocation for the

number of occupational selections in each size class, with the mi

*

’s the variables in

the second optimization. The term mi mi/

*

 is present in (5) to adjust for the effect

on the relative variance of selecting mi

*

occupations instead of mi.

To obtain the optimal mi

*

’s we minimize (5) subject to the constraint

mif

in n C

i

i i

*

( )

=

∑ + ′ =

1

6

, (6)

where ni

, n′

i

 are, respectively, the number of noncertainty and certainty

establishments in each size class for all areas and strata in the original allocation,
5

and C is the total number of occupational selections. The optimal mi

*

’s are

obtained from formulas analogous to (3) and (4) for the first optimization.

We now investigate the question of whether the f

i

’s and mi

*

’s obtained by the

two optimizations would be the same as the optimal values obtained by minimizing

both sets of variables simultaneously for the objective function (1)+(5) subject to

constraints (2) and (6). ((1)+(5) is the appropriate objective function since it is the

overall relative variance.)

In the special case when all establishments in all size classes are noncertainty, the

simultaneous optimization approach will yield the same allocation as obtained with

our two optimizations approach. To establish this claim we first observe that (1)

+(5) reduces, with the substitution xi = f

imi

*

 in (5), to

g$ g$

Bij

i

Wij i

i i j

f

m

x

2 2

1

2

1

6

+

















= =

∑∑ (7)

and (6) reduces to

xin C

i

i

=

∑ =

1

6

, (8)

with (2) remaining unchanged.

Then, note that since f

i

 is only present in the first term in (7) and in (2),

minimizing (7) subject to (2) and (8) yields the same f

i

 as minimizing (1) subject

to (2). Furthermore, since the xi’s are present only in the second term in (7) and

in (8), minimizing (7) subject to (2) and (8) yields xi which when divided by the

optimal f

i

 produce the same mi

*

as would be obtained by minimizing (5) subject to

(6).

If there are certainty establishments, as there are in our applications then the two

approaches do not generally yield the same allocations, and consequently, our

approach using two sequential optimizations does not yield the optimal

simultaneous allocation for both sets of variables.

Note if we were interested in finding only the optimum allocation for the number

of establishments by size class instead of the optimal allocation of the number of

establishments and occupations we would have minimized (1) subject to (2), with

the between establishment component of the relative variance replaced by the

overall relative variance. Likewise, to find the optimal allocation for the number of
6

occupational selections alone, we would have minimized (5) subject to (6) with f

ij

replaced by 1 in (5) and (6).

We have omitted here providing details of the of the calculations of the between

and within establishment variance components used in (1) and (5). A complete

description is provided in Tehonica, Ernst, and Ponikowski (1996). The following

is a very brief overview. The variance estimation formulas for mean wages are

obtained using a linearized Taylor Series form. For noncertainty establishments

the overall variance is estimated with a pps with replacement formula reflecting the

fact that the first stage of sampling in a PSU is a pps sample of establishments.

The within establishment component of variance for both certainty and

noncertainty establishments is estimated by a simple random sample without

replacement formula, reflecting the fact that the sample of occupations within an

establishment is typically obtained through a systematic sample of employees. The

between establishment variance estimate is obtained by subtracting the within

establishment variance estimate for noncertainty establishments from the total

variance estimate for noncertainty establishments.

An interesting feature of the objective functions (1) and (5) is that they allowed us

to find and see the effect of the optimal allocation, while using the original variance

formulas. The one exception is that we did not use the fpc term of the within

establishment variance in determining the optimal allocation for the second

optimization. However, the fpc term was used when comparing the variance with

the optimal allocation against the variance with the original allocation.

RESULTS

We are primarily interested in the effect the sequential optimal allocations have on

the variances for mean wages in three domains: overall, Major Occupational

Groups (MOGs), and work levels. Each of these domains and each group or level

within each domain calls for a different optimal allocation. Since only one

allocation is possible we use an allocation that is a weighted average of the

allocations that are optimal for these characteristics.

The overall domain simply includes all occupational selections. The MOGs

domain groups occupational selections into 10 categories, such as Professional,

Sales, and Service Occupations. The work levels domain groups occupational

selections into 15 different levels depending on the total score of the selection on

ten different factors, such as knowledge required, guidelines given, and

supervisory duties.

The adjusted allocation that we used was obtained as follows. An optimal

allocation was obtained for the sum over five test surveys of the relative variance

of the overall mean wages. Ten additional optimal allocations were obtained, each

for the sum of the relative variances of the mean wages for a specific MOG. The
7

final allocation was a weighted average of these 11 allocations, with each MOG

allocation equally weighted and the overall allocation given a weight 10 times

larger than the weight of each MOG allocation. It was decided not to base the

allocations on the work level, since there were so few observations at the higher

work levels in some of the size classes. We did not want the allocations to be

overly influenced by a handful of observations. However, we did observe the

effect the adjusted allocation had on the levels.

Note that an alternative allocation could have been obtained by using the using an

objective function that is a linear combination of the 11 objective functions actually

used with the relative variance overall being given 10 times larger weight in this

objective function then the relative variance for each MOG. That is, this

alternative uses a weighted average of the objective functions instead of a

weighted average of the allocations. With this approach the characteristics with

larger relative variances would influence the allocation more than the other

characteristics. This may be either a drawback or an advantage, depending on

whether there is more interest on improving the relative variance of all

characteristics or just those with larger relative variances. If the former is the case

then the linear combination of the 11 objective functions just described can be

modified by dividing the weight for each characteristic by the sum over the five

areas of the relative variances of that characteristic with the current allocations.

With this modification we would be optimizing a weighted percentage reduction in

the relative variances, summed over the five areas, of the 11 characteristics.

For the adjusted allocation that we ended up using, the factors, f

i

, which

determines the sampling intervals and the number of occupational selections are as

follows:

Table 2.

Size Class fi Original Occ. Selections Adjusted Occ. Selections

 0 - 49 1.0818 4 6

 50 - 99 0.8649 8 6

100 - 249 1.0127 10 8

250 - 499 1.0047 12 9

500 - 999 0.7478 16 8

1000 + 0.4460 20 31

At first glance, there appears to be an inconsistency between fi and the average

optimal number of selections in the largest size class. The factor says to decrease

the number of establishments to .4460 of the original number of establishments

which will reduce the number of occupational selections, but the adjusted number

of occupational selections says to increase the number of selections to 31 per

establishment. However, the factor affects noncertainty establishments only. This

apparent inconsistency is a result of the fact that only 10 of 113 establishments
8

with more than 1000 employees were noncertainty establishments. Since there

were so few noncertainty establishments in this size class, little credence should be

given to this factor. Note that because the factor only affects the few noncertainty

establishments it has little influence on the optimal number of selections in this size

class which is determined by both certainty and noncertainty establishments.

We did not find the small differences among the five smallest size classes in the

adjusted allocation of the number of occupational selections and the dramatically

larger allocation for the largest size class to be surprising. Typically, variances

tend to be lowered when the weights are inversely proportional to size. In the case

of an occupational selection the “size” is the number of employees in the

occupation. The employee weight, ignoring adjustments, is the product of the

establishment weight and the reciprocal of the probability of selecting the

occupation given that the establishment has been selected. The first term in this

product, the establishment weight, is for a noncertainty establishment in each

industry inversely proportional to the establishment employment. The second term

is the sampling interval used in the probability selection of occupations (known as

the PSO sampling interval) divided by the number of employees in the occupation.

The PSO sampling interval is the number of employees in the establishment divided

by the number of occupational selections. (The establishment employment on the

sampling frame used in selecting the establishment differs somewhat from the

employment used in selecting the occupations, which is done at the time of the

interview and which excludes certain classes of employees, but the difference is

generally small and will be ignored in this discussion.) Consequently, the employee

weight would be inversely proportional to the number of employees in an

occupation if the product of the establishment weight and the PSO sampling

interval is the same for all establishments. For noncertainty establishments this

condition would be met if the number of occupational selections were the same in

each of the size classes, since then the smaller establishment weight and the larger

PSO sampling interval for larger establishments would cancel each other out.

However, once the establishment employment goes above the certainty cutoff we

would no longer have this cancellation. That is, as the establishment size continues

to increase the establishment weight remains fixed at 1, but the PSO interval

continues to increase unless the number of occupational selections is increased.

Thus, we believe that the reason the allocation is so large for the largest size class

is that most of the establishments in this size class are well above the certainty

cutoff.

Since the factors for the differential sampling intervals are close to one, except in

the two highest size classes where there are not many noncertainty establishments,

there was little impact on the between establishment variance from this part of the

allocation. However, the adjusted allocation for the number of occupational

selections had a definite impact on the within variance, as can be ascertained from

Appendix I.
9

Appendix I has the individual results of the adjusted allocation for each of the six

test surveys identified by the test city’s name. Down the columns, we have the

original total relative variance (orig.rel.var), the between component of the

original relative variance (orig.rel.bet), and the within component of the original

relative variance (orig.rel.wi) compared to each of their corresponding

counterparts for the adjusted allocation (adj.rel.var, adj.rel.bet, adj.rel.wi). A

ratio is then given for each component of the variance (total.ratio, bet.ratio, and

wi.ratio), which is the adjusted component divided by the original component.

Across the rows, we have the results for all workers and then each MOG which

are as follows:

Table 3.

Code Description

 Y Professional

 Z Technical

 B Executive, Administrative, and Managerial

 C Sales

 D Administrative Support

 E Precision Production, Craft, and Repair

 F Machine Operators, Assemblers, and Inspectors

 G Transportation and Material Moving

 H Handlers, Equipment Cleaners, Helpers, and Laborers

 K Service 

We have the weighted average of the ratios (Wt. Avg.) in the last row. This is a

measure we can use to observe the overall impact of the adjusted allocation. The

Wt. Avg. of the ratios is a weighted mean of the ratios for the ten MOGs and

overall, with the ratio for the overall estimated weighted ten times any individual

MOG. For each entry in this row, the weighted average of the ratios is for the

component of variance given by the column heading.

The grand weighted average of the ratios for all five test surveys combined is

obtained as the arithmetic mean of the of the five weight averages. We get the

following:

Table 4.

Grand avg. of weighted total ratios = 0.9412

Grand avg. of weighted between ratios = 0.9969

Grand avg. of weighted within ratios = 0.8428

Salt Lake City was not included in these combined estimates or in finding the

adjusted allocation, because of the outliers in the relative variance calculations for

MOG C and MOG H.
10

Variance estimates for 11 characteristics in each of five areas were used in

determining the optimal allocations or a total of 55 estimates. The within ratio for

45 of these 55 characteristics was numerically less than 1, a striking result. If these

55 ratios were all independent estimates (which they are not) with each estimates

having probability 1/2 of being less than 1, then the probability of obtaining so

many ratios less than 1 would be negligible. That is, by the sign test the large

number of ratios numerically less than 1 is significant at any reasonable level of

significance. The within ratio for the overall estimate was less than 1 for each of

these five areas. Even though Salt Lake City was not used in determining the

allocation, 8 of the 11 within ratios were less than 1 for this area.

Appendix II has the results of the adjusted allocation on the work levels for each

of the six test surveys. The setup of the tables is similar to that of Appendix I

except the variance estimates of the levels move across the rows instead of the

MOGs and the results of the between variances are not given, since, as was the

case for the estimates in Appendix I, the allocation adjustment has little effect on

these variances. After the results of the six test surveys, the average ratio of each

level for the five areas used in finding the adjusted allocation are given. Salt Lake

City is again omitted from these averages because of the outlier problem in the

variances previously mentioned.

Even though the variances of the work levels were not taken into consideration in

finding our adjusted allocation, the adjusted allocation does quite well in reducing

the variances. The grand average of the total ratios is 0.9320. The grand average

of the within ratios is 0.8880. Here, there are variance estimates for 75

characteristics from 15 work levels in five areas. The within ratio for 52 of these

75 characteristics was less than 1. Again, if we consider these ratios to be

independent with each estimate having the probability 1/2 of being less than one,

then the probability of obtaining so many ratios less than one would be small. As

for Salt Lake City, 10 of the 15 within ratios were less than one.

The average ratios of the levels for the five test surveys are less than one for 13 of

the 15 levels, which by the sign test is significant at the level of significance

a =.01. The average ratio is greater than 1 for work levels 14 and 15. Because of

the small amount of data at these levels they happen to be the two levels for which

there is the most interest in decreasing the variance. However, the increase in the

variance estimates for these levels may be more a result of the limitations in the

data than in the adjusted allocation. For example, in Rochester for work level 15,

which shows the greatest percentage increase in the within variance from the

original to the adjusted allocation among all the areas, only about 0.4% of all

occupational selections are at this level, and none of them are in the highest size

class where the adjusted allocation has the greatest percentage increase in

occupational selections. This is a case where we believe the sample does not

provide an estimate of the distribution by employment class that is close to the
11

population distribution, since we do not believe that there are no level 15

employees in Rochester in establishments in the largest size class. There are

similar explanations, although not as dramatic, for some of the other increases in

the within variance for levels 14 and 15 with the adjusted allocation. Given the

sparse amount of data at the levels, we believe we need data from additional areas

to properly assess the effect of the adjusted allocation on variances for these levels.

CONCLUSIONS

In the NCS variance calculation for the locality mean wage estimates, there was

only a small difference in the between component of the relative variance using

differential sampling intervals compared to the between component of the original

direct pps allocation. The results we have obtained do not provide much support

for deviating from direct pps in selecting establishments.

However, the within component of the relative variance was quite different from

the optimal number of occupational selections. This allocation shows that for

variance purposes it may be more appropriate to use only one or two different

selection rates for establishments with less than 1000 employees, and that there

should be an increase in the number of occupational selections for establishments

with more than 1000 employees. This analysis does not include constraints

imposed by respondent burden considerations. For example, regardless of the

effect on variances, it is likely that an increase in the number of occupational

selections for the smallest size class would not be given serious consideration for

reasons of respondent burden.
12

APPENDIX I

 ALBUQUERQUE

orig.rel.var adj.rel.var total.ratio orig.rel.bet adj.rel.bet bet.ratio orig.rel.wi adj.rel.wi wi.ratio

ALL 0.00108 0.00107 0.9907 0.000786 0.000816 1.0382 0.000293 0.000254 0.8669

MOG Y 0.00309 0.00306 0.9903 0.001502 0.001647 1.0965 0.001585 0.001417 0.8940

MOG Z 0.00258 0.00229 0.8876 0.000743 0.000732 0.9852 0.001835 0.001554 0.8469

MOG B 0.00349 0.00314 0.8997 0.000417 0.000425 1.0192 0.003069 0.002710 0.8830

MOG C 0.01136 0.01004 0.8838 0.007658 0.007247 0.9463 0.003705 0.002791 0.7533

MOG D 0.00303 0.00278 0.9175 0.002619 0.002443 0.9328 0.000413 0.000337 0.8160

MOG E 0.00209 0.00212 1.0144 0.001642 0.001629 0.9921 0.000448 0.000490 1.0938

MOG F 0.00263 0.00227 0.8631 0.001289 0.001238 0.9604 0.001345 0.001032 0.7673

MOG G 0.02024 0.01963 0.9699 0.017164 0.016969 0.9886 0.003074 0.002663 0.8663

MOG H 0.00541 0.00530 0.9797 0.004080 0.003779 0.9262 0.001328 0.001516 1.1416

MOG K 0.00216 0.00214 0.9907 0.001601 0.001617 1.0100 0.000556 0.000522 0.9388

Wt.Avg. 0.9652 1.0120 0.8835

 ALLENTOWN

orig.rel.var adj.rel.var total.ratio orig.rel.bet adj.rel.bet bet.ratio orig.rel.wi adj.rel.wi wi.ratio

ALL 0.00065 0.00061 0.9385 0.000471 0.000463 0.9830 0.000176 0.000150 0.8523

MOG Y 0.00106 0.00097 0.9151 0.000381 0.000361 0.9475 0.000678 0.000604 0.8909

MOG Z 0.00146 0.00112 0.7671 0.000131 0.000118 0.9008 0.001332 0.001004 0.7538

MOG B 0.00127 0.00132 1.0394 0.000286 0.000268 0.9371 0.000980 0.001057 1.0786

MOG C 0.02246 0.01682 0.7489 0.008408 0.007959 0.9466 0.014049 0.008858 0.6305

MOG D 0.00156 0.00149 0.9551 0.000979 0.000993 1.0143 0.000585 0.000497 0.8496

MOG E 0.00097 0.00084 0.8660 0.000513 0.000491 0.9571 0.000458 0.000348 0.7598

MOG F 0.00373 0.00346 0.9276 0.002708 0.002699 0.9967 0.001025 0.000766 0.7473

MOG G 0.01120 0.01056 0.9429 0.008249 0.008222 0.9967 0.002953 0.002341 0.7928

MOG H 0.00347 0.00299 0.8617 0.001590 0.001526 0.9597 0.001878 0.001463 0.7790

MOG K 0.00232 0.00228 0.9828 0.000742 0.000720 0.9704 0.001581 0.001564 0.9892

Wt.Avg. 0.9196 0.9728 0.8397

 NEW ORLEANS

orig.rel.var adj.rel.var total.ratio orig.rel.bet adj.rel.bet bet.ratio orig.rel.wi adj.rel.wi wi.ratio

ALL 0.00156 0.00154 0.9872 0.001372 0.001371 0.9993 0.000190 0.000169 0.8895

MOG Y 0.00485 0.00453 0.9340 0.004541 0.004319 0.9511 0.000314 0.000214 0.6815

MOG Z 0.00322 0.00351 1.0901 0.001482 0.001578 1.0648 0.001734 0.001931 1.1136

MOG B 0.00299 0.00300 1.0033 0.001237 0.001208 0.9766 0.001750 0.001793 1.0246

MOG C 0.01501 0.01472 0.9807 0.007980 0.007970 0.9987 0.007031 0.006751 0.9602

MOG D 0.00141 0.00141 1.0000 0.000975 0.000986 1.0113 0.000435 0.000424 0.9747

MOG E 0.00229 0.00249 1.0873 0.001268 0.001326 1.0457 0.001022 0.001160 1.1350

MOG F 0.00560 0.00605 1.0804 0.004618 0.004701 1.0180 0.000984 0.001350 1.3720

MOG G 0.00314 0.00286 0.9108 0.002007 0.001990 0.9915 0.001136 0.000866 0.7623

MOG H 0.00508 0.00489 0.9626 0.004118 0.004073 0.9891 0.000957 0.000817 0.8537

MOG K 0.00381 0.00354 0.9291 0.002635 0.002576 0.9776 0.001173 0.000963 0.8210

Wt.Avg. 0.9925 1.0009 0.9297
13

 RALEIGH

orig.rel.var adj.rel.var total.ratio orig.rel.bet adj.rel.bet bet.ratio orig.rel.wi adj.rel.wi wi.ratio

ALL 0.00091 0.00083 0.9121 0.000632 0.000627 0.9921 0.000280 0.000200 0.7143

MOG Y 0.00384 0.00273 0.7109 0.001795 0.001683 0.9376 0.002041 0.001049 0.5140

MOG Z 0.00550 0.00448 0.8145 0.003375 0.003119 0.9241 0.002121 0.001361 0.6417

MOG B 0.00167 0.00168 1.0060 0.000282 0.000271 0.9610 0.001392 0.001413 1.0151

MOG C 0.01599 0.01452 0.9081 0.010841 0.010119 0.9334 0.005149 0.004397 0.8540

MOG D 0.00046 0.00038 0.8261 0.000225 0.000218 0.9689 0.000232 0.000165 0.7112

MOG E 0.00298 0.00219 0.7349 0.001210 0.001103 0.9116 0.001774 0.001090 0.6144

MOG F 0.00142 0.00139 0.9789 0.000999 0.001015 1.0160 0.000420 0.000373 0.8881

MOG G 0.01201 0.01199 0.9983 0.009450 0.009973 1.0553 0.002559 0.002022 0.7902

MOG H 0.00146 0.00170 1.1644 0.000649 0.001008 1.5532 0.000816 0.000692 0.8480

MOG K 0.00236 0.00212 0.8983 0.001535 0.001512 0.9850 0.000822 0.000611 0.7433

Wt.Avg. 0.9081 1.0084 0.7381

 ROCHESTER

orig.rel.var adj.rel.var total.ratio orig.rel.bet adj.rel.bet bet.ratio orig.rel.wi adj.rel.wi wi.ratio

ALL 0.00075 0.00071 0.9467 0.000547 0.000552 1.0091 0.000200 0.000162 0.8100

MOG Y 0.00136 0.00122 0.8971 0.000485 0.000495 1.0206 0.000878 0.000723 0.8235

MOG Z 0.00146 0.00121 0.8288 0.000832 0.000779 0.9363 0.000633 0.000434 0.6856

MOG B 0.00361 0.00293 0.8116 0.001544 0.001451 0.9398 0.002066 0.001483 0.7178

MOG C 0.01269 0.01217 0.9590 0.009915 0.009271 0.9350 0.002777 0.002896 1.0429

MOG D 0.00116 0.00098 0.8448 0.000494 0.000472 0.9555 0.000662 0.000505 0.7628

MOG E 0.00127 0.00110 0.8661 0.000437 0.000432 0.9886 0.000838 0.000667 0.7959

MOG F 0.00203 0.00197 0.9704 0.001446 0.001479 1.0228 0.000581 0.000488 0.8399

MOG G 0.00669 0.00668 0.9985 0.004918 0.004657 0.9469 0.001771 0.002025 1.1434

MOG H 0.00565 0.00476 0.8425 0.002428 0.002310 0.9514 0.003225 0.002445 0.7581

MOG K 0.00304 0.00283 0.9309 0.001893 0.001930 1.0195 0.001142 0.000903 0.7907

Wt.Avg. 0.9208 0.9904 0.8230

 SALT LAKE CITY

orig.rel.var adj.rel.var total.ratio orig.rel.bet adj.rel.bet bet.ratio orig.rel.wi adj.rel.wi wi.ratio

ALL 0.00121 0.00112 0.9256 0.000855 0.000850 0.9942 0.000356 0.000273 0.7669

MOG Y 0.00254 0.00228 0.8976 0.001160 0.001217 1.0491 0.001380 0.001063 0.7703

MOG Z 0.00191 0.00191 1.0000 0.000719 0.000786 1.0932 0.001192 0.001123 0.9421

MOG B 0.00262 0.00277 1.0573 0.000271 0.000295 1.0886 0.002345 0.002473 1.0546

MOG C 0.04390 0.03764 0.8574 0.032646 0.030369 0.9303 0.011252 0.007274 0.6465

MOG D 0.00473 0.00315 0.6660 0.000303 0.000343 1.1320 0.004423 0.002810 0.6353

MOG E 0.00157 0.00153 0.9745 0.001165 0.001170 1.0043 0.000406 0.000356 0.8768

MOG F 0.00461 0.00478 1.0369 0.003155 0.003209 1.0171 0.001456 0.001567 1.0762

MOG G 0.00644 0.00654 1.0155 0.005009 0.004955 0.9892 0.001436 0.001581 1.1010

MOG H 0.25560 0.20977 0.8207 0.167808 0.155415 0.9261 0.087791 0.054360 0.6192

MOG K 0.00453 0.00396 0.8742 0.002206 0.002217 1.0050 0.002329 0.001739 0.7467

Wt.Avg. 0.9228 1.0088 0.8069
14

APPENDIX II

 ALBUQUERQUE ALLENTOWN

Lvl orig.rel.var adj.rel.var tot.ratio orig.rel.wi adj.rel.wi wi.ratio orig.rel.var adj.rel.var tot.ratio orig.rel.wi adj.rel.wi wi.ratio

1 0.00293 0.00279 0.9522 0.00061 0.0006 0.9016 0.00265 0.00268 1.0113 0.00119 0.00122 1.0252

2 0.00277 0.00282 1.0181 0.00048 0.0005 1.0833 0.00255 0.00242 0.9490 0.00110 0.00101 0.9182

3 0.00521 0.00520 0.9981 0.00070 0.0007 1.0286 0.00307 0.00289 0.9414 0.00089 0.00077 0.8652

4 0.00434 0.00439 1.0115 0.00069 0.0008 1.1014 0.00272 0.00231 0.8493 0.00111 0.00079 0.7117

5 0.00103 0.00082 0.7961 0.00065 0.0005 0.7231 0.00116 0.00109 0.9397 0.00049 0.00039 0.7959

6 0.00109 0.00096 0.8807 0.00057 0.0005 0.8246 0.00215 0.00188 0.8744 0.00108 0.00082 0.7593

7 0.00130 0.00101 0.7769 0.00118 0.0009 0.7627 0.00076 0.00057 0.7500 0.00062 0.00043 0.6935

8 0.00143 0.00122 0.8531 0.00067 0.0005 0.7463 0.01548 0.01000 0.6460 0.01123 0.00604 0.5378

9 0.00086 0.00095 1.1047 0.00063 0.0007 1.1429 0.00076 0.00077 1.0132 0.00056 0.00057 1.0179

10 0.00396 0.00415 1.0480 0.00342 0.0036 1.0643 0.00138 0.00126 0.9130 0.00112 0.00101 0.9018

11 0.00308 0.00253 0.8214 0.00134 0.0009 0.6716 0.00135 0.00118 0.8741 0.00087 0.00073 0.8391

12 0.00213 0.00232 1.0892 0.00177 0.0020 1.1073 0.00116 0.00113 0.9741 0.00108 0.00105 0.9722

13 0.01401 0.01593 1.1370 0.00819 0.0095 1.1648 0.00164 0.00164 1.0000 0.00140 0.00141 1.0071

14 0.00470 0.00538 1.1447 0.00465 0.0053 1.1441 0.00136 0.00170 1.2500 0.00123 0.00157 1.2764

15 0.00722 0.00519 0.7188 0.00721 0.0052 0.7184 0.00381 0.00454 1.1916 0.00333 0.00404 1.2132

0.9567 0.9457 0.9451 0.9023

 NEW ORLEANS RALEIGH

Lvl orig.rel.var adj.rel.var tot.ratio orig.rel.wi adj.rel.wi wi.ratio orig.rel.var adj.rel.var tot.ratio orig.rel.wi adj.rel.wi wi.ratio

1 0.00568 0.00509 0.8961 0.00077 0.00050 0.6494 0.00425 0.00479 1.1271 0.00089 0.00096 1.0787

2 0.00445 0.00394 0.8854 0.00114 0.00082 0.7193 0.00277 0.00271 0.9783 0.00072 0.00070 0.9722

3 0.00162 0.00158 0.9753 0.00044 0.00037 0.8409 0.00148 0.00125 0.8446 0.00073 0.00051 0.6986

4 0.00402 0.00478 1.1891 0.00304 0.00372 1.2237 0.00973 0.00861 0.8849 0.00127 0.00075 0.5906

5 0.01661 0.01419 0.8543 0.00576 0.00412 0.7153 0.00279 0.00199 0.7133 0.00205 0.00129 0.6293

6 0.00490 0.00352 0.7184 0.00408 0.00271 0.6642 0.00179 0.00147 0.8212 0.00071 0.00045 0.6338

7 0.00221 0.00254 1.1493 0.00143 0.00169 1.1818 0.00098 0.00077 0.7857 0.00067 0.00048 0.7164

8 0.00211 0.00199 0.9431 0.00044 0.00035 0.7955 0.00288 0.00280 0.9722 0.00238 0.00230 0.9664

9 0.00157 0.00145 0.9236 0.00097 0.00086 0.8866 0.00069 0.00055 0.7971 0.00066 0.00052 0.7879

10 0.00458 0.00523 1.1419 0.00292 0.00314 1.0753 0.00288 0.00247 0.8576 0.00097 0.00070 0.7216

11 0.02768 0.02616 0.9451 0.00219 0.00258 1.1781 0.00200 0.00156 0.7800 0.00157 0.00115 0.7325

12 0.00465 0.00525 1.1290 0.00292 0.00347 1.1884 0.00209 0.00195 0.9330 0.00113 0.00101 0.8938

13 0.00362 0.00485 1.3398 0.00346 0.00465 1.3439 0.01764 0.01334 0.7562 0.01122 0.00729 0.6497

14 0.02131 0.02635 1.2365 0.01034 0.01378 1.3327 0.00490 0.00426 0.8694 0.00478 0.00413 0.8640

15 0.01773 0.01547 0.8725 0.01446 0.01230 0.8506 0.00491 0.00554 1.1283 0.00450 0.00514 1.1422

1.0133 0.9764 0.8833 0.8052
15

ROCHESTER SALT LAKE CITY

Lvl orig.rel.var adj.rel.var tot.ratio orig.rel.wi adj.rel.wi wi.ratio orig.rel.var adj.rel.var tot.ratio orig.rel.wi adj.rel.wi wi.ratio

1 0.00341 0.00325 0.9531 0.00173 0.00152 0.8786 0.00471 0.00515 1.0934 0.00113 0.00108 0.9558

2 0.00307 0.00255 0.8306 0.00143 0.00098 0.6853 0.00257 0.00240 0.9339 0.00072 0.00058 0.8056

3 0.00389 0.00313 0.8046 0.00236 0.00160 0.6780 0.19089 0.16961 0.8885 0.02256 0.01394 0.6179

4 0.00100 0.00080 0.8000 0.00076 0.00056 0.7368 0.00133 0.00127 0.9549 0.00033 0.00026 0.7879

5 0.00177 0.00136 0.7684 0.00111 0.00075 0.6757 0.00527 0.00532 1.0095 0.00153 0.00157 1.0261

6 0.00223 0.00157 0.7040 0.00209 0.00143 0.6842 0.00098 0.00102 1.0408 0.00057 0.00060 1.0526

7 0.00074 0.00064 0.8649 0.00040 0.00031 0.7750 0.00087 0.00085 0.9770 0.00031 0.00024 0.7742

8 0.00205 0.00206 1.0049 0.00059 0.00058 0.9831 0.02450 0.02041 0.8331 0.00709 0.00423 0.5966

9 0.00150 0.00149 0.9933 0.00122 0.00117 0.9590 0.00104 0.00073 0.7019 0.00094 0.00062 0.6596

10 0.00189 0.00168 0.8889 0.00155 0.00134 0.8645 0.00282 0.00204 0.7234 0.00190 0.00119 0.6263

11 0.00217 0.00163 0.7512 0.00184 0.00129 0.7011 0.00123 0.00099 0.8049 0.00093 0.00071 0.7634

12 0.00538 0.00452 0.8401 0.00225 0.00160 0.7111 0.00136 0.00151 1.1103 0.00083 0.00101 1.2169

13 0.00515 0.00389 0.7553 0.00492 0.00368 0.7480 0.00178 0.00188 1.0562 0.00167 0.00177 1.0599

14 0.02334 0.01700 0.7284 0.02322 0.01686 0.7261 0.08872 0.10068 1.1348 0.08586 0.09645 1.1233

15 0.03825 0.04727 1.2358 0.01741 0.02354 1.3521 0.01606 0.01289 0.8026 0.01463 0.01148 0.7847

0.8616 0.8106 0.9377 0.8567

 Avg. Ratios

Lvl tot.ratio wi.ratio

1 0.9880 0.9067

2 0.9323 0.8757

3 0.9128 0.8222

4 0.9469 0.8728

5 0.8143 0.7078

6 0.7998 0.7132

7 0.8654 0.8259

8 0.8839 0.8058

9 0.9664 0.9588

10 0.9699 0.9255

11 0.8343 0.8245

12 0.9931 0.9746

13 0.9977 0.9827

14 1.0458 1.0687

15 1.0294 1.0553

0.9320 0.8880
16

REFERENCES

Cochran, W. G.(1977), Sampling Techniques (3rd ed), New York: John Wiley.

Ernst, L. R., and Ponikowski, C. H. (1995), “Specifications for Calculating

Variance Components for an Integrated Compensation Survey,” Bureau of Labor

Statistics memorandum to The Record, dated February 27.

Tehonica, J., Ernst, L. R., and Ponikowski, C. H. (1996), “Summary of Estimation

and Variance Specifications for the 1996 Albuquerque, NM COMP2000 Test

Survey,” Bureau of Labor Statistics memorandum to The Record, dated August 1.

Any opinions expressed in this paper are those of the author and do not constitute

policy of the Bureau of Labor Statistics.