e.

Calculating the number of years that it would take to achieve parity or an equitable distribution

This note explains the calculations used to derive Charts 17 and 18. The first step is to subtract the percent of all professionals at a particular grade with less than a year of time in grade from the percent of the minority group professionals (blacks, for example) with time in grade of less than a year. If the difference is positive it is multiplied times the percent blacks comprise of the grade. This gives the percentagepoint increase in the proportion that blacks will comprise of all professionals at that grade next year based on last year's rate of entry for blacks compared to the rate for all professionals at this grade. The percentage-point increase is then divided into the difference between the goal for the representation of blacks and the proportion they comprise of the grade. This provides the percent of their goal that blacks would attain over a one year period. Dividing the percent into 1.0 gives the number of years that it would take to achieve the goal.

The survey was conducted to collect information on the educational attainment of DOL employees for inclusion in the Task Force's evaluation of the status of minorities and women. This information seemed crucial to our study, but, unfortunately it was not contained in the Department's computerized personnel records. A survey of a sample of DOL employees appeared to be most efficient means of gathering the data on education. 1/

The information from the survey will be included in a regular quantitative analysis as well as in a more sophisticated statistical study. The quantitative analysis will measure and evaluate the difference or similarity in education among racial and sexual groups within the professional and nonprofessional classifications. It will also compare the status of employees with equal levels of education across racial and sexual groups. The sophisticated statistical analysis will estimate the effect of education along with other explanatory factors in accounting for the lower position of minorities.

Sample design

The ideal is to select the smallest sample which will provide a specified level of certainty in generalizing for the population. Without advance knowledge of the characteristics of the information being sampled, it is difficult to determine the sample size needed to achieve a required level of certainty. As a result of the absence of data on the educational attainment of either DOL or Federal employees, we were unable to derive a sample size that would assure a specified degree of certainty. Only a general estimate of the required size was possible. This was based mainly on the advice of statisticians who had substantial experience in sampling. The size of the sample finally selected was determined by this advice together with our evaluation of the limitations on what size sample could be collected within a certain time period. A sample of 1,000 employees was chosen.

Having decided on a sample size, the second major consideration was to select the sample in a manner which would insure that it adequately represented all the racial and sexual groups for which separate information was desired. This is especially important since these groups are represented in different numbers in the Department's workforce and a completely random sample of the whole population might not include enough employees of a particular group nonblack minority females, for example

1/ This decision was reached during discussions with Chuck Roberts and Bill Dedham.

Consequently,

three racial groups

to say anything significant about that group. the sample was stratified into six groups: whites, blacks, and nonblack minorities each divided according to male and female.

The number of employees included in each of the six stratified groups was determined on the basis of a priori assumptions concerning the need for information about the particular groups. We attached equal importance to information concerning blacks and whites, and males and females. Because nonblack minorities comprise only 3 per cent of the Department's workforce it was felt that a smaller sample size could be used for this group compared to that for whites and blacks. These a priori assumptions yield the sample distribution shown below.

Since the overall study included only GS employees, the

sample contains only these workers.

Sample selection

The sample was selected from a computer printout of all DOL employees listed separately according to the six stratified groups. Within each group, the employees were listed on the printout by Social Security number in ascending order. From each of the six listings a random sample of employees was chosen corresponding to the number of employees allotted to represent that group. Because of the geographic and age bunching that appears in an ordered listing by Social Security number, the technique which is described below seemed best suited to choosing a random sample from each of the six groups. This technique was applied to each of the groups as follows:

1.

2.

3.

The number of employees in the group is divided by
the number of employees allotted in the sample for
that group to yield a "ratio of employees sampled."
For example, since the sample includes 214 white
males out of the total 4,964 (4964 23) the "ratio"

214

of white males sampled to all white males would be 1 out of 23.

A random number smaller than the "ratio of employees
sampled" is chosen to select the first employee included
in the sample. In the example above this number would
be between one and 23. The first employee chosen is
the one designated by the random number counting down
the listing of employees. For example, if the random
number is five, then the fifth employee is the first one
selected for the sample.

After choosing the first employee, the remainder
are selected according to the "ratio of employees
sampled." In the example used here this would
mean that starting with the first employee selected,
every 23rd would be chosen consecutively over the
remainder of the list.

Sample collection

The most efficient means of collecting the information in the sample appeared to be by retrieving the educational data from the employees' personnel records. We realized that the information contained in the files might not be completely up-to-date. However, the alternative of gathering the data from each of the employees in the sample would have consumed much more time. Trading off the factors of accuracy against time it seemed that collecting the data quickly was the overriding consideration. We felt that gathering the information from the files would provide a sufficient degree of accuracy, and would satisfy a severe time constraint.

Questionnaires were sent out to the seven central personnel offices and the eight RAOS. The forms listed the employees in the sample and requested the following information:

Responses were received for all of the 1,000 employees for whom information was requested. One aspect of the response which should be noted is that 8 per cent of the personnel folders were not located where the computer master file indicated. Almost none of this could be accounted for