Estimating a Common Relative Risk: Application in Equal Employment

原文摘要

To analyze hiring data in equal employment cases, the available positions should be stratified in accordance with the qualifications needed for the jobs. It is then necessary to combine the results of each stratum to obtain an overall test of equal hiring rates. Furthermore, a summary measure, which compares the hiring rate of a minority applicant to that of a majority one, is then estimated. Indeed, the relative risk measure is used by the government in assessing an employment practice for possible discriminatory impact. Sometimes reliable data on the applicants is unavailable, but an accurate estimate of the minority fraction, πi, of qualified persons in the appropriate labor market is obtainable from census or other external data. Usually the number of hires, t i, in each occupation is small relative to the number of applicants, which itself is a small fraction of the large external pool of qualified persons. Then the number of minority hires, x i, in each occupation can be regarded as a binomial variable with parameters ((t i, πi). This binomial model has been used to analyze hires in a single occupation where there was no need for stratification. This article develops analogs of the Mantel—Haenszel (1959) and maximum likelihood estimators of a common odds ratio for several 2 × 2 tables for the binomial situation. In addition to presenting the large sample theory of these estimators, two tests to check the validity of the assumption of a common odds ratio are developed. The methods are used to analyze data from two cases, one in which the assumption of a common odds ratio was appropriate and one in which it was not. The sensitivity of the results to the assumed values of πi, is also explored, and the assumptions implicit in the use of the binomial model for minority hires are given.

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