Statistics and Its Interface

Volume 7 (2014)

Number 2

Adaptive procedures for nested processes: application to equal employment

Pages: 153 – 165

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n2.a1

Authors

Wenjing Xu (Department of Statistics, George Washington University, Washington, D.C., U.S.A.)

Qing Pan (Department of Statistics, George Washington University, Washington, D.C., U.S.A.)

Joseph L. Gastwirth (Department of Statistics, George Washington University, Washington, D.C., U.S.A.)

Abstract

Typically, equal employment cases concern the fairness of an employer’s hiring, promotion or layoff decisions. Sometimes both the hiring and promotion practices are under scrutiny. An unappreciated issue in the analysis of promotion data is that Fisher’s exact test may have low power for detecting a legally meaningful disparity in promotion rates when the number of minorities previously hired was small due to unfair hiring. The two employment processes are nested. Thus, before promotion data is analyzed, one should first check whether the hiring was fair. The choice of an appropriate test for fairness in promotions should depend on the result of the test on hiring. Two adaptive procedures are presented in this paper. One uses the Breslow-Day test as the preliminary procedure for choosing between a test having a mixture $\chi^2$ null distribution and a test assuming a common odds ratio between the success rates of minority and majority members in both hiring and promotion. The second adaptive procedure was motivated by a court’s suggestion that when the fairness of both the hiring and promotion practices are under review, rather than applying Fisher’s exact test to data of promotions made from those hired, the promotions should be viewed as a random sample from the applicants for the lower level position. The statistical properties of the test procedures are presented and the tests are applied to data from four actual cases. Because the choice of the test at the second stage depends on the results of the first stage analysis, in cases concerning promotion, courts should give plaintiffs access to data concerning hiring in the feeder positions. Thus, the courts should take a broad view of potentially relevant data at the discovery stage.

Keywords

adaptive inference, discovery in civil cases, equal employment, mixture $\chi^2$ test, legal statistics, nested processes, two-stage tests

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