Changepoint tests designed for the analysis of hiring data arising in employment discrimination cases

When a complaint of discrimination is made, an employer may respond by hiri ng more minorities. From a legal viewpoint, the practices in effect during the time period prior to the complaint are more relevant for determining li ability than those of the postcharge period. In Gay v. Waiters, the trial j udge observed that the data suggested that a change occurred after the char ge was filed. Because the data had not been subject to a formal statistical analysis, the court was reluctant to base its decision on this observation . Gastwirth and Freidlin and Gastwirth proposed cumulative-sumbased procedu res for the analysis of hiring data following the binomial model. In this a rticle, the procedures are extended to data following the hypergeometric mo del and to analysis of stratified data. Several datasets that were submitte d to the courts in the United States are analyzed by the proposed methods. Because the data are usually reported by year, the ordinary large-sample th eory is not sufficiently accurate. Therefore, we obtain the p values of the statistics by simulation. For binomial data, recent improvements in the Bo nferroni inequality are used to derive a new upper hound.