Changepoint Tests Designed for the Analysis of Hiring Data Arising in Employment Discrimination Cases
Freidlin, Boris, Gastwirth, Joseph L., Journal of Business & Economic Statistics
When a complaint of discrimination is made, an employer may respond by hiring more minorities. From a legal viewpoint, the practices in effect during the time period prior to the complaint are more relevant for determining liability than those of the postcharge period. In Gay v. Waiters, the trial judge observed that the data suggested that a change occurred after the charge 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-sum-based procedures for the analysis of hiring data following the binomial model. In this article, the procedures are extended to data following the hypergeometric model and to analysis of stratified data. Several datasets that were submitted 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 theory is not sufficiently accurate. Therefore, we obtain the p values of the statistics by simulation. For binomial data, recent improvements in the Bonferroni inequality are used to derive a new upper bound.
KEY WORDS: Binomial data; Changepoint; Fair hiring practices; Hypergeometric data.
After a complaint of discrimination in hiring is filed, the employer may change its practices. By the time the trial occurs, the defendant may submit hiring data showing that a protected group received its "fair share" of hiring over a time frame that includes both the precharge and postcharge periods. From a legal viewpoint the most relevant time period is the one just prior to a complaint (see O'Brien v. Sky Chefs. Inc. 1982). The issue of whether there has been a change in employment practices has occurred in several cases (e.g., Gay v. Waiters 1982).
When a test procedure is being developed for a particular application, one can increase its power by directing the test at a specific alternative. Agresti (1990, pp. 97-102) presented several examples of such procedures; Levin and Kline (1985) developed a changepoint test to detect a sudden increase in the proportion of chromosomally abnormal abortions and a subsequent decline to the normal level. The pattern of concern in the legal setting is underrepresentation before the charge and a change to fair or even overhiring of minorities sometime after the charge but prior to the trial. This article modifies the tests based on the cumulative sums (CUSUM's) to have more power against this alternative. In statistical literature, changepoint methods were discussed by Page (1954), Chernoff and Zacks (1964), Hinkley and Hinkley (1970), Pettitt (1979, 1980), Worsley (1983), Siegmund (1986), James, James, and Siegmund (1987), Lombard (1987), Csorgo and Horvath (1988), Bhattacharya (1987, 1994), and Brostrom (1997). Econometric applications often involve dependent observations. Appropriate changepoint techniques were developed by Ploberger and Kramer (1990), Banerjee, Lumsdaine, and Stock (1992), Chu and White (1992), Jandhyala and MacNeill (1992), Andrews and Ploberger (1994), and Vogelsang (1997).
The data available for examining hiring practices typically follow either a hypergeometric or a binomial model (Baldus and Cole 1980; Gastwirth 1988; Finkelstein and Levin 1990; Paetzold and Willborn 1994). When data on the actual applicants are available and reliable, the hypergeometric model is appropriate. When the applicant data are unavailable or when fair recruitment is an issue, the minority share of the qualified labor force is determined from the census data on the members of the labor force in the area with the relevant skills. Then the hiring data are modeled by a binomial distribution. Section 1 describes procedures for the binomial model, including an upper bound for the p value of our statistics. The additional insight obtained from the CUSUM methods is illustrated on data from a case that settled. …