The Usefulness of Exact Statistical Methods in Equal Employment Litigation

Statisticians giving testimony in the courts face a special problem in presenting their results as courts tend to make intuitive judgements about the adequacy of the sample size without inquiring as to the statistical implications. In the equal employment context, this is compounded by the fact that when it accepted statistical tests, the U.S. Supreme Court adopted the large sample normal approximation to the binomial distribution (Castenada vs. Partida, 1977). Although Baldus and Cole (1987), Gastwirth (1988) have mentioned the arbitrariness of letting each judge accept or reject an analysis on the basis of the sample size, without any analysis of statistical concepts of power (Fienberg and Straf, 1982), courts have only recently begun to consider small samples. With the development of convenient computer packages, not only can issues involving the accuracy of large sample approximations be avoided, the important concept of power (Goldstein, 1985; Gastwirth and Wang, 1987) can be presented to courts. Hopefully, this will enable judges to reflect on the propriety of choosing a non- significant result when a test of power zero is used in preference to a significant result with a powerful test (Gastwirth and Wang, 1987) or of accepting an argument that significance would disappear had one or two more minorities been hired (Kadane, 1990) without considering the consequent reduction in power.