Statistical evidence of discrimination

Generally speaking, laws against discrimination prohibit treating similarly situated persons differently. Legal analysis or social policy supplies the criteria for ascertaining which persons are similarly situated. Statistical evidence has been used in cases, among others, alleging discrimination in criminal prosecutions, educational opportunities, jury selection, and employment practices. The United States Supreme Court has been ambivalent about the need for significance testing in such cases, and it has yet to consider carefully the use of formal inferential methods. Various techniques for conveying information to a court about the inferential value of sample statistics are illustrated in the context of two jury-selection discrimination cases. The role of statistical evidence in certain employment discrimination cases is also considered. It is suggested that the classical method of hypothesis testing used by the Supreme Court is not appropriate to testing whether a given defendant discriminated. Presentation of p values, prediction or confidence intervals, and likelihood functions are shown to be preferable. Bayesian methods are also considered.