Statistical Evidence in Salary Discrimination Studies: Nonparametric Inferential Conditions

Fairness in the allocation of salary is often evaluated using statistical reasoning. A common principle is that among employees of equal merit, there should be no systematic differences in salary distributions between demographic groups. In practice, complete information on merit may be lacking. When observed measures of merit are incomplete or unreliable, statistical analyses that use such measures may be misleading. We present theoretical, nonparametric conditions under which evidence from salary studies using observed merit measures can provide a basis for inferences of fairness. Two types of fairness are defined that contrast fairness with respect to true merit versus observed merit. Latent variable models that have been proposed for use in salary equity studies are reviewed as parametric special cases of the general conditions presented. These models are illustrated using real salary data, demonstrating their specification as structural models with latent means. Implications of the inferential conditions for empirical studies of salary equity are discussed.