The traditional approach to measuring the extent of discrimination by decomposing group mean differences into endowment and residual differences implicitly treats estimated coefficients as deterministic. Since these estimates are affected by sampling variability, they are, in part, stochastic. Hence, procedures are available to test the statistical significance of these differences. This paper shows that Chow-type tests can be used as direct tests of the statistical significance of the residual difference. Further, it demonstrates that the application of these formal inferential statistical tests to models of wage and salary discrimination can lead to interpretations of the results which differ from earlier interpretations. Two studies, Blinder (1973) and Hirsch and Leppel (1982), are replicated and the testing criteria suggested in this paper is used to determine results. The conclusions of these earlier studies are not supported by the statistical analysis presented in this study. There is no statistical support for discrimination in the replication of the Blinder study. In the Hirsch and Leppel replication, there is no support for the claim of differences in entry salaries, but there is support for differences in salary profiles once employed.