On the One-Mediator Null Hypothesis of Salary Equity

certain values of a than Birnbaum's diagnostic test would allow. What values of a and m would be plausible in any given application, of course, would depend on the specifics of the situation. Ideally, one might wish to construct a model of the past salary policies pursued by the institution, treating each of the components of M as individual variables to obtain reasonable estimates of m and a. However, in the absence of any information about the reliability and validity of M or the extent to which salaries have been influenced by these fallible measures, it becomes impossible to draw confident conclusions about the existence of sex bias even if the correlation between sex and salary is very high. In short, Birnbaum's criticisms of the ordinary regression approach to detecting sex bias in salaries are well taken; however, when salaries are likely to have been influenced by imperfect measures of merit, the diagnostic test he recommends can be misleading. The problems in using regression analysis to detect and interpret sex effects in these kinds of situations are exactly those encountered in using analysis of covariance in nonequivalent groups designs with fallible covariates. Investigators of sex bias would do well to familiarize themselves with the difficulties involved in drawing firm conclusions in these situations (e.g., see Cronbach, Rogosa, Floden, & Price, 1977; Reichardt, 1979).