The analysis of sex segregation: when is index measurement not index measurement?

In their paper in this issue, Grusky and Charles (1998) make a number of dubious claims about the measurement and interpretation of sex segregation. First, they incorrectly claim that only log-odds measures yield margin-free measures of segregation. Second, the estimation and testing of a limited class of log-linear models does not provide an independent test of the appropriateness of a log-odds ratio index to measure segregation. Their estimation in forms them of the statistically justifiable degree of occupational disaggregation, not whether a log-odds ratio is superior to, say, a linear index in the measurement of segregation. Finally, their index A is beset with problems of interpretation, not withstanding their arguments, and their additional measures, AW and AB, suffer similar problems. Grusky and Charles are, however, correct in arguing that measurement procedures should be margin-free. Further, I concur with the view that the adoption of a single annual summary measure of segregation cannot be justified, because it is premised on the assumption that individual occupations, or groups of occupations, exhibit similar trends in sex segregation.