Discrimination Measures Using Contingency Tables

Discrimination in organizations based on race or sex is a contentious issue. Sensible discussion of the issue will be enhanced by the availability of measures of discrimination enabling comparisons to be made between organizations and across time. Linear models are of limited validity. A contingency table approach is suggested. Given an observed distribution of categorical variables (such as rank, sex and qualifications) loglinear modelling of the odds ratios across ranks enables maximum likelihood measures distinguishing direct and total discrimination to be established. The analogy between item bias and direct discrimination is discussed, and the proposed maximum likelihood measure of direct discrimination is compared with the Mantel-Haenszel estimator and with a measure derived by collapsing fitted subtables. The proposed discrimination measure can be shown to have a chi-square distribution, and therefore can readily be tested for significance. The methods are illustrated by applying them to examine the extent of sex discrimination in the ranks of staff within an Australian university, but can readily be used to measure discrimination in respect of a sub-group in any employment or membership context.