Heterogeneity Coefficients for Mahalanobis' D as a Multivariate Effect Size

The Mahalanobis distance D is the multivariate generalization of Cohen's d and can be used as a standardized effect size for multivariate differences between groups. An important issue in the interpretation of D is heterogeneity, that is, the extent to which contributions to the overall effect size are concentrated in a small subset of variables rather than evenly distributed across the whole set. Here I present two heterogeneity coefficients for D based on the Gini coefficient, a well-known index of inequality among values of a distribution. I discuss the properties and limitations of the two coefficients and illustrate their use by reanalyzing some published findings from studies of gender differences.