P* Index of Segregation: Distribution Under Reassignment

Abstract

Students of intergroup relations have measured segregation with a P^* index. In this article, we describe the distribution of this index under a stochastic model. We derive exact, closed-form expressions for the mean, variance, and skewness of P^* under random segregation. These yield equivalent expressions for a second segregation index: η². Our analytic results reveal some of the distributional properties of these indices, inform new standardizations of the indices, and enable small-sample significance testing. Two illustrative examples are presented.