Difference of Means Formulations for Selected Indices

Abstract

In this chapter I review the implementation of the difference of means framework for calculating indices of uneven distribution for five indices: the delta or dissimilarity index (D), the gini index (G), the separation index (S), the Theil entropy index (H), and the Hutchens square root index (R). For each index I introduce the relevant scoring systems for residential outcomes (y) that makes it possible to obtain the index scores as simple differences of group means on individual residential outcomes (y). To facilitate discussion, I replace the abstract terms “Group 1” and “Group 2” with the more concrete example of Whites and Blacks which has been investigated in hundreds of empirical analyses of uneven distribution in U.S. cities, urban areas, and metropolitan areas. As I move from index to index, I provide comments on the nature of the scaling function that maps scores for contact and exposure based on pairwise area proportion White (p) onto index-specific residential outcome scores (y). In addition, I sometimes offer commentary on the index. Note, however, that I do not provide a comprehensive review of the five indices because this task has been addressed previously in the existing literature and does not need to be repeated here.