Entropy-Based Segregation Indices

Abstract

Recent research has shown that two entropy-based segregation indices possess an appealing mixture of basic and subsidiary but useful properties. It would appear that the only fundamental difference between the mutual information or M index, and the entropy information or H index, is that the second is a normalized version of the first. This paper introduces another normalized index in that family, the H* index, which captures segregation as the tendency of racial groups to have different distributions across schools. More importantly, the paper shows that applied researchers may do better using the M index than using either H or H* in two circumstances: (1) if they are interested in the decomposability of the measurement of segregation, and (2) if they are interested in a margin-free measurement of segregation changes. The shortcomings of the H and H* indices are illustrated below by means of numerical examples, as well as with school segregation data by ethnic group in the U.S. public school system between 1989 and 2005.