A Note on the Measurement of Racial Integration of Schools by Means of Informational Concepts

Abstract

This note is concerned with the measurement of racial integration of schools in a way that permits a simple aggregation of the measure to sets of schools such as school districts. [The procedure can be applied to institutions other than schools, but we prefer a more specific terminology.] There are several standard procedures for measuring integration, but the dissimilarity index appears to be more popular than any other index.² This index is based on a comparison of the number of white students in each school, measured as a fraction of the total number of white students in the city, and the analogous nonwhite proportion of the same school. The index is defined as one-half of the sum over all schools of the absolute differences of these proportions. The value of the index is zero when the racial compositions of all schools are identical and it takes larger and larger positive values (up to a maximum of 1) when the racial compositions are more different; also, it has a simple interpretation in terms of minimum shifts which are needed in order to obtain identical racial compositions in all schools. However, the use of absolute differences makes the dissimilarity index less suitable when one wants to aggregate schools to school districts.³ The objective of this note is to show that there are some simple measures derived from information theory which are superior in this respect, and to illustrate their use by means of data on the elementary schools of the Chicago public school system for the years 1963–1969.

This article first appeared in The Journal of Mathematical Sociology 1 (1971) 187–194. Reprinted with permission. Copyright © Gordon and Breach Science Publishers Inc.

The authors wish to thank the Chicago Board of Education and the Chicago Urban League for providing the data which are used in this article. The staffs of several school districts were helpful in correcting a number of errors in the data. The research reported in this article was supported in part by the National Science Foundation under grant GS-2607.