An Investigation of Alternative Measures of School Segregation. Discussion Paper No. 229-74

This paper examines, both theoretically and empirically, three measures of segregation, with the empirical focus on school segregation. The first measure is based on the absolute deviation of the racial composition of a school from that of the school district, the second is based on the square of that deviation, and the third is derived from information theory. The purpose of this paper is to examine and compare the properties of these three measures in terms of how useful they are both as descriptive devices and as indicators of appropriate policy actions. Separate discussions of the theoretical nature of each index are accompanied by summaries of their calculated values based on a sample of school districts. Several arguments are given for preferring the information theory measure: it incorporates the notion of diminishing marginal payoff to desegregation; it depends on the entire distribution of students by race across schools; it may be interpreted as a measure of association between race and school assignment; it can be meaningfully aggregated; and, once aggregated, it can be decomposed into "between" and "within" components. Its main drawbacks are that it is somewhat more complicated to calculate and that its interpretation is not as easily grasped intuitively. The use of any of the three indexes presented here as a policy aid would be substantially better than subjective judgment. (Author/JM)