Statistical methods are presented for studying “correlates of diversity”: characteristics of educational organizations which predict dispersion on the dependent variable. The conceptual framework for these methods distinguishes between variance heterogeneity that arises from educational program effects and heterogeneity that merely reflects heterogeneity of variance of inputs. The estimation theory is empirical Bayes, requiring probabilistic models both for the data and for the random dispersion parameters from each of many groups. Two strategies are considered, one based on exact distribution theory and the second based on an asymptotic normal approximation. The accuracy of the approximation is evaluated analytically and its use illustrated by an analysis of mathematics achievement data from a random sample of U.S. high schools.
Raudenbush et al. (Tue,) studied this question.