Approximations to the Mean and Variance of the Index of Dissimilarity in 2 x C Tables Under a Random Allocation Model

Approximations to the mean and variance of the index of dissimilarity in 2 x C tables under a random allocation model are derived, using a multivariate normal approximation to the multivariate hypergeometric distribution for the cell frequencies and the appropriate multivariate folded-normal distribution for the components of the index. To illustrate one application of these approximations, we standardize values of the dissimilarity index computed from tract-level census data to compare the levels of racial segregation in Birmingham and Richmond in 1970 and 1980, following Cortese, Falk, and Cohen (1976).