How useful are approximations to mean and variance of the index of dissimilarity?

Sociologists, demographers, and economists often use the index of dissimilarity, D, to describe the extent of racial, ethnic, spatial, or areal dissimilarity (or segregation) of different socio-economic groups. Derivation of the mean and variance of D to develop inference techniques has been a subject of studies for over three decades. Some have attempted to develop approximations for the mean and variance in order to simplify calculations. However, due to difficulties in deriving the measure of variation and complex nature of approximations, D is almost always employed in practice for descriptive rather than inferential purposes. In this study, simulation technique is used to compare different approaches for approximating the mean and variance of D and standardizing of D values. The usefulness of approximation is discussed using residential segregation data classified by race and personal income data classified by gender and age group. The results show that the amount of bias in approximations negates the usefulness of these approximations in standardization process and possibly inference.