Statistical Analysis of Qualitative Variation

Many variables of interest in the social sciences are measurable only at the nominal level. That is, they represent types of phenomena such as race, ethnicity, religious affiliation, or political party preference. It is sometimes of interest to measure the amount of variation, or heterogeneity, within a population with respect to one or more of these variables. By a measure of variation for a qualitative variable, we mean a description of the dispersion of the population over a number of nominal categories. We shall refer to such measures as indices of qualitative variation or diversity. The ecological sciences have made considerable use of