Index of diversity

The index of diversity (also referred to as the Index of Variability) is a commonly used measure, in demographic research, to determine the variation in categorical data.

The most common index of diversity measure was created by Gibbs and Martin (Gibbs, Jack P., and William T. Martin, 1962. “Urbanization, technology and the division of labor.” American Sociological Review 27: 667–77; also referred to by Judith Blau (Group Enmity and Accord: The Commercial Press in Three American Cities, Social Science History 24.2, 2000: 395-413) -


 * $$D=1-\sum_{p=i}^N p_i^2$$

where
 * p = percent of individuals or objects in a category
 * N = number of categories.

A perfectly homogeneous population would have a diversity index score of 0. A perfectly heterogeneous population would have a diversity index score of 1 (assuming infinite categories with equal representation in each category). As the number of categories increases, the maximum value of the diversity index score also increases (e.g., 4 categories at 25% = .75, 5 categories with 20% = .8, etc.)

An example of the use of the index of diversity would be a measure of racial diversity in a city. Thus, if Sunflower City was 85% white and 15% black, the index of diversity would be: .255.

The interpretation of the diversity index score would be that the population of Sunflower City is not very heterogeneous but is also not homogeneous.