The Inequality Between Two Distributions: Applications to the Analysis of Diversity Data

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Abstract

A new measure called diversity difference is proposed for the inequality of a pair of distributions. The diversity difference measure satisfies eight properties of a measure of inequality. This measure is simple to calculate and provides easily interpreted results.

Existing inequality measures examine the distribution of a single variable whose data are arranged in a monotonic order. The new measure can employ multiple variables and does not require each to be monotonic but can be used if the data happen to be monotonic. The pair of distributions is useful for organizational diversity data because one of the distributions represents the actual proportions of employees in any class or set of classes and the other distribution is the benchmark or anchoring distribution. Data from the measure can be displayed in diversity difference trees for quick interpretation.

The diversity difference measure can be arranged to define a Lorenz curve. An example with three classes (gender, race, and age) is employed to provide examples of the measure, the resulting Lorenz curve, and the disparity ratio.

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