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

  • Authors:

  • Kenneth D. Mackenzie

  • Affiliations:

  • School of Business, University of Kansas, Lawrence, KS 66045. hologram@falcon.cc.ukans.edu

  • Venue:
  • Computational & Mathematical Organization Theory
  • Year:
  • 1999

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Abstract

A new measure called diversity difference is proposed for the inequality of apair of distributions. The diversity difference measure satisfies eightproperties of a measure of inequality. This measure is simple to calculate andprovides easily interpreted results.Existing inequality measures examine the distribution of a single variablewhose data are arranged in a monotonic order. The new measure can employmultiple variables and does not require each to be monotonic but can be used ifthe data happen to be monotonic. The pair of distributions is useful fororganizational diversity data because one of the distributions represents theactual proportions of employees in any class or set of classes and the otherdistribution is the benchmark or anchoring distribution. Data from the measurecan be displayed in diversity difference trees for quick interpretation.The diversity difference measure can be arranged to define a Lorenz curve. Anexample with three classes (gender, race, and age) is employed to provideexamples of the measure, the resulting Lorenz curve, and the disparity ratio.