Nominal data and qualitative Variation

\({\LARGE \frac{1}{\sum P_{i}^{2}}}\)

aEffective number of classes=EffectiveNumberOfClasses

Qualitative variation

 http://en.wikipedia.org/wiki/Information_entropy   http://en.wikipedia.org/wiki/Qualitative_variation http://en.wikipedia.org/wiki/Multinomial_distribution http://en.wikipedia.org/wiki/Categorical_distribution    

References

  • Gibbs, Jack P.; Poston, Jr., Dudley L. (March 1975), “The Division of Labor: Conceptualization and Related Measures”, Social Forces 53 (3): 468–476, doi:10.2307/2576589, JSTOR 2576589
  • Lieberson, Stanley (December 1969), “Measuring Population Diversity”, American Sociological Review 34 (6): 850–862, doi:10.2307/2095977, JSTOR 2095977
  • Swanson, David A. (September 1976), “A Sampling Distribution and Significance Test for Differences in Qualitative Variation”, Social Forces 55 (1): 182–184, doi:10.2307/2577102, JSTOR 2577102

Wilcox, Allen R. (June 1973), “Indices of Qualitative Variation and Political Measurement”, The Western Political Quarterly 26 (2): 325–343, doi:10.2307/446831, JSTOR 446831