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Abstract:
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The need to measure the diversity of a population often arises in real life. For example, determining the diversity of microorganisms in defined ecosystems is an important task in quantitative microbial ecology. Measuring the reproductive success of several competing pathogenic microorganisms in a host is crucial in descriptive epidemiology. In social sciences, measuring the diversity within and between social aggregates classified by one or more qualitative variables (e.g. ethnicity, political affiliation, religion, etc.) is routinely done. On the other hand, while several measures of variability for quantitative variables are mentioned in introductory statistics textbooks, the concept of variability in qualitative variables is rarely dealt with. Here we show how one way of conceptualizing variability in qualitative variables(that is quite interesting in statistics education due to its intuitive appeal) leads us to a measure of population diversity. After a brief literature survey of existing diversity measures and their statistical properties, we consider possible generalizations of the concept of variability in categorical variables and explore statistical inference using them.
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