Formulae
Wilcox gives a number of formulae for various indices of QV (Wilcox 1973), the first, which he designates DM for "Deviation from the Mode", is a standardized form of the variation ratio, and is analogous to variance as deviation from the mean.
One formula for IQV, given as M2 in (Gibbs 1975, p. 472) is:
where K is the number of categories, and is the proportion of observations that fall in a given category i. The factor of is for standardization.
The unstandardized index, denoted as M1 (Gibbs 1975, p. 471), can be interpreted as the likelihood that a random pair of samples will belong to the same category (Lieberson 1969, p. 851), so this formula for IQV is a standardized likelihood of a random pair falling in the same category. M1 and M2 can be interpreted in terms of variance of a multinomial distribution (Swanson 1976) (there called an "expanded binomial model").
Read more about this topic: Qualitative Variation
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