Kontorovich–Lebedev transform
The variation ratio is a simple measure of statistical dispersion in nominal distributions; it is the simplest measure of qualitative variation.
It is defined as the proportion of cases which are not the mode:
where fm is the frequency (number of cases) of the mode, and N is the total number of cases. While a simple measure, it is notable in that some texts and guides suggest or imply that the dispersion of nominal measurements cannot be ascertained. It is defined for instance by Template:Harv.
Just as with the range or standard deviation, the larger the variation ratio, the more differentiated or dispersed the data are; and the smaller the variation ratio, the more concentrated and similar the data are.
For example, a group which is 55% female and 45% male has a proportion of 0.55 females and therefore variation ratio of (1.0- 0.55) = 0.45; and is more dispersed in terms of gender than a group which is 95% female and has a variation ratio of only 0.05. Similarly, a group which is 25% Catholic (where Catholic is the modal religious preference) has a variation ratio of 0.75 and is much more dispersed religiously than a group which is 85% Catholic and has a variation ratio of only 0.15.
See also
- Qualitative variation, for a number of other measures of dispersion in nominal variables
References
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