“Variation ratio”的意思、由来-开放百科全书

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Variation ratio

释义

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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 in the mode category:

where f_m 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 {{Harv|Freeman|1965}}.

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.

References

{{Citation

|last=Freeman
|first=Linton C.
|title=Elementary Applied Statistics
|publisher=John Wiley and Sons
|location=New York
|year=1965
|pages=40–43
}}

3 : Statistical deviation and dispersion|Statistical ratios|Summary statistics for categorical data

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