Variation ratio

The variation ratio is a measure of statistical dispersion in nominal distributions. It is defined as the proportion of cases which are not the mode.

The formula for calculating the variation ration is, thus:

variation ratio = (total number of cases - cases in the mode) / total number of cases

Eg, three groups (n=100, each) made of more women than men:
Mode = women (n=90); variation ratio = (100-90) / 100 = 0.1
Mode = women (n=80); variation ratio = (100-80) / 100 = 0.2
Mode = women (n=60); variation ratio = (100-60) / 100 = 0.4

The variation ratio, however, cannot truly ascertain dispersion, only the proportion of cases not in the mode.

Eg, assume two independent surveys randomly done on a city street and asking people their provenance in relation to the location where the survey took place. The results are the following:

Provenance North East West South Mode Var.ratio
Survey A 3 2 5 7 South 0.6
Survey B 0 4 6 7 South 0.6

Both surveys yield the same mode and variation ratio, even when survey A is expected to be more dispersed. A modified formula, the modal dispersion, is proposed as a better measure of dispersion for nominal variables.

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