# Comparison of Coefficients of Variation (CVs)

I have to compare the variability of measures between 2 groups (geographical regions). Each group consists of a limited number of elements (i.e., the number of districts of each region); hence, a limited number of observations for each.

How could I statistically compare the variability between the two groups ? Given that the means of the 2 groups are not necessarily equal, I would rather go for a test on CVs (coefficients of variation).

So,

• Is there a known statistical test for comparing CVs? If so, what are the conditions required to perform it (especially, related to the number of observations) ?
• If not, could we use any kind of bootstrapping method ? Again, is there a minimal number of observations so that such a method is actually meaningful ?
• A permutation test or bootstrap procedure might be OK. Can you give a specific number of observations in each group, and some data for an actual situation? // Four in each group would be the absolute minimum for significance at the 5% level, and then the data would have to be just right. If you have even 6 in each group the procedures might be less fussy about the exact data // Also, it would be important to look at both means and standard deviations and know exactly what hypothesis you want to test in order to be able to choose from among all feasible methods. Jan 28, 2021 at 15:38
• If the observations can be considered as forming two independent samples, a possibility is to fit a suitable parametric distribution (for positive r.vs) for which the CV can be viewed as a parameter: gamma, inverse-gamma, Weibull, Generalized Pareto, ... And then perform a likelihood-ratio test for the equality of the CVs or compare profile-likelihood confidence intervals on CVs.
– Yves
Jan 28, 2021 at 17:13