I want to compare the variability of two log-normal samples. They are being summarized as Coefficient of variations (CVs) and I want to test if one sample's CV is different from the other's.
To compare the geometric means, I performed a t-test on log-transformed data, then applied the antilog to go back to the original scale of the problem.
In the same logic, is it appropriate to apply the F-test for variances on log-transformed data and then revert to the antilog scale?
If not, is there a significance test for CVs or geometric CVs?