Asymptotic permutation tests for coefficients of variation and standardised means in general one-way ANOVA models

Coefficients of variations are unit-free measures that can, for example, be used to compare the variability of different samples. To this end, we study inference methods for them as well as their reciprocal given by standardised means in general heterogeneous one-way ANOVA designs. As no specific model assumptions are made, a permutation method is proposed to guarantee good finite sample performance. Building on recent limit theorems for randomisation techniques, we prove that the permutation procedure is asymptotically correct in general and finitely exact when data is exchangeable. These results are fostered in extensive simulation studies and two illustrative data analyses.