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New inference methods for the multivariate coefficient of variation and itsreciprocal, the standardized mean, are presented. While there are varioustesting procedures for both parameters in the univariate case, it is less knownhow to do inference in the multivariate setting appropriately. There are someexisting procedures but they rely on restrictive assumptions on the underlyingdistributions. We tackle this problem by applying Wald-type statistics in thecontext of general, potentially heteroscedastic factorial designs. In additionto the $k$-sample case, higher-way layouts can be incorporated into thisframework allowing the discussion of main and interaction effects. Theresulting procedures are shown to be asymptotically valid under the nullhypothesis and consistent under general alternatives. To improve the finitesample performance, we suggest permutation versions of the tests and shown thatthe tests' asymptotic properties can be transferred to them. An exhaustivesimulation study compares the new tests, their permutation counterparts andexisting methods. To further analyse the differences between the tests, weconduct two illustrative real data examples.

Permutation test for the multivariate coefficient of variation in factorial designs