Inference for all variants of the multivariate coefficient of variation in factorial designs

Abstract The multivariate coefficient of variation (MCV) is an attractive and easy‐to‐interpret effect size for the dispersion in multivariate data. Recently, the first inference methods for the MCV were proposed for general factorial designs. However, the inference methods are primarily derived for one special MCV variant while there are several reasonable proposals. Moreover, when rejecting a global null hypothesis, a more in‐depth analysis is of interest to find the significant contrasts of MCV. This paper concerns extending the nonparametric permutation procedure to the other MCV variants and a max‐type test for post hoc analysis. To improve the small sample performance of the latter, we suggest a novel bootstrap strategy and prove its asymptotic validity. The actual performance of all proposed tests is compared in an extensive simulation study and illustrated by real data analysis. All methods are implemented in the R package GFDmcv, available on CRAN.