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

TL;DR

This paper extends inference methods for various multivariate coefficient of variation variants in factorial designs, introducing new permutation and bootstrap-based tests for global and post hoc analysis, validated through simulations and real data.

Contribution

It generalizes existing inference methods to all variants of the MCV and develops a new max-type post hoc test with bootstrap improvement.

Findings

Extended permutation procedures to all MCV variants.

Proposed a bootstrap-based post hoc test with validated asymptotic properties.

Simulation studies show improved small sample performance.

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 by Ditzhaus and Smaga (2022) for general factorial designs covering k-sample settings but also complex higher-way layouts. However, two questions are still pending: (1) The theory on inference methods for MCV is primarily derived for one special MCV variant while there are several reasonable proposals. (2) When rejecting a global null hypothesis in factorial designs, a more in-depth analysis is typically of high interest to find the specific contrasts of MCV leading to the aforementioned rejection. In this paper, we tackle both by, first, extending the aforementioned nonparametric permutation procedure to the other MCV variants and, second, by proposing a max-type test for post hoc analysis. To improve the small sample performance of the latter, we suggest a novel studentized bootstrap strategy and prove its asymptotic validity. The actual performance of all proposed tests and post hoc procedures are compared in an extensive simulation study and illustrated by a real data analysis.