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.

翻译：多变量变异系数（MCV）是一种衡量多元数据离散度的吸引人且易于解释的效应量。近期，Ditzhaus和Smaga（2022）首次提出了针对MCV的推断方法，适用于涵盖k样本设置及更复杂高阶布局的通用因子设计。然而，仍有待解决两个问题：（1）MCV推断方法的理论主要针对一种特定MCV变体推导，而实际存在多种合理方案；（2）在因子设计中拒绝全局零假设后，通常需进行更深入分析以找到导致上述拒绝的特定MCV对比。本文通过以下方式同时应对这两个问题：首先，将前述非参数置换方法扩展到其他MCV变体；其次，提出用于事后分析的最大值型检验。为改善后者的有限样本性能，我们提出了一种新颖的学生化自助法策略，并证明其渐近有效性。通过广泛模拟研究比较所有提出检验及事后程序的实际表现，并结合真实数据分析加以说明。