We introduce the non-parametric techniques for inference of the multivariate coefficients
of variation and their reciprocals, called standardized means. While several testing 
procedures exist for the univariate coefficient of variation, the methods for performing
inference in a multivariate setting are less well-established. Existing approaches often 
rely on restrictive assumptions about the underlying distributions. To address this issue,
we propose the use of Wald-type statistics within the framework of general factorial designs,
which can accommodate heteroscedasticity. Our methodology extends beyond the traditional 
k-sample case, allowing for the incorporation of higher-way layouts and enabling the 
examination of main and interaction effects. Additionally, we consider a post hoc testing
strategy that employs multiple contrast tests, facilitating a more comprehensive analysis
of the data. We establish the asymptotic validity of these procedures. To enhance their 
performance in finite samples, we propose permutation and bootstrap versions of the tests
and demonstrate that their asymptotic properties carry over to these resampling-based 
methods. To evaluate the performance of the new tests and existing parametric methods, 
we conduct an extensive simulation study. All methods are implemented in the R package 
GFDmcv, which is publicly available on CRAN.