Quantile-based MANOVA: A new tool for inferring multivariate data in factorial designs

Multivariate analysis-of-variance (MANOVA) is a well established tool to examine multivariate endpoints. While classical approaches depend on restrictive assumptions like normality and homogeneity, there is a recent trend to more general and flexible procedures. In this paper, we proceed on this path, but do not follow the typical mean -focused perspective. Instead we consider general quantiles, in particular the median, for a more robust multivariate analysis. The resulting methodology is applicable for all kind of factorial designs and shown to be asymptotically valid. Our theoretical results are complemented by an extensive simulation study for small and moderate sample sizes. An illustrative data analysis is also presented. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper introduces a more robust multivariate analysis method by using general quantiles, particularly the median, instead of the traditional mean, and applies and validates this method on various factorial designs. The effectiveness of this method is demonstrated through theoretical and simulation studies on small and moderate sample sizes.