Nonparametric MANOVA in Mann-Whitney effects

TL;DR

This paper introduces a new nonparametric MANOVA method that uses Mann-Whitney effects and bootstrap inference, providing robust analysis for ordinal and metric multivariate data with heterogeneity.

Contribution

It develops a novel nonparametric MANOVA procedure based on Mann-Whitney effects, extending applicability to ordinal data and complex models with bootstrap-based inference.

Findings

Reliable for ordinal and metric data with covariance heterogeneity

Asymptotically exact and consistent inference for complex models

Validated through simulations and real data analysis

Abstract

Multivariate analysis of variance (MANOVA) is a powerful and versatile method to infer and quantify main and interaction effects in metric multivariate multi-factor data. It is, however, neither robust against change in units nor a meaningful tool for ordinal data. Thus, we propose a novel nonparametric MANOVA. Contrary to existing rank-based procedures we infer hypotheses formulated in terms of meaningful Mann-Whitney-type effects in lieu of distribution functions. The tests are based on a quadratic form in multivariate rank effect estimators and critical values are obtained by the bootstrap. This newly developed procedure consequently provides asymptotically exact and consistent inference for general models such as the nonparametric Behrens-Fisher problem as well as multivariate one-, two-, and higher-way crossed layouts. Computer simulations in small samples confirm the reliability of the developed method for ordinal as well as metric data with covariance heterogeneity. Finally, an analysis of a real data example illustrates the applicability and correct interpretation of the results.