  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.
