  Existing tests for factorial designs in the nonparametric case are based on
hypotheses formulated in terms of distribution functions. Typical null
hypotheses, however, are formulated in terms of some parameters or effect
measures, particularly in heteroscedastic settings. Here this idea is extended
to nonparametric models by introducing a novel nonparametric
ANOVA-type-statistic based on ranks which is suitable for testing hypotheses
formulated in meaningful nonparametric treatment effects in general factorial
designs. This is achieved by a careful in-depth study of the common
distribution of rank-based estimators for the treatment effects. Since the
statistic is asymptotically not a pivotal quantity we propose three different
approximation techniques, discuss their theoretic properties and compare them
in extensive simulations together with two additionalWald-type tests. An
extension of the presented idea to general repeated measures designs is briefly
outlined. The proposed rank-based procedures maintain the pre-assigned type-I
error rate quite accurately, also in unbalanced and heteroscedastic models.
