Most existing tests for nonparametric factorial designs are based on 
ranks and hypotheses are formulated in terms of distribution functions. 
However, especially in heterogeneous settings, null hypotheses 
formulated in terms of parameters or effect measures and corresponding 
confidence intervals would be of more interest. In this talk, we explain 
that the effect measures, underlying existing rank-based procedures, may 
either lead to possibly paradox results or/and depend on sample sizes 
(except in the case of completely balanced designs). Moreover, we point 
out that this undesirable property may particularly cause problems in 
interpretation of effects but also for inference. Thus, we propagate to 
work with unweighted nonparametric effect measures that can be motivated 
from so-called pseudo-ranks. We then introduce novel test procedures 
that are suitable for testing hypotheses formulated in these effects in 
general uni- and multivariate factorial designs and analyze their large 
and small sample properties theoretically and in simulations. We note 
that the R-package rankFD performing the computations in general 
univariate factorial designs can be downloaded from CRAN.
References.

Brunner, E, Konietschke, F, Bathke, A and Pauly, M (2018). Ranks and 
Pseudo-Ranks - Paradoxical Results of Rank-Tests. Submitted Preprint.

Brunner, Edgar, Konietschke, Frank, Pauly, Markus and Puri, Madan L. 
(2017). Rank-Based Procedures in Factorial Designs: Hypotheses for 
Nonparametric Treatment Effects. Journal of the Royal Statistical 
Society - Series B 79, 1463–1485.

Dobler, D, Friedrich, S and Pauly, M (2017). Nonparametric MANOVA in 
Mann-Whitney effects. Submitted Preprint.

Umlauft, M, Placzek, M, Konietschke, F, and Pauly, M (2017). Wild 
Bootstrapping Rank-Based Procedures: Multiple Testing in Nonparametric 
Split-Plot Designs. Submitted Preprint.

Keywords: Factorial designs, Kruskal–Wallis test, Rank-based Methods, 
Multivariate Ordinal Data, Wild Bootstrap.

Einladung von Prof. Werner Brannath