Title: Permutation Tests for Unbalanced Heteroscedastic Factorial Designs

 

Dr. Frank Konietschke

Department of Medical Statistics, University Medical Center Göttingen

 

May 22nd

3:00 p.m.

MDS 335

 

Refreshments: 312 MDS building

 

Abstract: In many trials, data are collected in terms of a factorial design, e.g., when male and female patients are randomized to a>1 different treatment groups. Hereby, we are interested in testing the null hypotheses of no sex effect, no treatment effect, and / or no interaction between sex and treatment. Usually, the data are modeled by assuming homogeneous variances - an unrealistic assumption in higher way layouts. In particular, normality of the error term is often assumed. In several trials, however, the normality assumption is not justifiable, e.g. for skewed data.

In this talk, we consider inference methods (quadratic tests) for unbalanced heteroscedastic factorial designs under non-normality. Brunner et al. (1997) considered the so-called ANOVA-type statistic, which can be seen as an improvement over the classical Wald-type statistic. Both statistics, however, are quite poor in terms of controlling the type-I error rate under non-normality. Although the data are not exchangeable under heteroscedasticity, we investigate an unified permutation approach to achied valid procedures. We derive different conditional central limit theorems for the permuted statistics. Hereby, it will be shown that the conditional permutation dstributions are invariant under the main effects and interactions. The theoretical results verify the validity of the new approaches.  Extrensive simulation studies show that these permutation approaches greatly improve the standard procedures. A real data set illustrates the application.