Das nichtparametrische Behrens-Fisher-Problem: ein studentisierter Permutationstest und robuste Konfidenzintervalle für den Shift-Effekt

For the nonparametric Behrens-Fisher problem a permutation test based on the studentized rank statistic of Brunner and Munzel is proposed. This procedure is applicable to count or ordered categorical data. By applying the central limit theorem of Janssen, it is shown that the asymptotic permutational distribution of this test statistic is a standard normal distribution. For very small and very different sample sizes, frequently occuring in medical and biological applications, an extensive simulation study suggest that this permutation test works well for data from several underlying distributions. Furthermore the permutational quantiles of this rank statistic are used to construct robust confidence intervals for the shift effect in a Behrens-Fisher situation. A simulation study shows good properties of these confidence intervals for different underlying distributions. The proposed test and the confidence interval are applied to data from a clinical trial.