The Several Sample Nonparametric Behrens-Fisher Problem

• Activity Number: 232
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Frank Konietschke*+
• Companies: Department of Medical Statistics
• Keywords: Relative Effects ; Nonparametric ; Behrens-Fisher Problem

Abstract

In this talk, we consider the several sample case of the so-called nonparametric Behrens-Fisher problem where k -samples with independent observations are given and the equality of the distribution functions under the hypothesis in the groups is not assumed. Moreover, we do not require the continuity of the distribution functions so that data with ties and, particularly, ordered categorical data are covered by this model. A relative treatment effect is defined which can be estimated by using pairwise mid-ranks of the observations and we derive the asymptotic distribution of this estimator. To test the hypothesis of no treatment effect, we consider the rank versions the ANOVA-type statistic which was suggested by Brunner et al.(1994). Simulations show that the ANOVA-type statistic appears to maintain the pre-assigned level of the test quite accurately.