Nonparametric multiple contrast tests for general multivariate factorial designs

Abstract

We develop purely nonparametric multiple inference methods for general multivariate data that neither assume any specific data distribution nor identical covariance matrices across the treatment groups. Continuous, discrete, and even ordered categorical (ordinal) data can be analyzed with these procedures in a unified way. To test hypotheses formulated in terms of purely nonparametric treatment effects, we derive pseudo-rank based multiple contrast tests and simultaneous confidence intervals. Hereby, the simultaneous confidence intervals are compatible with the multiple comparisons. The small-sample performance of the procedures is examined in a simulation study which indicates that the proposed procedures (i) control the family-wise error rate quite accurately and (ii) have a substantially higher power under non-normality than mean-based parametric competing methods. Application of the proposed tests is demonstrated by analyzing a real data set.