2000/01/01 by Edgar Brunner, Ullrich Munzel · 5 citations
Mathematics · #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials
paper · doi:10.1002/(sici)1521-4036(200001)42:1<17::aid-bimj17>3.0.co;2-u
openalex publication_date 2000/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
A generalization of the Behrens-Fisher problem for two samples is examined in a nonparametric model. It is not assumed that the underlying distribution functions are continuous so that data with arbitrary ties can be handled. A rank test is considered where the asymptotic variance is estimated consistently by using the ranks over all observations as well as the ranks within each sample. The consistency of the estimator is derived in the appendix. For small samples (n 1 , n 2 > 10), a simple approximation by a central t-distribution is suggested where the degrees of freedom are taken from the Satterthwaite-Smith-Welch approximation in the parametric Behrens-Fisher problem. It is demonstrated by means of a simulation study that the Wilcoxon-Mann-Whitney-test may be conservative or liberal depending on the ratio of the sample sizes and the variances of the underlying distribution functions. For the suggested approximation, however, it turns out that the nominal level is maintained rather accurately. The suggested nonparametric procedure is applied to a data set from a clinical trial. Moreover, a confidence interval for the nonparametric treatment effect is given.