Baumgartner, Weiß, and Schindler (1998) introduced a novel nonparametric test for the two-sample comparison that is superior to commonly used tests such as the Wilcoxon rank-sum test. A modification of the novel test statistic can be used for one-sided comparisons based on ordinal data. Such comparisons frequently occur in psychological research, and the Wilcoxon test is often recommended for their analysis. Here, the two tests were compared in a simulation study. According to this study the tests have a similar type I error rate, but the modified Baumgartner-Weiß-Schindler test is more powerful than the Wilcoxon test.
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