Some Important Two-Sample Tests
We start this chapter with some general guidelines for setting null and alternative hypotheses, while stressing their relation with the choice of a test statistic and the interplay between the null hypothesis and the distributional assumptions one is willing to make. In Section 9.2 this is illustrated for the two-sample problem in the discussion of the well-known Wilcoxon rank sum test. We study the Wilcoxon test from several points of view. From this discussion it becomes clear that its interpretation is not always as clear-cut as one would hope. For example, we demonstrate that the test may not always be used for detecting differences in means. This brings us back to the diagnostic propertythat was also important in Part I. We further elaborate on this in Section 9.3, in which we again consider the Wilcoxon test as an example. The same reasoning is applied in Section 9.5, where we discuss some of the nonparametric tests for detecting differences in scale. Section 9.6 focusses on the Kruskal–Wallis test for the K-sample problem, and we conclude this chapter with an introduction to adaptive tests.
KeywordsNull Hypothesis Null Distribution Distributional Assumption Adaptive Test Asymptotic Null Distribution
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