Article ID Journal Published Year Pages File Type
1144650 Journal of the Korean Statistical Society 2015 10 Pages PDF
Abstract

Finding the unbiasedness and biasedness of test statistics is important in testing a hypothesis. In this study, the unbiasedness/biasedness of the Jonckheere–Terpstra test is investigated for ordered alternatives. Our results show that the one-sided Jonckheere–Terpstra test is unbiased for the location parameter family of distributions and that the non-randomized two-sided Jonckheere–Terpstra test is biased for the shifted location parameter. Additionally, the unbiasedness/biasedness of the Kruskal–Wallis test is considered for the general two-sided alternatives. By giving a counter example, our investigation reveals that the Kruskal–Wallis test is biased against a shifted location parameter for unequal sample sizes. Our results indicate that we require to consider a bias correction for the nonparametric tests.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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