Unbiasedness and biasedness of the Jonckheere–Terpstra and the Kruskal–Wallis tests

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 locat...

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Bibliographic Details
Published in:Journal of the Korean Statistical Society 2015, 44(3), , pp.342-351
Main Authors: Murakami, Hidetoshi, Lee, Seong Keon
Format: Article
Language:English
Subjects:
Applied Statistics
Bayesian Inference
Jonckheere–Terpstra test
Kruskal–Wallis test
Power function
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Unbiasedness
통계학
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Summary: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.
ISSN:1226-3192
2005-2863
DOI:10.1016/j.jkss.2014.10.001