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Nonparametric Procedures Based on Rank Statistics

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Abstract

We consider distribution-free multiple comparison procedures among mean effects in homoscedastic k-sample models. We propose closed testing procedures based on the maximum values of some two-sample Wilcoxon test statistics and based on Kruskal–Wallis test statistics. The results reveal that the proposed procedures are more powerful than single-step procedures and the REGW-type tests. Furthermore, under simple order restrictions of k means, we discuss distribution-free multiple comparison procedures.

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References

  • Critchlow DE, Fligner MA (1991) Nonparametric multiple comparisons in the one-way analysis of variance. Commun Stat Ser A 20:127–139

    Article  Google Scholar 

  • Dwass M (1960) Some k-sample rank order tests, contributions to probability and statistics. Stanford University Press, Stanford, pp 198–202

    Google Scholar 

  • Kruskal WH, Wallis WA (1952) Use of ranks in one-criterion variance analysis. J Am Stat Assoc 47:583–621

    Article  Google Scholar 

  • Shiraishi T (2007) The upper bound for the distribution of Tukey-Kramer’s statistic. Bull Comput Stat Jpn 19:77–87 (in Japanese)

    Google Scholar 

  • Shiraishi T (2011a) Closed testing procedures for pairwise comparisons in multi-sample models. Biom Soc Jpn 32:33–47 (in Japanese)

    Google Scholar 

  • Shiraishi T (2011b) Multiple comparison procedures under continuous distributions. Kyoritsu-Shuppan Co., Ltd. (in Japanese)

    Google Scholar 

  • Shiraishi T (2014) Closed testing procedures in multi-sample models under a simple order restriction. J Jpn Stat Soc Jpn Issue 43:215–245 (in Japanese)

    Google Scholar 

  • Shiraishi T, Sugiura H (2018) Theory of multiple comparison procedures and its computation. Kyoritsu-Shuppan Co., Ltd. (in Japanese)

    Google Scholar 

  • Steel RGD (1960) A rank sum test for comparing all pairs of treatments. Technometrics 2:197–207

    Article  MathSciNet  Google Scholar 

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Correspondence to Taka-aki Shiraishi .

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© 2019 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Shiraishi, Ta., Sugiura, H., Matsuda, Si. (2019). Nonparametric Procedures Based on Rank Statistics. In: Pairwise Multiple Comparisons. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-15-0066-4_4

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