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January, 1980 $(k - 1)$-Mean Significance Levels of Nonparametric Multiple Comparisons Procedures
J. H. Oude Voshaar
Ann. Statist. 8(1): 75-86 (January, 1980). DOI: 10.1214/aos/1176344892


We consider the nonparametric pairwise comparisons procedures derived from the Kruskal-Wallis $k$-sample test and from Friedman's test. For large samples the $(k - 1)$-mean significance level is determined, i.e., the probability of concluding incorrectly that some of the first $k - 1$ samples are unequal. We show that in general this probability may be larger than the simultaneous significance level $\alpha$. Even when the $k$th sample is a shift of the other $k - 1$ samples, it may exceed $\alpha$, if the distributions are very skew. Here skewness is defined with Van Zwet's $c$-ordering of distribution functions.


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J. H. Oude Voshaar. "$(k - 1)$-Mean Significance Levels of Nonparametric Multiple Comparisons Procedures." Ann. Statist. 8 (1) 75 - 86, January, 1980.


Published: January, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0434.62055
MathSciNet: MR557555
Digital Object Identifier: 10.1214/aos/1176344892

Primary: 62J15
Secondary: 62G99

Keywords: $(k - 1)$-mean significance level , $c$-comparison of distribution functions , $k$-sample problem , block effects , Multiple comparisons , shift alternatives , skewness , strongly unimodal

Rights: Copyright © 1980 Institute of Mathematical Statistics


Vol.8 • No. 1 • January, 1980
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