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.
Publié le : 1980-01-14
Classification:
Multiple comparisons,
$k$-sample problem,
block effects,
$(k - 1)$-mean significance level,
shift alternatives,
$c$-comparison of distribution functions,
skewness,
strongly unimodal,
62J15,
62G99
@article{1176344892,
author = {Voshaar, J. H. Oude},
title = {$(k - 1)$-Mean Significance Levels of Nonparametric Multiple Comparisons Procedures},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 75-86},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344892}
}
Voshaar, J. H. Oude. $(k - 1)$-Mean Significance Levels of Nonparametric Multiple Comparisons Procedures. Ann. Statist., Tome 8 (1980) no. 1, pp. 75-86. http://gdmltest.u-ga.fr/item/1176344892/