## The Annals of Statistics

### $(k - 1)$-Mean Significance Levels of Nonparametric Multiple Comparisons Procedures

J. H. Oude Voshaar

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 8, Number 1 (1980), 75-86.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176344892

Digital Object Identifier
doi:10.1214/aos/1176344892

Mathematical Reviews number (MathSciNet)
MR557555

Zentralblatt MATH identifier
0434.62055

JSTOR
Voshaar, J. H. Oude. $(k - 1)$-Mean Significance Levels of Nonparametric Multiple Comparisons Procedures. Ann. Statist. 8 (1980), no. 1, 75--86. doi:10.1214/aos/1176344892. https://projecteuclid.org/euclid.aos/1176344892