Talk:Kruskal-Wallis one-way analysis of variance

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Mathematics rating: Start Class Low Priority  Field: Probability and statistics

The formula of the test statistic K is unnecessarily complicated. There is a much simpler form:

K = \frac{12}{n(n+1)}\sum_{i=1}^m n_i\left(R_{i\cdot} - \frac{n+1}{2}\right)^2=\frac{12}{n(n+1)}\sum_{i=1}^m \left(\frac 1{n_i} \left(\sum_{j=1}^{n_i} R_{ij}\right)^2 \right) - 3(n+1)

Nijdam 21:17, 18 August 2006 (UTC)

Does the Kruskal-Wallis test rely on an assumption of Homoscedasticity (equal variances)? I've found conflicting references on the web which state both sides.

It is stated that the Kruskal-Wallis test does not require the populations to be normal nor does it require them to have equal variability; the article then says that this is a limitation. This is very misleading, as these properties are usually seen as advantages, allowing an ANOVA-like analysis to be performed even when the assumptions of the parametric ANOVA are violated. The limitation is that non-parametric tests typically have less statistical power than parametric tests (i.e. they require some combination of larger sample sizes and effect sizes to reach the equivalent power of parametric tests).130.88.246.109 09:15, 9 May 2007 (UTC)

[edit] not testing medians

the kruskal-wallis test does not test the significance of medians between samples, it tests the means. So this sentence is wrong: "In statistics, the Kruskal-Wallis one-way analysis of variance by ranks (named after William Kruskal and W. Allen Wallis) is a non-parametric method for testing equality of population medians among groups" —Preceding unsigned comment added by 71.76.4.55 (talk) 03:18, 4 October 2007 (UTC)