My question does't duplicate this question, even if the titles are nearly similar.
Is there an alternative for the Kruskal–Wallis test for groups with different shaped distributions?
$\begingroup$
$\endgroup$
2
-
$\begingroup$ Please do read through a number of highly ranked answers on this site about Kruskal-Wallis or Mann-Whitney tests. The issue of assumptions in these congeneric tests has been extensively discussed. $\endgroup$– ttnphnsDec 19, 2014 at 16:01
-
$\begingroup$ Just one of many good threads about it stats.stackexchange.com/q/56649/3277 $\endgroup$– ttnphnsDec 19, 2014 at 16:09
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
7
I don't think the statement in the quote is accurate.
The Kruskal-Wallis is effectively a test for at least one variable being stochastically larger than at least one other, which doesn't require identity of shape. Indeed, even if it was being used as a test of identical distribution under the null, it would only be necessary for the shape to be identical under the null; if the null is false, there's still no requirement for the shape to be the same then.
If, however, one was looking specifically at say a location shift alternative, in order to use it specifically as say a test of location difference (a test of medians, or of means, or of tenth percentiles or ... against a shift in the same) then the shapes would then be assumed the same under both null and alternative in order that rejection of the null implied that location shift.
-
$\begingroup$ @glen-b Thank you for your answer! What you think, is incorect to use the Kruskal-Wallis test only for two groups comparison? $\endgroup$– IurieDec 23, 2014 at 20:57
-
1$\begingroup$ When you have two groups you'd normally use a Wilcoxon-Mann-Whitney test rather than K-W (though they should be equivalent for the two tailed case if you use the exact null distribution for both). It can be incorrect to use a Kruskal-Wallis in a variety of situations, but the statement doesn't of itself characterize those situations. It's possible for the Kruskal-Wallis to apply in a fairly broad range of situations. $\endgroup$– Glen_bDec 23, 2014 at 22:35
-
2$\begingroup$ @Iurie And when you have >2 groups, you would use the Kruskal-Wallis, and if you wanted to pin down which groups differed from which post hoc (a la the post hoc t tests following rejection of a one-way ANOVA), you would use a something like Dunn's test, or the Conover-Iman test. $\endgroup$– AlexisJun 26, 2016 at 17:32
-
$\begingroup$ Do you have any citation to back up your comment on the distribution shape regarding KW? Your comment is very helpful, and since I'm writing a paper I need a citation. Thanks $\endgroup$ Oct 18, 2016 at 21:26
-
$\begingroup$ @Carlos I'm not sure I could find you a reference for a basic statement about how hypothesis tests work. I can prove it easily enough - but I can't imagine any stats journal worth submitting to would let a statistician keep such a statement in a paper. The editor's comment would be "take out all that nanny-state stuff -- you get 5 pages, not 15". ... and if we find a journal where something like that was not seen as obvious, simply getting something into print would be no guarantee of it being true. Some journal outside statistics might publish a paper that says it perhaps. ...ctd $\endgroup$– Glen_bOct 18, 2016 at 23:46