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?
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Sign up to join this communityMy 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?
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.