[R-sig-ME] Welch's ANOVA

[Robert Kushler]

There are (at least) two ways to think about rank-based tests:

(1) the null hypothesis is "equal medians" and you must assume all distributions
have the same shape (which includes constant variance).  The only thing you avoid
(compared to standard one-way ANOVA) is the normality assumption.

(2) the null hypothesis is "equal distributions" and the alternative is "they're
not all the same."  In other words, all the assumptions (aside from "independent
random samples," which is of course the most critical) become part of the hypothesis.

Regards,    Rob Kushler



On 8/23/2011 10:30 AM, Paul Miller wrote:
> Hi Rafael,
>
> Not sure if what I just prposed  will actually work or not. I searched online and found some places suggesting that
> the Kruskal-Wallis test doesn't require an assumption of equal variances. As an equivalent test, this would seem to
> suggest that an ANOVA on ranks also would not require this assumption either.
>
> The Kruskal-Wallis test is also an extension of the Wilcoxon Rank-Sum test though. I've found information suggesting
> that this test assumes that distribution have the same dispersion and that this is analogous to the assumption of
> variance homogeneity in the two-sample t-test.
>
> So now I'm confused.
>
> Perhaps a more expert statistician than myself could lend some insight into this matter.
>
> Thanks,
>
> Paul
>
> _______________________________________________ R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>