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Once in a statistics class I've seen the suggestion that one non-parametric approach for ANOVA would be to perform the ANOVA analysis on the ranks of the original data (basically as an alternative to Kruskal-Wallis). In an answer to a different question (Rank transformed 2-way ANOVA), @FrankHarrel suggests that "A two-way ANOVA on ranks is not based on strong statistical principles."

So, more generally, is it advisable/sane to do ANOVA on ranks? And why?

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    $\begingroup$ One way ANOVA on ranks (as long as you correctly compute significance via the permutation distribution of the test statistic under the null) is the Kruskal-Wallis. However, in the case of two- (and higher-) way ANOVA, things become somewhat more complicated. See here. The whole article and its references have both some good news and some bad news. $\endgroup$ – Glen_b -Reinstate Monica Sep 16 '14 at 3:19

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