I'm looking for a non-parametric (!) alternative to the Friedman test. I have > 2 subjects and measured one quantity per subject. I want to know whether there is a significant difference between any of these subjects. Please note that I used the Friedman test before because there were repeated measured per subject.

Is the Kruskal-Wallis test suitable here? Can you recommend any post-hoc test to identify which of the subjects are significantly different?


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    $\begingroup$ If I understand correctly, you now have independent observations and KW ANOVA followed by any suitable nonparametric technique for pairwise comparisons should be ok. However, what is your classification factor? $\endgroup$ – chl May 14 '14 at 10:26
  • $\begingroup$ @chl: Thanks. What do you mean by "classification factor"? Here's an example: I have 3 different algorithms which are evaluated on the same data, resulting in three performance measures. Now I want to know: 1) Whether there is any significant difference in the three algorithms at all; 2) Whether there is a significant(post-hoc) pairwise difference. Which test/post-hoc test fits this scenario? $\endgroup$ – Chris May 14 '14 at 12:51
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    $\begingroup$ In this case, I would say that your classification (grouping, independent) factor is the type of algorithms. $\endgroup$ – chl May 14 '14 at 13:29
  • $\begingroup$ Right. Does anyone have a suggestion for a post-hoc test? Is Tukey HSD suitable here? $\endgroup$ – Chris May 14 '14 at 14:25

Dunn's test is the appropriate post hoc test for after rejecting a Kruskal-Wallis test. See more here: Post-hoc tests after Kruskal-Wallis: Dunn's test or Bonferroni corrected Mann-Whitney tests?.

You might perform using the npmc package for R, or the dunntest package for Stata.

Dunn, O. J. (1964). Multiple comparisons using rank sums. Technometrics, 6(3):241–252.


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