Hello Javiera,

For any effect of a given magnitude, small sample sizes translate to lower statistical power, regardless of whether you are using parametric, nonparametric, or exact/permutation tests.

What you can say about the Friedman test is that, if all of the parametric assumptions associated with repeated measures anova were satisfied (which is not the case for your data, apparently), the Friedman test has a power-efficiency (compared to RM anova) that depends on the number of levels of the repeated measures dimension: ~ .955 * k / (k + 1), where k is number of levels). See Zimmerman, D. W., & Zumbo, B. D. (1993). Relative power of the Wilcoxon test, the Friedman test, and repeated-measures ANOVA on ranks. Journal of Experimental Education, 62, 75-86.

Good luck with your work.

N.B. changed formula multiplier to k/(k+1)...had incorrectly used "k-1" in first version.

First David Morse is correct in everything he said. I would like to add that robustness of nonparametric tests to similar parametric tests is oftentimes just not true. You might want to look at the attached google search for some studies on the topic. Best wishes, David Booth

David Morse , I wonder how you can compare the power of tests testing different null hypotheses. In cases where it "matters", the Friedmann-test is not testing mean differences. If you cannot compare the tested effects, how can you compare the power? I see many occasion where such comparisons are made and discussed, but no one mentiones the incomparability of the tested hypotheses. I hope you can shed some light on that?

Jochen, studies of power-efficiency for rank-based analogs to parametric tests have implicitly embraced the perspective that what is being tested is "equality" vs. the alternative of "inequality." Nowhere in my reply do I assert that the respective hypotheses/parameters under test are identical. However, you could adopt the idea that both approaches evaluate a nil-null hypothesis of identical distributions vs. non-identical distributions. Yes, that translates to different parameters being evaluated. No, it likely doesn't change how people react to a result that suggests the distributions are not identical. So, the likelihood that a method will or won't identify when distributions are not identical seems like a useful property to evaluate.

Thank you David Morse , this is in fact helpful. I had problems to "see" this because I cannot imagine how the conclusion ("the samples are not drawn from the same distribution") would be interpreted. I can construct the case where, for instance, the mean difference is positive but the median difference is negative, and both, t-test and the Wilcoxon-test are "significant". What is the conclusion, apart from the obvious that the two samples are not from the same distribution. Usually (at least in the world I live in) a conclusion is helpful only when I can decide for a "direction" of the effect, e.g. if a treatment does increase or decrease the response (this is formulated too vague, leaving open how an increase or decrease is measured!). And I also think that, if really only the equallity-of-distribution matters, the KS test should be used much more often.