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I am comparing scores of the same group of people over 7 days. I first did a Friedman's test to know where the differences were between the 7 days and I did a Wilcoxon signed rank test for the Post Hoc. Is this an appropriate test? I'm also thinking I should apply Bonferroni correction, but should I do this based on how many groups I have, or how many comparisons I make? I'm only interested in if days 2-7 are different from the first day, not if they're different from each other.

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    $\begingroup$ See this post (Friedman's test is very significant, but its post-hoc comparisons (SPSS) are not significant) for some discussion of post hocs and Friedman. It looks like some potential references may be Pereira et al (2015) "Overview of Friedman's Test and Post-hoc Analysis" Overview of Friedman's Test and Post-hoc Analysis, Communications in Statistics - Simulation and Computation, 44:10, 2636-2653. and ... $\endgroup$
    – Glen_b
    Mar 16, 2018 at 8:22
  • $\begingroup$ ... (in particular for comparisons against a single group) Garcia et al, (2010), "Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power", Information Sciences 180, 2044–2064. I have only read a little of these papers, however, so I can't really say anything about their value yet. $\endgroup$
    – Glen_b
    Mar 16, 2018 at 8:22

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The discussion cited by @glen_b has valuable information, but can can be confusing to tease out what the correct answers are.

My understanding is that Friedman test is a generalization of the sign test, so that if you were looking for a pairwise post-hoc, the sign test would be the appropriate one.

Pairwise Wilcoxon signed-rank tests would likely have more power than the sign tests, though my understanding is that the Quade test is actually the generalization of the signed-rank test. You might consider using Quade test as the omnibus and pairwise signed-rank as the post-hoc tests. It is sometimes suggested that Friedman be used if there are five or more groups, and Quade be used for four or fewer groups. But I don't have any opinion on this.

There is also a Conover test that can be used as post-hoc for Friedman's. I don't know much about this test, but in playing with the implementation in R, it seems to give reasonable results, and appears rather powerful.

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For the pairwise tests mentioned above, it makes sense to use a p-value correction method, such as Bonferroni. Personally, I find Bonferroni to be too conservative for most cases. You might look in to other methods, such as those listed here.

The implementation of the Conover test may need no a-value adjustment. I'm not sure.

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  • $\begingroup$ +1. I agree that Friedman can be seen as a generalization of the sign test. This, however, does not mean that the backward pass, "particularization" of Friedman, yields us the sign test as the proper after-Friedman post hoc. (Neither Wilcoxon is a proper after-Friedman post hoc.) $\endgroup$
    – ttnphns
    Mar 16, 2018 at 19:06
  • $\begingroup$ (cont.) Imagine a respondent's ratings for X1 X2 X3 X4 are 4 2 7 5. Friedman ranks it to 2 1 4 3. Post hoc pairwise comparison of X1vsX3 shows greater distance (2 4) than in X1vsX2 (2 1). But sign test will just say that one value is greater than the other: (- +) and (+ -), respectively. $\endgroup$
    – ttnphns
    Mar 16, 2018 at 19:06
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    $\begingroup$ What do you think would be a proper after-Friedman post hoc instead of Wilcoxon? Is a Conover better then? $\endgroup$
    – Marissa
    Mar 16, 2018 at 23:34
  • $\begingroup$ Conover test is a good candidate. $\endgroup$ Mar 17, 2018 at 0:50

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