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.
Solved – Bonferroni correction for Wilcoxon signed rank test with 6 related samples
bonferronifriedman testnonparametricstatistical significancewilcoxon-signed-rank
Best Answer
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.