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I have to do a non-parametric test on data because the distribution is not normal. The data is about the effectiveness of 2 different Aphasia therapies.

There are 54 Aphasia patients tested before any treatment, after treatment type A and after treatment type B. Each patient has undergone both treatments.

I'm doubting between a Wilcoxon-signed-rank and a Friedman's Anova. Can anyone help me? I think I have to do the Wilcoxon compairing the pre-test with treatment type A scores and again compairing the pre-test with treatment type B scores, but I'm not sure.

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The Wilcoxon signed-rank test is used when there are a pair of repeated measurements. It is the non-parametric equivalent of the paired(/related) samples $t$-test.

The Friedman test is used when there are 2> sets of repeated measurements. It is the non-parametric equivalent of the repeated measures one-way ANOVA.

The answer to which you want to use seems less a statistical question, and more one of what hypotheses you want to test. If you want to test whether there's a difference between the three conditions (i.e. pre- vs. post-A vs. post-B) overall, then you would use the Friedman test, and then potentially perform post hoc tests as needed.

If you want to test whether there's a difference between pre- vs. post-A, and pre- vs. post-B, then you would conduct two Wilcoxon signed-rank tests. In this case, you may also want to correct for the inflated chance of a Type I error.

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  • $\begingroup$ I have to test whether treatment A is more effective than treatment B, so I think that the Friedman test is the one I need. Thank you! $\endgroup$
    – user137130
    Commented Nov 2, 2016 at 9:28
  • $\begingroup$ @user137130 Of course the Friedman test alone will only tell you if there is a difference somewhere between pre, post-A and post-B. It won't tell you where the difference lies, or whether one treatment is more effective than the other. For this, you will need some form of post hoc test. If you found this answer resolved the question for you then you may want to accept it. $\endgroup$
    – Ian_Fin
    Commented Nov 2, 2016 at 9:36
  • $\begingroup$ The Friedman's output in SPSS showed somehow that the difference between pre and post-A and between pre and post-B was significant, and that the difference between post-A and post-B was non-significant. These values were adjusted by the Bonferroni correction. So my conclusion would be that therapy has effect but that there was not a significant difference between both therapies. $\endgroup$
    – user137130
    Commented Nov 2, 2016 at 9:53

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