Currently I'm working on a AB-BA test for cochlear implant patients. Here a simple design description:
Each test person is tested with his old / normal "settings". (A1)
At the same day he does the same test again with the new / alternative "setting". (B1)
After some weeks, the new / alternative setting he now got used to is tested again. (B2)
At the same day, the old / normal "setting" is tested. (A2)
As it's a pre/post test I could use Wilcoxon or sign test. On the other hand, we actually got 4 groups (A1,A2,B1,B2), so do we need Kruskal-Wallis? Or is it possible to use Mann-Whitney U test?
Thank you very much for your help.
If values have a normal distribution, then use ANOVA (as you have 4 groups) with a post-hoc analysis (if equal variances are assumed, Tukey if not, you could use Tamhane's T2. This will give you a pair-wise comparisson that would give you the answer you need.
If data does not have a normal distribution, then Kruskal-Wallis. As a post-hoc you can run Mann-Whitney U test for each possible pair, but in that case you have to use Bonferroni adjustment for the p value.
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