Hello. We have some questions concerning the statistical analysis of a dataset. We aim to compare the sample means of more than 2 independent samples; the sample sizes are unbalanced. The requirements of normality distribution and variance homogeneity were not met even after transforming the data. Thus we applied a nonparametric test: the Kruskal-Wallis-test (H-Test). The null hypothesis was rejected. Now we try to find a suitable posthoc-test in order to find out which sample means actually are statistically different. 1. We think that the Behrens-Fisher-test and multiple steel test are not applicable, because they assume normality distribution as far as we know. Is that right? 2. Statistical literature suggested to do a Nemenyi-test as posthoc-test. But this test in general requires balanced sample sizes; so we need a special type of this test. Is it possible to do such a test in R? 3. We could also test all the samples against each other with a nonparamatric Mann-Whitney-U-test and correct for the multiple comparisons (m = 11) according to Bonferroni. Is this testing method allowed? We would be very grateful, if anyone could help us. Thank you very much! Christine Hellmann and Rabea Sutter
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