Small sample size: Permutation test or Wilcoxon test? What do you think about using a permutation test each time the sample size is too small to meet the the assumptions of normality and homogeneity of variance etc ? Why do we use a non parametric wilcoxon test most of the time?
If there is any, could you please give me the pros of using a permutation test instead of a wilcoxon test ? can we say, since there is many repetitions and since an empirical distribution is generated with the permutation test, that the results are more "trustworthy" in presence of a small size (n=14) ?..
Context: I want to know if there is a significant different between two groups (placebo/treated group) but the distributions don't meet the normality assumption so i have to use a nonparametric test. I heard that permutation test is better than wilcoxon test why n is small but I don't get why? Is it because there is many repetition (permutations of the samples) in the permutation test and in the wilcoxon test there is not, so it give more "reality" to the result? or its just maybe because a permutation test is more powerful since the statistic usually used i just like the t-test ?...
If you have some sources, papers etc feel free to share !
 A: I think the answer to the question as to which test to use comes down to, Which hypothesis do you want to test ?
The Wilcoxon-Mann-Whitney test essentially tests if the values in one group tend to be larger in than the values in the other group.
In contrast, a permutation test on the means tests if there is a difference in the means.
You could also use a permutation test on the medians, or any other statistic of interest.
Start by deciding what you want to know, and then find an approach that addresses this. Note that your description of your goal: "I want to know if there is a significant different between two groups." is vague.  There are many ways the values for those two groups could be different. (Mean, median, 90th percentile, ranked values, overall distribution...)
As general advice, be cautious of claims you encounter that you might phrase as, "I heard that permutation test is better than wilcoxon test why n is small".  What's the source?  Is it reliable?  Was there any support or explanation?
