How to test for differences between two group means when the data is not normally distributed and the sample size is small? I have a preliminary study with very small sample size (n=26), and I want to test for differences between males and females and similar things, so I have to divide the sample and make comparisons of 13 vs 13 subjects.
Is there a test I can use to give an idea of what the differences might be? Is it possible to use the two-independent-sample t-test even if the sample is this small and the variable is not normally distributed? What can I do otherwise? 
 A: Since your dataset is small, you are in the fortunate situation where you can calculate all possible partitions into two groups.
In your case, you want two groups of size 13, so you have "26 choose 13" combinations, which is about 10.4 million combinations. Now, for every given statistic you want to test (it could be mean but doesn't have to be), you can go over all combinations and count in how many of them the statistic was equal or higher than what you observed in your partition. There is of course a theoretical limit on the p-value, which is 1 over the number of combinations. If you have some minimal programming skills this should be easy to implement (10.4 million combinations would run very fast on any modern computer) and would give you the most accurate results without assuming much.
Another option, but less robust, is to use a permutation test which means the same as above but instead of explicitly calculating all combinations, sampling from them randomly. This will be less accurate and will limit your p-value to the number of permutations you try. Also, beyond some number of permutations these results will become less accurate because of the limited number of possible combinations.
