I am applying some statistical tests using python's scipy.stats library to some datasets that I have (taken in pairs), testing whether they both come from the same unknown distribution.
I don't have much background in statistics, so forgive me for the following questions. I was looking at the documentation and I have some doubts.
- scipy.stats.mannwhitneyu: It returns a "One-sided p-value assuming a asymptotic normal distribution" . Why is it assuming a normal distribution? Should't this test work on any underlying distribution?
- scipy.stats.ttest_ind: This test assumes that the populations have identical variances. In my case I can compute the sample variance, so once I do should I apply the test only if it doesn't differ by a certain threshold (which one?)? Interestingly, this is only statistical test rejected only a few of my hypothesis, while most of the other ones rejected some 80% of them.
- As a matter of fact, I want to test whether the distribution of one data set is significantly larger than that of all other data sets put together. Should I use a one-sided or a two-sided test here? This may sound silly, but in the case of a one-sided test, how I can test for one distribution being significantly greater than as opposed to significantly smaller? I coudln't find anything in scipy documentation about this. Swapping the arguments yields the same result.