# I Nonparametric Hypothesis Tests

#### Conservation

Summary
Nonparametric alternatives to unpaired t-tests given that the sample distributions are different
Hello everyone,

Say you have two sample distributions that are known to be two different distributions (one randomly drawn from a Poisson distribution, other randomly drawn from an uniform distribution). Given that you know the distributions are not going to be normal, a two-sample t-test would not be appropriate here. What are some non-parametric alternatives for comparing sample means in a scenario like this? I was thinking Mann-Whitney U test, but the Mann-Whitney test assumes that the two distributions are the same and measures shift. In this case, we would know that the two distributions are different.

Thanks!

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#### Ygggdrasil

Gold Member
You could consider a Permutation Test/Randomization Test, which relies on almost no assumptions about the underlying datasets:

#### Conservation

@Ygggdrasil Thank you; permutation test seems to be what I'm looking for. I'm probably going to use Two-Sample Fisher-Pitman Permutation Test implemented in R; however, I'm finding conflicting reports on whether permutation test assumes equality of variance when used as a test of different means. Do you know whether I can assume non-homogeneous variances for permutation tests?

#### Ygggdrasil

Gold Member
I don't think that permutation tests assume equal variances. What sources do you have that suggest otherwise?

#### Conservation

This paper (https://www.ncbi.nlm.nih.gov/pubmed/15077763, sorry behind a paywall) seems to suggest that Fisher-Spearman permutation test is sensitive to differences in variances; however, I've also read other literature suggesting that this is not the case for permutation tests.

"Nonparametric Hypothesis Tests"

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