# Non-parametric version of paired t-test (Mann–Whitney U test)

I have data from 100 individuals doing a 2AFC under a control and a manipulated setting. I want to compare the means. I initially used a paired t-test. My supervisor noticed the distributions were not normal and recommended me using the Mann–Whitney U test instead of the t-test. However, as far as I can tell, the Mann–Whitney U test does not allow for paired data. Or does it? What non-parametric test should I use? What test generalizes the paired t-test? In other words, I have a non-normal distribution and I want to test how different its mean is from zero.

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## 1 Answer

The non-parametric analog of the paired $t$-test is the Wilcoxon.

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Simple and effective answer. Thanks. –  LBogaardt Aug 24 at 15:51
It it solved your issue, you may want to accept it by clicking the check mark below the vote total to its left. However, I'm still not sure if it is the actual answer you need. Are your data binary? –  gung Aug 24 at 15:53
My data are "True"/"False" answers, averaged for both control and experimental over 36 trials. Each individual, therefore, has two numbers between 0 and 1 indicating the 'proportion correct'. –  LBogaardt Aug 24 at 15:57
In that case, the Wilcoxon is not the ideal test to use. For each participant you have 36 or 72 data, ie >2. When you reduce your data to 2 points by averaging, you are throwing data away. You would have better power by using a GLMM or GEE logistic regression (my answer here: Difference between generalized linear models & generalized linear mixed models in SPSS discusses the difference). –  gung Aug 24 at 16:20
Well, Wilcoxon deserves credit somewhere for the Mann-Whitney, since the rank sum test is his invention and that and the U-test are equivalent. Mann and Whitney's contribution is substantial (Wilcoxon's tables were very limited for starters, to the point of being not very useful, and the whole U-statistics thing is a big deal), but Wilcoxon certainly has priority. –  Glen_b Aug 25 at 2:22