# Does the Mann-Whitney U-test require the groups to have the same distribution?

If one of my data sets is normally distributed and the other is not, can I do a Mann-Whitney U-test on them, or would they both have to be non-normal?

• It may be okay. What are the null and alternative you're actually interested in testing? (don't look up how your book says to word it for M-W -- what are you trying to find out in plain words?) – Glen_b -Reinstate Monica Nov 24 '14 at 23:29

## 1 Answer

For the Mann-Whitney $U$-test, the distributions can be arbitrary (any old thing--they do not have to be normal). However, the test does assume that the distributions would be identical under the null (e.g., both chi-squared with the same parameters). If you believe the distributions are not the same and certainly would not be, even if the null hypothesis were true, then it is not clear why you are testing if the distributions differ or what exactly you are trying to test. Tests can still be conducted to scrutinize less common aspects of the distributions (making something up: to see if two different types of distributions, but with the same mean, differ in variance), but it would require some hard thinking to determine what such a difference would mean and how to validly test it.

• whats the most accurate method of testing for normality in a large group (270 sample size) – Zoe Campbell Nov 24 '14 at 20:13
• @ZoeCampbell, as I mentioned in my answer to your other question, testing for normality is probably not necessary w/ your sample size & not a good thing to do anyway. You should read the thread I linked in that answer. – gung - Reinstate Monica Nov 24 '14 at 20:17
• so what test should I use then for to see if there is a significant difference between the means? sorry to ask so much, have absolutely no idea about stats and now have to use them! – Zoe Campbell Nov 24 '14 at 20:46
• @ZoeCampbell, as I mentioned in my answer to your other question, based on your description of your situation, I suspect you are safe to use a t-test b/c you have a lot of data & both histograms look normal. – gung - Reinstate Monica Nov 24 '14 at 20:48
• @ZoeCampbell, please try reading the thread I linked in your other question. If you have a lot of data, any trivial difference will make the test of normality significant, even if your data are fine for the t-test. – gung - Reinstate Monica Nov 24 '14 at 20:57