I'm performing some Mann-Whitney U tests on datasets for a project, and I'm a little confused about what the P value as shown in this question means. Where it states for example "(Mann–Whitney U = 10.5, n1 = n2 = 8, P < 0.05 two-tailed)" (and that "the significance level" should be included) as an inline reference to the test performed, does the P refer to the significance level? I've found critical values for my values of n1, n2 and U, but I'm not really sure what the P means in this context.

For example, in one of my tests I've obtained a U value of 28.5, a critical value for U at 0.05 significance level of 13, and thus concluded insufficient evidence to reject H0. In this case, when reporting the test, would I be stating P > 0.05 as the U value exceeded the critical value, or would I still be stating P < 0.05 just as the "significance level"?

I'd really appreciate some clarification, I haven't done much of this before.

  • $\begingroup$ Strictly 'significance level' means $\alpha$, which that 0.05 presumsbly indicates. Beware, sometimes statisticsl laypeople use it when they mean mean the p-value instead. That may have been the intent here. $\endgroup$
    – Glen_b
    Commented Jan 29, 2023 at 21:09

1 Answer 1


You should be reporting the p < 0.05 as the significance level. Recall, for a critical value of $U_{\alpha, n1, n2}$ and given that the null hypothesis is true (the null hypothesis for the Mann-Whitney test is that the locations of the two distributions are equal), then $P(U_{sample} > U_{\alpha, n1, n2}) = \alpha$ If, as in your case, $U_{sample} > U_{0.05, n1, n2}$ then $p < 0.05$

  • $\begingroup$ Thank you, that's very helpful. $\endgroup$ Commented Jan 29, 2023 at 16:31
  • $\begingroup$ One more thing, if I were to reject H0, following from that reasoning, would it then be that p > 0.05? $\endgroup$ Commented Jan 29, 2023 at 16:36
  • 1
    $\begingroup$ No. You reject H0 at alpha = 0.05 when the p-value is less than 0.05 or when the sample value of U is greater than the critical value. When p > 0.05, you fail to reject H0 due to insufficient evidence. $\endgroup$
    – R Carnell
    Commented Jan 29, 2023 at 18:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.