# What exactly does the P value when reporting a Mann-Whitney test mean?

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.

• 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. Commented Jan 29, 2023 at 21:09

## 1 Answer

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 $$p < 0.05$$

• Thank you, that's very helpful. Commented Jan 29, 2023 at 16:31
• One more thing, if I were to reject H0, following from that reasoning, would it then be that p > 0.05? Commented Jan 29, 2023 at 16:36
• 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. Commented Jan 29, 2023 at 18:06