# Comparing P value from t test vs. Mann-Whitney test

If you analyze the same data with a t test and the nonparametric Mann-Whitney test, which do you expect to have the lower P value?

• Someone asked me this, so I am posting both the question and my answer. – Harvey Motulsky Aug 31 '12 at 15:19

• @JoelW: an analytic approach to the relative power of the Wilcoxon-Mann-Whitney and t-test is discussed in this question. As Harvey says, for data from a normal distribution the t-test has more power in large samples - it's relative power versus the U test is $\pi/3$ - but for non-normal data, the U test can have rather more power (3 times on exponential, 1.5 on double exponential, infinitely so on Cauchy). For uniformly distributed data, they're equally powerful. – Silverfish Jan 1 '15 at 22:44