Mann-Whitney U-Test

$n_1 = $ $n_2 = $

This applet computes probabilities for the Mann-Whitney $U$ Test. Let $X_1,\ldots,X_{n_1}$ and $Y_1,\ldots,Y_{n_2}$ be independent random samples. The Mann-Whitney statistic $U$ is the number of pairs $(X_i,Y_j)$ where $X_i > Y_j$.

Note: Although the Wilcoxon Rank Sum test uses a different statistic, it will yield an identical $p-$value as a test based on the Mann-Whitney U-statistic. Both tests are equivalent; the statistics simply differ by a shift in location.


To compute a probability, select $P(U=u)$ from the drop-down box, enter a numeric $u$ value, and press "Enter" on your keyboard. The probability $P(U=u)$ will appear in the pink box. Select $P(U \leq u)$ from the drop-down box for a left-tail probability (this is the cdf).


The Mann-Whitney $U$ statistic has: