Wilcoxon Rank Sum Test

$n_1 = $ $n_2 = $

This applet computes probabilities for the Wilcoxon Rank Sum Test. Let $X_1,\ldots,X_{n_1}$ and $Y_1,\ldots,Y_{n_2}$ be independent random samples. Suppose the $n_1+n_2$ values are ranked. The Wilcoxon rank sum statistic $W_1$ is the sum of the ranks in the first sample.

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


To compute a probability, select $P(W_1=w_1)$ from the drop-down box, enter a numeric $w$ value, and press "Enter" on your keyboard. The probability $P(W_1=w_1)$ will appear in the pink box. Select $P(W_1 \leq w_1)$ from the drop-down box for a left-tail probability (this is the cdf).


The Wilcoxon rank sum statistic $W_1$ has: