Wilcoxon-Mann-Whitney Test

JavaScript

Given two samples, X₁,...,X_m, and Y₁,...,Y_n, from continuous distributions F and G,
the Wilcoxon rank-sum statistic, R_m,n, for testing the equality of F and G is defined
as the sum of the ranks of the X's when all m+n observations are ranked
from smallest to largest. The related statistic, U_m,n, of Mann and Whitney
is the number of pairs, (X_i,Y_j), with X_i less than Y_j.
These statistics are related by R_m,n = U_m,n + m(m+1)/2.

      Enter sample sizes and cutoff point.

    Sample size m: 
    Sample size n: 
          u-value:

P(U_m,n <= u) :

The probabilities calculated here are for U_m,n, under the null hypothesis, F=G.
The distribution of U_m,n is symmetric on the interval from 0 to mn.
It has mean mn/2 and variance mn(m+n+1)/12.

If both m and n are less than or equal to 20, the probabilities are calculated exactly.
Otherwise, a normal approximation with continuity correction is used.
This approximation has maximum absolute error at most .001 when m,n > 20.