This dialog is activated by selecting the **Mann-Whitney Test...** command from the Statistics -> Nonparametric Tests -> menu. It can be used in order to determine whether two independent samples were selected from populations having the same distribution. The Wikipedia article on the Mann-Whitney U test makes for excellent reading on this topic.

Let us consider two independent samples of size `n1`

and `n2`

respectively. The test procedure includes the following steps:

1. Combine the two samples in a group.

2. Rank them in ascending order, beginning with 1 for the smallest value. Where there are groups of tied values, assign a rank equal to the average of unadjusted rankings.

3. Add up the ranks for the observations which came from the first sample (`R1`

).
The sum of ranks in the second sample, `R2`

, can now be calculated, since the sum of all the ranks equals *N(N+1)/2*, `N`

being the total number of observations: *N = n1+n2*.

4. Calculate *U1 = R1-n1(n1+1)/2* and *U2 = R2-n2(n2+1)/2*.
The test statistic `U`

is the smaller value of `U1`

and `U2`

.

5. Calculate the approximate normal test statistic *Z = (U-mean-0.5*(U-mean))/sqrt(variance)*, where 0.5 is a continuity correction factor, *mean = n1*n2/2* and *variance = mean*(N+1)/6*, in the absence of ties.

6. If there are ties in ranks, the following correction value is substracted from the variance:
*mean/(N(N-1))*T*, where `T`

can be calculated by summing the values *tj(tj-1)(tj+1)/6* for each group of ties, `tj`

being the number of ties in the j-th group.

7. Calculate a p-value for the approximate normal test statistic Z. The null hypothesis is rejected if the probability is lower than the value of the significance level.