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 `n`

and _{1}`n`

respectively. The test procedure includes the following steps:_{2}

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 (`R`

).
The sum of ranks in the second sample, _{1}`R`

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

being the total number of observations: *N = n _{1}+n_{2}*.

4. Calculate *U _{1} = R_{1}-n_{1}(n_{1}+1)/2* and

`U`

is the smaller value of `U`_{1}

and `U`_{2}

.5. Calculate the approximate normal test statistic *Z = [U-m-0.5(U-m)]/Var ^{1/2}*, where 0.5 is a continuity correction factor,

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

can be calculated by summing the values *t _{j}(t_{j}-1)(t_{j}+1)/6* for each group of ties,

`t`_{j}

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.