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
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 (
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
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:
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.