Mann-Whitney Test Dialog

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.

Figure 5-125. The two sample Mann-Whitney test dialog.

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-m-0.5(U-m)]/Var1/2, where 0.5 is a continuity correction factor, m = n1n2/2 is the mean and the variance Var = m(N+1)/6, in the absence of ties.

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 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.