# Two-Independent-Samples Test Types

Test Type. Four tests are available to test whether two independent samples (groups) come from the same population.

The Mann-Whitney U test is the most popular of the two-independent-samples tests. It is equivalent to the Wilcoxon rank sum test and the Kruskal-Wallis test for two groups. Mann-Whitney tests that two sampled populations are equivalent in location. The observations from both groups are combined and ranked, with the average rank assigned in the case of ties. The number of ties should be small relative to the total number of observations. If the populations are identical in location, the ranks should be randomly mixed between the two samples. The test calculates the number of times that a score from group 1 precedes a score from group 2 and the number of times that a score from group 2 precedes a score from group 1. The Mann-Whitney U statistic is the smaller of these two numbers. The Wilcoxon rank sum W statistic is also displayed. W is the sum of the ranks for the group with the smaller mean rank, unless the groups have the same mean rank, in which case it is the rank sum from the group that is named last in the Two-Independent-Samples Define Groups dialog box.

The Kolmogorov-Smirnov Z test and the Wald-Wolfowitz runs test are more general tests that detect differences in both the locations and shapes of the distributions. The Kolmogorov-Smirnov test is based on the maximum absolute difference between the observed cumulative distribution functions for both samples. When this difference is significantly large, the two distributions are considered different. The Wald-Wolfowitz runs test combines and ranks the observations from both groups. If the two samples are from the same population, the two groups should be randomly scattered throughout the ranking.

The Moses extreme reactions test assumes that the experimental variable will affect some subjects in one direction and other subjects in the opposite direction. The test tests for extreme responses compared to a control group. This test focuses on the span of the control group and is a measure of how much extreme values in the experimental group influence the span when combined with the control group. The control group is defined by the group 1 value in the Two-Independent-Samples Define Groups dialog box. Observations from both groups are combined and ranked. The span of the control group is computed as the difference between the ranks of the largest and smallest values in the control group plus 1. Because chance outliers can easily distort the range of the span, 5% of the control cases are trimmed automatically from each end.