# 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.