You should use the Mann-Whitney test when you want to test for differences between two groups but you are testing an ordinal variable or you have a scale variable that in some other ways does not conform to the assumptions of the independent-samples t test. The Mann-Whitney and Wilcoxon tests assume that the variable you are testing is at least ordinal and that its distribution is similar in both groups. You can use the two-sample Kolmogorov-Smirnov test to validate the assumption of similar distributions.

The two-sample Kolmogorov-Smirnov test tests the null hypothesis that two samples have the same distribution. It's a very flexible test because no specific shape is assumed for the underlying distribution. However, because the test makes no assumptions, it is sensitive to differences in both location and scale. You may want to center the test variable if you are not interested in location differences; additionally, you may want to standardize the test variable to remove both location and scale.

- You can alternatively use the Crosstabs procedure to test for differences between two or more groups of an ordinal or nominal variable.
- If your test variable passes the stricter conditions of the two-sample t test, you can use the Independent-Samples T Test procedure.
- If your grouping variable has more than two groups, try the Tests for Several Independent Samples Tests procedure.
- If the samples defined by your grouping variable are not independent, try the Two-Related-Samples Tests procedure.