You should use the Mann-Whitney procedure when you want to test for differences between two groups, but are testing an ordinal variable, or have a scale variable which 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 procedure 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 wish to center the test variable if you are not interested in location differences; additionally, you may wish to standardize the test variable to remove both location and scale. Finally, the two-sample Kolmogorov-Smirnov procedure also allows you to display descriptive statistics and/or quartiles of the test and grouping variables.