Mann-Whitney U test

The Mann-Whitney U test procedure uses the rank of each case to test whether the groups are drawn from the same population. 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.

Example
New dental braces have been developed that are intended to be more comfortable, to look better, and to provide more rapid progress in realigning teeth. To find out whether the new braces have to be worn as long as the old braces, 10 children are randomly chosen to wear the old braces, and another 10 children are chosen to wear the new braces. From the Mann-Whitney U test, you might find that, on average, children with the new braces did not have to wear the braces as long as children with the old braces.
Statistics
Mean, standard deviation, minimum, maximum, number of non-missing cases, and quartiles. Tests: Mann-Whitney U.

Data considerations

Data
Use numeric variables that can be ordered.
Assumptions
Use independent, random samples. The Mann-Whitney U test tests equality of two distributions. In order to use it to test for differences in location between two distributions, one must assume that the distributions have the same shape.

Obtaining a Mann-Whitney U test

This feature requires Statistics Base Edition.

  1. From the menus choose:

    Analyze > Group comparison - nonparametric > Mann-Whitney U test

  2. Click Select variables under the Dependent variables section and select one or more numeric dependent variables whose variation will be studied. Click OK when done.
  3. Click Select variable under the Group variable section and select a single grouping variable to group cases for independent-samples U tests. Click OK when done.
  4. Optionally, you can select the following options from the Additional settings menu:
    • Click Options to specify the confidence interval, significance level, and missing values settings.
  5. Click Run analysis.

This procedure pastes NPTESTS command syntax.