How to: Mann-Whitney test

The Mann-Whitney test is a nonparametric test that compares the distributions of two unmatched groups. Look elsewhere if you want to compare three or more groups with the Kruskal-Wallis test, or perform the parametric unpaired t test.

This test is also called the Wilcoxon rank sum test. Don't confuse it with the Wilcoxon matched pairs test, which is used when the values are paired or the Wilcoxon signed-rank test which compares a median with a hypothetical value.

1. Enter data

From the Welcome (or New Table and graph) dialog, choose the Column tab, and then choose a scatter plot with a line at the median.

If you are not ready to enter your own data, choose sample data and choose: t test - unpaired.

Since the Mann-Whitney tests compares the sum-of-ranks in the two groups, the test needs to have your raw data. It is not possible to perform a Mann-Whitney test if you entered your data as mean and SD (or SEM).

Enter the data for each group into a separate column. The two groups do not have to have the same number of values, and it's OK to leave some cells empty. Since the data are unmatched, it makes no sense to enter any row titles.

Stop. If you want to compare three or more groups, use the Kruskal-Wallis test.

2. Choose the Mann-Whitney test

1.	From the data table, click on the toolbar.

2.	Choose t tests from the list of column analyses.

3.	On the t test dialog, choose the Mann-Whitney test.

4.	Choose a one- or two-tail P value. If in doubt, choose a two-tail P value.

3. Review the results

Learn more about interpreting the results of a Mann-Whitney test.

Before accepting the results, review the analysis checklist.

4. Polish the graph

Graphing notes:

•	A scatter plot shows every point. If you have more than several hundred points, a scatter plot can become messy, so it makes sense to plot a box-and-whiskers graph instead. We suggest avoiding bar graphs, as they show less information than a scatter plot, yet are no easier to comprehend.

•	The horizontal lines mark the medians. Set this choice (medians rather than means) on the Welcome dialog, or change on the Format Graph dialog.

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To add the asterisks representing significance level copy from the results table and paste onto the graph. This creates a live link, so if you edit or replace the data, the number of asterisks may change (or change to 'ns'). Use the drawing tool to add the line below the asterisks, then right-click and set the arrow heads to "half tick down'.