# Mann-Whitney U test in SPSS (cont...)

## Interpreting and reporting: Getting started

If you have been following this guide from the very beginning, you'll know that how you interpret your results after running a Mann-Whitney U test depends on whether your two distributions have a similar shape (i.e., whether the distributions of the two groups of your independent variable have a similar shape). However, if you haven't been following the guide and are unaware of this critical assumption of the Mann-Whitney U test, we suggest reading up on the characteristics of the Mann-Whitney U test on page 2 first.

What SPSS output you have to interpret from the Mann-Whitney U test will also depend on whether you ran the legacy procedure or new procedure in SPSS to carry out the Mann-Whitney U test (the procedures we outlined in the Procedures section). Therefore, in the four pages that follow, we show you how to interpret your results based on these two criteria: (a) whether your two distributions had a similar shape; and (b) whether you ran the legacy procedure or the new procedure in SPSS.

• Similar distributions after running the new or legacy procedures: If you have met the assumption of similarly shaped distributions, you are in the fortunate position to determine whether the median score for your two groups (e.g., "males" and females" for our independent variable, "gender") are different in terms of the dependent variable (e.g., "engagement", in our example). We say that you are 'fortunate' because if you had failed this assumption, you would not be able to determine how large any differences between your two groups were. You could only say whether one group's values was higher or lower than the others (e.g., females' engagement scores were higher than males; or vice versa). Instead, you can go further and say, for example, that engagement scores were not only higher in females than males, but they were a median of 0.8 higher (e.g., males had an engagement score of 3.4, but females' engagement score was 4.2). Therefore, on pages 17 and 19, we show you how to: (a) determine whether there was a statistically significant median difference in the two groups of your independent variable in terms of your dependent variable; (b) if you can accept or reject the null hypothesis; (c) how you can accurately interpret the SPSS output for the Mann-Whitney U test, including the group medians, U score, z score, and asymptotic and exact p-values; and (d) how you can bring all of this together into a statement that explains your results. We do this on page 17 if you have used the new procedure and page 19 if you have used the legacy procedure.
• Dissimilar distributions after running the new or legacy procedures: If you have run the new procedure in SPSS and have failed the assumption of similarly shaped distributions, you can only determine whether the values in one group are lower or higher than the values in the other group (e.g., females higher than males), by comparing the mean ranks of each distribution of scores (e.g., males and females engagement scores). Therefore, you lose some of the descriptive power that you get when comparing medians, which you can do when the assumption of similarly shaped distributions is met. Nonetheless, you can still obtain valuable information about your two groups in terms of the dependent variable (i.e., did one group have higher or lower values than the other). Therefore, on pages 18 and 20, we show you how to: (a) determine whether there was a statistically significant difference in the mean ranks of the two groups of your independent variable in terms of your dependent variable; (b) if you can accept or reject the null hypothesis; (c) how you can accurately interpret the SPSS output for the Mann-Whitney U test, including the group mean ranks, U score, z score, and asymptotic and exact p-values; and (d) how you can bring all of this together into a statement that explains your results. We do this on page 18 if you have used the new procedure and page 20 if you have used the legacy procedure.

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