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Mann-Whitney U Test using SPSS (cont...)

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SPSS

Output and Interpretation

If you have been following this guide from page one, you will know that the following output and interpretation relates to the Mann-Whitney U test results when your two distributions have a different shape, such that you are comparing mean ranks rather than medians. This is what happens when your data has violated Assumption #4 of the Mann-Whitney U test. The output is also based on the use of the Legacy Procedure in SPSS. If you have used the New Procedure in SPSS or you need to know how to interpret medians because your data has met Assumption #4 of the Mann-Whitney U test, we explain how to do this in our enhanced Mann-Whitney U test guide, which you can access by subscribing to the site here.

In the SPSS output below, we show you how to report the Mann-Whitney U test using mean ranks. To do this, SPSS produces three tables of output:

Descriptives

The Descriptive Statistics table looks as follows:

Descriptives Output from the Mann-Whitney U Test

Published with written permission from SPSS Inc., an IBM Company.

Although we have decided to show you how you can get SPSS to provide descriptive statistics for the Mann-Whitney U test, they are not actually very useful. The reason for this is twofold. Firstly, in order to compare the groups, we need the individual group values, not the amalgamated ones. This table does not provide us with this vital information, so we cannot compare any possible differences between the exercise and diet groups. Secondly, we chose the Mann-Whitney U test because one of the individual groups (exercise group) was not normally distributed. However, we have not tested to see if the amalgamation of the two groups results in the larger group being normally distributed. Therefore, we do not know whether to use the mean and standard deviation or the median and interquartile range (IQR). The IQR is the 25th to 75th percentile. This will act as a surrogate to the standard deviation we would otherwise report if the data were normally distributed. For these reasons, we recommend that you ignore this table.

Ranks Table

The Ranks table is the first table that provides information regarding the output of the actual Mann-Whitney U test. It shows mean rank and sum of ranks for the two groups tested (i.e., the exercise and diet groups):

Descriptives Output from the Mann-Whitney U Test

Published with written permission from SPSS Inc., an IBM Company.

The table above is very useful because it indicates which group can be considered as having the higher cholesterol concentrations, overall; namely, the group with the highest mean rank. In this case, the diet group had the highest cholesterol concentrations.

Test Statistics Table

This table shows us the actual significance value of the test. Specifically, the Test Statistics table provides the test statistic, U statistic, as well as the asymptotic significance (2-tailed) p-value.

Descriptives Output from the Mann-Whitney U Test

Published with written permission from SPSS Inc., an IBM Company.

From this data, it can be concluded that cholesterol concentration in the diet group was statistically significantly higher than the exercise group (U = 110, p = .014). Depending on the size of your groups, SPSS will produce both exact and asymptotic statistical significance levels. Understanding which one to use is explained in our enhanced guide.

In our enhanced Mann-Whitney U test guide, we show you: (a) how to use SPSS to determine whether your two distributions have the same shape or a different shape; (b) the two procedures – new and legacy – that you can use to carry out a Mann-Whitney U test; (c) how to use SPSS to generate medians for the Mann-Whitney U test if your two distributions have the same shape; and (d) how to fully write up the results of the Mann-Whitney U test procedure whether you are comparing mean ranks or medians. We do this using the Harvard and APA styles. You can access our enhanced Mann-Whitney U test guide, as well as all of our SPSS content, by subscribing to the site here, or learn more about our enhanced content in general here.

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