The Mann-Whitney U test is used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed. For example, you could use the Mann-Whitney U test to understand whether attitudes towards pay discrimination, where attitudes are measured on an ordinal scale, differ based on gender (i.e., your dependent variable would be "attitudes towards pay discrimination" and your independent variable would be "gender", which has two groups: "male" and "female"). Alternately, you could use the Mann-Whitney U test to understand whether salaries, measured on a continuous scale, differed based on educational level (i.e., your dependent variable would be "salary" and your independent variable would be "educational level", which has two groups: "high school" and "university"). The Mann-Whitney U test is often considered the nonparametric alternative to the independent t-test although this is not always the case.
Unlike the independent-samples t-test, the Mann-Whitney U test allows you to draw different conclusions about your data depending on the assumptions you make about your data's distribution. These conclusions can range from simply stating whether the two populations differ through to determining if there are differences in medians between groups. These different conclusions hinge on the shape of the distributions of your data, which we explain more about later.
In our enhanced Mann-Whitney U test guide, we take you through all the steps required to understand when and how to use the Mann-Whitney U test, showing you the required procedures in SPSS Statistics, and how to interpret and report your output. You can access this enhanced Mann-Whitney U test guide by subscribing to the site here. In this "quick start" guide, we show you the basics of the Mann-Whitney U test using one of SPSS Statistics's procedures when the critical assumption of this test is violated. Before we show you how to do this, we explain the different assumptions that your data must meet in order for a Mann-Whitney U test to give you a valid result. We discuss these assumptions next.
When you choose to analyse your data using a Mann-Whitney U test, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a Mann-Whitney U test. You need to do this because it is only appropriate to use a Mann-Whitney U test if your data "passes" four assumptions that are required for a Mann-Whitney U test to give you a valid result. In practice, checking for these four assumptions just adds a little bit more time to your analysis, requiring you to click a few more buttons in SPSS Statistics when performing your analysis, as well as think a little bit more about your data, but it is not a difficult task.
Before we introduce you to these four assumptions, do not be surprised if, when analysing your own data using SPSS Statistics, one or more of these assumptions is violated (i.e., is not met). This is not uncommon when working with real-world data rather than textbook examples, which often only show you how to carry out a Mann-Whitney U test when everything goes well! However, don’t worry. Even when your data fails certain assumptions, there is often a solution to overcome this. First, let’s take a look at these four assumptions:
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You can check assumption #4 using SPSS Statistics. Before doing this, you should make sure that your data meets assumptions #1, #2 and #3, although you don't need SPSS Statistics to do this. Just remember that if you do not check assumption #4, you will not know whether you are correctly comparing mean ranks or medians, and the results you get when running a Mann-Whitney U test may not be valid. This is why we dedicate a number of sections of our enhanced Mann-Whitney U test guide to help you get this right. You can learn more about assumption #4 and what you will need to interpret in the Assumptions section of our enhanced Mann-Whitney U test guide, which you can access by subscribing to the site here.
In the Test Procedure in SPSS Statistics section of this "quick start" guide, we illustrate the SPSS Statistics procedure to perform a Mann-Whitney U test assuming that your two distributions are not the same shape and you have to interpret mean ranks rather than medians. First, we set out the example we use to explain the Mann-Whitney U test procedure in SPSS Statistics.
The concentration of cholesterol (a type of fat) in the blood is associated with the risk of developing heart disease, such that higher concentrations of cholesterol indicate a higher level of risk, and lower concentrations indicate a lower level of risk. If you lower the concentration of cholesterol in the blood, your risk for developing heart disease can be reduced. Being overweight and/or physically inactive increases the concentration of cholesterol in your blood. Both exercise and weight loss can reduce cholesterol concentration. However, it is not known whether exercise or weight loss is best for lowering cholesterol concentration. Therefore, a researcher decided to investigate whether an exercise or weight loss intervention was more effective in lowering cholesterol levels. To this end, the researcher recruited a random sample of inactive males that were classified as overweight. This sample was then randomly split into two groups: Group 1 underwent a calorie-controlled diet (i.e., the 'diet' group) and Group 2 undertook an exercise-training programme (i.e., the 'exercise' group). In order to determine which treatment programme was more effective, cholesterol concentrations were compared between the two groups at the end of the treatment programmes.
In SPSS Statistics, we entered the scores for cholesterol concentration, our dependent variable, under the variable name Cholesterol. Next, we created a grouping variable, called Group, which represented our independent variable. Since our independent variable had two groups - 'diet' and 'exercise' - we gave the diet group a value of "1" and the exercise group a value of "2". If you do not label your two groups, SPSS Statistics will not be able to distinguish between them and the Mann-Whitney U test will not run.
Note: There are two different procedures in SPSS Statistics to run a Mann-Whitney U test: a new and legacy procedure. How we have explained the data setup above relates to the legacy procedure (and the new procedure when your dependent variable is continuous), which is what we take you through in the Test Procedure in SPSS Statistics section next. We mention this because if you are using the new procedure, you have to make changes to your data setup if your dependent variable is ordinal (i.e., as opposed to being continuous). 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 our enhanced Mann-Whitney U test guide, we show you all the steps required to correctly enter data into SPSS Statistics to run a Mann-Whitney U test for both the new and legacy procedures discussed in the note above.
If you read assumption #4 earlier, you'll know that the SPSS Statistics procedure when analysing your data using a Mann-Whitney U test is different depending on the shape of the two distributions of your independent variable. In our example, where our dependent variable is cholesterol concentration, Cholesterol, we are referring to the two distributions of the independent variable, Group (i.e., the distribution of scores for Group 1 – the 'diet' group – and Group 2 – the 'exercise' group). In the 10 steps below, we show you how to analyse your data using a Mann-Whitney U test in SPSS Statistics when these two distributions have a different shape, and therefore, you have to compare the mean ranks of your dependent variable rather than medians.
To use SPSS Statistics to determine whether your two distributions have the same or different shapes, or if you want to know how to use SPSS Statistics to carry out a Mann-Whitney U test when your two distributions have the same shape, such that you need to compare medians rather than mean ranks, you will need to access the Procedures section of our enhanced Mann-Whitney U test guide (N.B., you can do this by subscribing to the site here). Furthermore, the 10 steps below also show you how to carry out a Mann-Whitney U test using the legacy procedure in SPSS Statistics. As we explained earlier, there are two different procedures in SPSS Statistics to run a Mann-Whitney U test: a new and legacy procedure. We recommend the new procedure if your two distributions have the same shape because it is a little easier to carry out, but the legacy procedure is fine if your two distributions have different shapes. We show you the new and legacy procedures in our enhanced Mann-Whitney U test guide.
At the end of the 9 steps below, we show you how to interpret the results from this test using mean ranks.
Click Analyze > Nonparametric Tests > Legacy Dialogs > 2 Independent Samples... on the top menu, as shown below:
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You will be presented with the Two-Independent-Samples Tests dialogue box, as shown below:
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Transfer the dependent variable, Cholesterol, into the Test Variable List: box and the independent variable, Group, into the
Grouping Variable: box by using the button or by dragging-and-dropping the variables into the boxes.
Published with written permission from SPSS Statistics, IBM Corporation.
Note: Make sure that the Mann-Whitney U checkbox is ticked in the –Test Type– area and the Grouping Variable: box is highlighted in yellow (as seen above). If it is not highlighted in yellow, simply click your cursor in the Grouping Variable: box to highlight it.
Click the button. The button will not be clickable if you have not highlighted the Grouping Variable: box as instructed in Step 4. You will be presented with the following screen:
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Click through to the next page for the remaining procedure and how to interpret the output.