# Mann Whitney U Test

Concept, How to Run, Interpret, and Report Mann Whitney U Test

### Concept of Mann Whitney U Test

The **Mann–Whitney U test** is the non-parametric alternative to the Independent-samples t-test. The test is used to test for differences between two independent groups on ordinal data or non-normal continuous data. Instead of comparing the means of the two groups, as in the case of the t-test, the Mann-Whitney U Test compares medians. It then evaluates whether the ranks for the two groups differ significantly. As the scores are converted to ranks, the actual distribution of the scores does not matter.

Following are a few scenarios in which you could use the Mann-Whitney *U* test

- A company Quality manager would like to know if there is a difference in the service quality received by Suppliers and Customers.
- A market researcher would like to investigate if there are differences in attention to Social Media differs between Male and Female
- An HR Manager would like to investigate if the compensation offered to the two departments (Finance & HR) is significantly different. So the HR manager collected data from 10 personnel from each department.
- An educationist would like to evaluate the difference in attentiveness of male and female students.

### Example

**The Problem:**

To identify if there exists a difference in Service Quality between Supplier and Customer

**Hypothesis**

**H _{1}:** There are significant differences in perception of Service Quality between Supplier and Customer

### Information Required

- Dependent variable on Ordinal Scale (Service Quality)
- A Grouping variable – Type of Stakeholder (Supplier or Customer)

### Steps to run Mann Whitney U Test

**Step 1:** Go to **Analyze → Nonparametric Tests → Legacy Dialogs → 2 Independent Samples**

**Step 2:** The resulting dialog box is shown in Figure

**Step 3:** Two-Independent-Samples Test dialog box is displayed, asking for the **Test Variable** (Service Quality) and **Grouping Variable **(Type). Add the respective variables into the desired boxes.

**Step 4:** Once the Grouping Variable Gender is added, Click Define Groups, Add 1 (Supplier) into Group 1 box and add 2 (Customer) into Group 2 box and Press Continue.

**Note. **If you are unable to click on the Define Groups Button, first select the Grouping Variable Box.

**Step 5:** Make sure Mann-Whitney U checkbox is selected. The final dialog box should look like one in figure

**Step 6:** Now Press OK

### Interpreting Mann Whitney U Test

The results shows a number of values, we as research students do not need to look at each and every value, main values of interest include Z value and the Asymp.Sig. (2-tailed). In the results of above example the Z-value is -2.600 and p-value is .009 which is less than .05 and hence we will reject the null hypothesis. There are significant differences in service quality perceptions between supplier and customer.

In case one finds a significant differences between groups, you need to describe the direction of the difference (which group is higher). This can be seen from the **Ranks** table under the column mean rank however when you are presenting your results it is important that median values for each group are reported. This is not available in the test, for this you will have to follow the following procedure.

**Finding Median for Each Group**

- Choose
**Analyze → Compare Means → Means** - Move
**SocialPreference**variable into the Dependent List Box - More
**Gender**into the Independent List Box - Now Click the
**Options**Button, Click on Median from Statistics list box and move it to the Cell Statistics, Remove everything else, since for this particular scenario we do not need other measures - Click Continue
- Press OK

#### Find Median for Each Group

- Choose
**Analyze → Compare Means → Means** - Move
**Service Quality**variable into the Dependent List Box - Move
**Type**into the Independent List Box - Now Click the
**Options**Button, Click on Median from Statistics list box and move it to the Cell Statistics, Remove everything else, since for this particular scenario we do not need other measures - Click Continue
- Press OK

Table 1 shows the case processing summary. The table of interest is table 2. The results shows median value of 2 for Service Quality for both Supplier and Customer.

#### Effect Size Calculation for Mann Whitney U Test

SPSS doesn’t provide an effect size statistic, but the value of z that is reported in the output be used to calculate an approximate value of r.

r = Z/√N

Where Z is the Z Statistics and N is number of cases. For our example value of Z is 2.600 and N is 304, the value of r can be calculated as follows

r = 2.600/√304

r = 2.600/17.435

r = 0.14

According to Cohen (1988) criteria .1 = Small Effect, .3 = Medium Effect, and .5 = Large Effect. In this scenario, the effect size is small.

#### Reporting Mann Whitney U Test

**The Problem:**

To identify if there exists significant differences in Service Quality offered to Supplier and Customer

**Hypothesis**

**H _{1}:** There are significant differences in perception of Service Quality between Supplier and Customer

To evaluate the difference between Supplier and Customer for Service Quality, Mann-Whitney *U* Test was utilized. The test revealed significant differences in the Service Quality perception of Suppliers (Median = 2, n = 158) and Customer (Median = 2, n = 146), *U* = 9711, z = 2.600, p = .009, r = .14. Hence, H1 was supported.