The Mann-Whitney U Test, also known as the Wilcoxon rank-sum test, is a non-parametric test used to determine whether there is a significant difference between the distributions of two independent samples. It is commonly used when the assumptions of a t-test are not met, particularly when the data is ordinal or not normally distributed. This comprehensive guide will walk you through the process of running and interpreting the Mann-Whitney U Test using SPSS, with real examples and detailed results interpretation.
Assumptions of the Mann-Whitney U Test
- The dependent variable should be measured at the ordinal or continuous level.
- The independent variable should consist of two categorical, independent groups.
- Observations should be independent of each other.
- The distributions of the two groups should have the same shape (homogeneity of variances).
Running the Mann-Whitney U Test in SPSS
To run the Mann-Whitney U Test in SPSS, follow these steps:
- Open your dataset in SPSS.
- Go to Analyze > Nonparametric Tests > Legacy Dialogs > 2 Independent Samples.
- In the dialog box, move your dependent variable to the Test Variable List and your independent variable to the Grouping Variable.
- Click on Define Groups and specify the two groups you want to compare.
- Make sure the Mann-Whitney U option is selected under Test Type.
- Click OK to run the test.
Example Dataset
Let’s consider a dataset where we want to compare the test scores of two groups of students who used different study methods. The dataset includes:
- Group: Study method (1 = Method A, 2 = Method B)
- Score: Test scores of the students
SPSS Output and Interpretation
After running the Mann-Whitney U Test, SPSS will provide several tables. Below is an example output:
| Ranks | Group | N | Mean Rank | Sum of Ranks |
|---|---|---|---|---|
| Method A | 30 | 20.45 | 613.5 | |
| Method B | 30 | 40.55 | 1216.5 | |
| Total | 60 |
| Test Statistics | Score |
|---|---|
| Mann-Whitney U | 188.5 |
| Wilcoxon W | 613.5 |
| Z | -3.24 |
| Asymp. Sig. (2-tailed) | .001 |
Interpretation in APA Style
The results of the Mann-Whitney U Test indicated that there was a significant difference in test scores between the two study methods, U = 188.5, Z = -3.24, p = .001. Students who used Method B had significantly higher test scores (M = 40.55) compared to those who used Method A (M = 20.45).
FAQs
1. Mann-Whitney U Test vs. T-Test
The Mann-Whitney U Test is used when the assumptions of the t-test are not met, such as when the data is not normally distributed or when it is ordinal. The t-test, on the other hand, is used for normally distributed interval or ratio data.
2. How to Run the Mann-Whitney U Test in SPSS?
Follow the steps provided above to run the Mann-Whitney U Test in SPSS. Ensure your variables are correctly specified in the test dialog box.
3. Interpreting Mann-Whitney Mean Rank
The mean rank indicates the average rank of the values in each group. A significant Mann-Whitney U Test suggests that the mean ranks between the groups are significantly different.
4. Mann-Whitney U Test Results Interpretation
Interpret the test results based on the U value, Z value, and p-value provided in the SPSS output. A significant p-value (typically < .05) indicates a significant difference between the groups.
5. Assumptions of the Mann-Whitney U Test
Ensure your data meets the assumptions of the Mann-Whitney U Test: the dependent variable should be ordinal or continuous, the independent variable should consist of two independent groups, and the observations should be independent.
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