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Kruskal-Wallis

Compare three or more independent groups on an ordinal outcome

The Kruskal-Wallis test is used to answer research questions that compare three or more independent groups on an ordinal outcome. The Kruskal-Wallis test is considered non-parametric because the outcome is not measured at a continuous level. Instead of reporting means and standard deviations, researchers will report the median and interquartile range of each group ​when using a Kruskal-Wallis test. 

This figure depicts the use of a Kruskal-Wallis test. The assumption of independence of observations has been met, there are three or more independent groups being compared in a between-subjects fashion, and an ordinal outcome is being used.
The Kruskal-Wallis test is used when comparing three or more independent groups on an ordinal outcome. The assumption of independence of observations must be met as well with Kruskal-Wallis tests.

The steps for conducting a Kruskal-Wallis test in SPSS

1. The data is entered in a between-subjects fashion.

2. Click Analyze.

3. Drag the cursor over the Nonparametric Tests drop-down menu.

4. Drag the cursor over the Legacy Dialogs drop-down menu.

5. Click K Independent Samples.

6. Click on the continuous outcome variable to highlight it.

7. Click on the arrow button to move the outcome variable into the Test Variable List: box.

8. Click on the "grouping" variable to highlight it and then click on the arrow to move the "grouping" variable into the Grouping Variable: box.

9. Click on the Define Range button.

10. Enter the categorical value for the independent group that has the smallest value into the Minimum: box. Example: "0"

11. Enter the categorical value for the independent group that has the largest value into the Maximum: box. Example: "2"

12. Click Continue.

13. Click OK. 

The steps for interpreting the SPSS output for a Kruskal-Wallis test

1. In the Test Statistics table, look at the p-value associated with Asymp. Sig. row. This is the p-value that is interpreted.

If it is LESS THAN .05, then researchers have evidence of a statistically significant difference in the continuous outcome variable between the two independent groups.

If the p-value is MORE THAN .05, then researchers have evidence that there is not a statistically significant difference in the continuous outcome variable between the two independent groups.

If researchers find a significant main effect, or p-value below .05, then they will need to run subsequent Mann-Whitney U tests to test for pairwise comparisons in a post hoc fashion.

This figure depicts Mann-Whitney U tests being used in a post hoc fashion to explain a significant main effect found with a Kruskal-Wallis test.
Mann-Whitney U tests are used in a post hoc fashion when significant main effects are found for a Kruskal-Wallis test.

The steps for conducting post hoc Mann-Whitney U tests in SPSS

1. The data is entered in a between-subjects fashion.

2. Click Analyze.

3. Drag the cursor over the Nonparametric Tests drop-down menu.

4. Drag the cursor over the Legacy Dialogs drop-down menu.

5. Click 2 Independent Samples.

6. Click on the continuous outcome variable to highlight it.

7. Click on the arrow button to move your outcome variable into the Test Variable List: box.

8. Click on the "grouping" variable to highlight it and then click on the arrow to move the "grouping" variable into the Grouping Variable: box.

9. Click on the Define Groups button.

10. Enter the categorical value for the first independent group into the Group 1: box. Example: "0"

11. Enter the categorical value for the second independent group into the Group 2: box. Example: "1"

12. Click Continue.

13. Click OK.

14. Click Analyze.

15. Drag the cursor over the Nonparametric Tests drop-down menu.

16. Drag the cursor over the Legacy Dialogs drop-down menu.

17. Click 2 Independent Samples.

18. Click on the continuous outcome variable to highlight it.

19. Click on the arrow button to move the outcome variable into the Test Variable List: box.

20. Click on the "grouping" variable to highlight it and then click on the arrow to move the "grouping" variable into the Grouping Variable: box.

21. Click on the Define Groups button.

22. Enter the categorical value for the first independent group into the Group 1: box. Example: "0"

23. Enter the categorical value for the third independent group into the Group 2: box. Example: "2"

24. Click Continue.

25. Click OK.

26. Click Analyze.

27. Drag the cursor over the Nonparametric Tests drop-down menu.

28. Drag the cursor over the Legacy Dialogs drop-down menu.

29. Click 2 Independent Samples.

30. Click on the continuous outcome variable to highlight it.

31. Click on the arrow button to move the outcome variable into the Test Variable List: box.

32. Click on the "grouping" variable to highlight it and then click on the arrow to move the "grouping" variable into the Grouping Variable: box.

33. Click on the Define Groups button.

34. Enter the categorical value for the second independent group into the Group 1: box. Example: "1"

35. Enter the categorical value for the third independent group into the Group 2: box. Example: "2"

36. Click Continue.

37. Click OK.

The steps for interpreting the SPSS output for post hoc Mann-Whitney U tests

1. In the Test Statistics table for each subsequent Mann-Whitney U analysis, look at the p-value associated with Asymp. Sig. (2-tailed) row. These are the p-values that will be interpreted.

If a p-value is LESS THAN .05, then researchers have evidence of a statistically significant difference in the continuous outcome variable between those two independent groups.

If a p-value is MORE THAN .05, then researchers have evidence that there is not a statistically significant difference in the continuous outcome variable between those two independent groups.

Click on the Download Database and Download Data Dictionary buttons for a configured database and data dictionary for a Kruskal-Wallis test. Click on the Adjusting of Multiple Comparisons ​button to learn more about Bonferroni, Tukey's HSD, and Scheffe's test. Click on the Validation of Statistical Findings button to learn more about bootstrap, split-group, and jack-knife validation methods.
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Adjusting for Multiple Comparisons
Validation of Statistical Findings
Between-Subjects Three Groups
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