Wilcoxon
Compare two observations of an ordinal outcome
The Wilcoxon test is a within-subjects analysis that assesses the change of an ordinal outcome across two within-subjects observations or two time points. The medians and interquartile ranges for both observations of the outcome should be presented with a Wilcoxon test. Wilcoxon is the non-parametric equivalent of a repeated-measures t-test.
This figure depicts the use of a Wilcoxon test. There is only one groups being observed. There is a baseline and a "post" observation of an ordinal outcome. Wilcoxon tests are used to assess the amount of change in an ordinal variable across two within-subjects observations or two time points.
The Wilcoxon test is also employed when a violation of the statistical assumption of normality of difference scores for a repeated-measures t-test is violated. This figure depicts the use of a Wilcoxon test when normality is violated for repeated-measures t-test. There is only one group being observed and individual participants have a baseline and a "post" observation of a continuous outcome. However, the difference scores between the two within-subjects observations of the outcome are not normally distributed. A Wilcoxon test is used when normality of difference scores is violated for a repeated-measures t-test.
Finally, Wilcoxon tests are used as post hoc tests when a significant main effect is found for a Friedman's ANOVA analysis. This figure depicts the use of post hoc Wilcoxon tests. A significant main effect has been found for Friedman's ANOVA. Wilcoxon tests are then used to explain the differences within each observation of the outcome.
The steps for conducting a Wilcoxon test in SPSS
1. The data is entered in a within-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 Related Samples.
6. Click on the first observation of the ordinal outcome.
7. Click on the arrow button to move the first observation of the outcome variable into the Test Pairs box under the Variable1 column.
8. Click on the second observation of the ordinal outcome.
9. Click on the arrow button to move the second observation of the outcome variable into the Test Pairs box under the Variable2 column.
10. Click OK.
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 Related Samples.
6. Click on the first observation of the ordinal outcome.
7. Click on the arrow button to move the first observation of the outcome variable into the Test Pairs box under the Variable1 column.
8. Click on the second observation of the ordinal outcome.
9. Click on the arrow button to move the second observation of the outcome variable into the Test Pairs box under the Variable2 column.
10. Click OK.
The steps for interpreting the SPSS output for a Wilcoxon test
1. In the Test Statistics table, look at the p-value associated with Asymp. Sig. (2-tailed) row. This is the p-value that is interpreted.
If it is LESS THAN .05, then researchers have evidence of a statistically significant effect in the ordinal outcome across time or within-subjects.
If the p-value is MORE THAN .05, then researchers have evidence that there is NOT a statistically significant effect in the ordinal outcome across time or within-subjects.
If it is LESS THAN .05, then researchers have evidence of a statistically significant effect in the ordinal outcome across time or within-subjects.
If the p-value is MORE THAN .05, then researchers have evidence that there is NOT a statistically significant effect in the ordinal outcome across time or within-subjects.
Click on the Download Database and Download Data Dictionary buttons for a configured database and data dictionary for a Wilcoxon test. Click on the Adjusting for 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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