Wilcoxon Signed Rank Test

The Wilcoxon Signed Rank Test is a non-parametric test for comparing the means of variables within one group (Repeated).

Assumptions
The assumptions of this test are as follows:
 * 1) Data must be at least at the ordinal level.

Parametric Equivalent
The parametric equivalent of this test is the Paired T-Test.

Example
You have a group of participants who fill out a pain score questionnaire before and after a 4 week long, twice weekly acupuncture treatment course. A Wilcoxon Signed Rank Test can be used to see if a significant difference exists between the pre-score and the post-score.

In SPSS
Click Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples...

By examining the final Test Statistics table, we can discover whether these changes, due to acupuncture treatment, led overall to a statistically significant difference in Pain Scores. We are looking for the Asymp. Sig. (2-tailed) value, which in this case is 0.071. This is the p value for the test. We report the Wilcoxon signed-ranks test using the Z statistic.

Writing up
A Wilcoxon signed-rank test showed that a 4 week, twice weekly acupuncture treatment course did not elicit a statistically significant change in lower back pain in individuals with existing lower back pain (Z = -1.807, p = 0.071). Indeed, median Pain Score rating was 5.0 both pre- and post-treatment.