Wilcoxon Signed-Rank Test: How to Run It Online and Report It in APA7
The Wilcoxon signed-rank test compares two related measurements using the ranks of the differences. It is the non-parametric counterpart of the paired-samples t-test.
What is Wilcoxon Signed-Rank Test?
The Wilcoxon signed-rank test compares two related measurements using the ranks of the differences. It is the non-parametric counterpart of the paired-samples t-test.
When to use it
Use it for before and after data or matched pairs when the differences are not normal, the outcome is ordinal, or the sample is small.
Example question: Did stress ratings change from before to after the programme?
Preparing your data
Wide format: one row per participant and two numeric columns (for example before and after).
Example dataset (simulated; first rows of 25): id, before, after (0 to 10 stress ratings for the same participants); wide format.
| id | before | after |
|---|---|---|
| 1 | 6 | 3 |
| 2 | 4 | 3 |
| 3 | 10 | 9 |
| 4 | 2 | 0 |
| 5 | 5 | 4 |
| 6 | 3 | 0 |
Download the full example CSV to practise. If the tool asks for a different layout, follow the instructions on its page.
How to run it on StatFas
- Open the Wilcoxon Signed-Rank Test tool. You do not need an account to run an analysis.
- Enter your data or upload your file, laid out as described in Preparing your data.
- Select your variables. Select the two paired columns.
- Choose any options the tool offers (for example the confidence level, a post hoc test or the error bar type) and run the analysis.
- Read the results on the page. Check the assumptions first, then the test statistic, the p-value and the effect size.
- To save your results, log in or create a free account. Every analysis stays free; the account is only needed to download.
Assumptions and checks
- The pairs are the same participants (or matched pairs) and are independent of other pairs.
- The outcome is at least ordinal and the differences can be ranked.
- The distribution of the differences is roughly symmetric around the median.
- Pairs with a difference of exactly zero are dropped, which reduces the effective sample size.
Key numbers to look at
- Sum of positive and negative ranks and the test statistic (T or W).
- Standardised z and p-value.
- Number of positive, negative and tied differences.
- Medians at both time points.
Effect size
Report r = z / √N, where N is the total number of observations (two per participant), or the matched-pairs rank-biserial correlation. About .10 small, .30 medium, .50 large.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Wilcoxon Signed-Rank Test in APA7 style
Template
Worked example (simulated data)
The numbers below were computed from the example CSV above, so you can reproduce them. They illustrate the format and are not real findings.
APA7 reminders: italicise statistical symbols (M, SD, t, F, p, r), report exact p-values to two or three decimals (use p < .001 for very small values), omit the leading zero for values that cannot exceed 1 (.45, not 0.45), and put degrees of freedom in parentheses. See the APA7 cheat sheet.
Common mistakes
- Using it for independent groups (use Mann–Whitney instead).
- Ignoring the large number of zero differences with short scales.
- Not reporting how many pairs were used.
Related analyses and alternatives
- Paired t-Test: If the differences are roughly normal.
- Friedman Test: Three or more related measurements.
- Mann-Whitney U-test: Independent groups.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
What does the sign of z mean?
It depends on the software and on which measurement is subtracted from which. Always state the direction of the change in words, supported by the medians or mean ranks.
Can I use it for one sample?
Yes, by testing the differences from a hypothesised median, but the one-sample t-test is more common for continuous data.
References
American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
This guide is for learning and for preparing results for your own reports. You remain responsible for choosing an appropriate analysis, checking its assumptions and interpreting the results. Follow the formatting rules of your journal or institution where they differ from APA7.