The Wilcoxon signed-rank test is the non-parametric alternative to the paired-samples t-test: it compares two related measurements (before and after, or two conditions from the same participants) when the difference scores are not normally distributed. Because it works on ranks, the APA 7 write-up uses medians and a rank-based effect size. This guide gives you the exact format, a worked example you can copy, and the mistakes reviewers catch.
What you need before you write a single word
An APA 7 write-up of a Wilcoxon signed-rank test needs these values from your output:
- The median (Mdn) for each condition. Report medians, not means.
- The test statistic (T or W, depending on your software) and, for larger samples, the z approximation.
- The exact p value.
- An effect size: r = z divided by the square root of N, where N is the number of observations (pairs times 2, or as your software defines it).
The APA 7 format template
Report the result in running text using this pattern:
A Wilcoxon signed-rank test showed that [dependent variable] was significantly higher/lower at [condition 2] (Mdn = XX) than at [condition 1] (Mdn = XX), z = X.XX, p = .XXX, r = .XX.
Formatting rules reviewers actually check:
- Italicize Mdn, z, p, and r.
- Report medians for each condition, not means and standard deviations.
- No leading zero on p or on r.
- Round z and r to two decimals. If p is below .001, write p < .001.
- State the direction of the change.
A worked example
Suppose you measured a symptom score (0 to 20, skewed) before and after treatment in 18 participants.
- Before (n = 18): Mdn = 12
- After (n = 18): Mdn = 8
- Result: z = -2.98, p = .003, r = .50
Written up in APA 7, that becomes:
A Wilcoxon signed-rank test showed that symptom scores were significantly lower after treatment (Mdn = 8) than before treatment (Mdn = 12), z = -2.98, p = .003, r = .50.
The sentence carries the medians, the z approximation, the significance, and the effect size.
The APA 7 table (optional)
For a results chapter, a small table keeps the summary out of the prose. APA tables use horizontal rules only:
| Condition | n | Mdn |
|---|---|---|
| Before | 18 | 12 |
| After | 18 | 8 |
Note. Symptom score on a 0 to 20 scale. The reduction was significant, z = -2.98, p = .003, r = .50.
Mistakes reviewers catch
- Reporting means and SDs. The test ranks the difference scores, so report medians.
- Using it on independent groups. For two separate groups of different people use the Mann-Whitney U test, not the signed-rank test. See our guide on reporting a Mann-Whitney U test.
- No effect size. Report r (z divided by the square root of N). Roughly, .10 is small, .30 is medium, .50 is large.
- Confusing the two Wilcoxon tests. The signed-rank test is paired; the rank-sum test is the same as Mann-Whitney and is for independent groups.
- Writing p = .000. Report p < .001.
- A leading zero on p or r. APA drops it.
When to use it instead of a paired t-test
Use the Wilcoxon signed-rank test when:
- The difference scores are badly non-normal, especially in small samples, or
- The dependent variable is ordinal, or
- Extreme outliers would distort the mean difference.
If the difference scores are approximately normal, the paired t-test is more powerful. See our guide on reporting a paired-samples t-test.
Let KyroStat do the write-up for you
Formatting a rank-based paired test, with medians and the right effect size, is where errors creep in. KyroStat runs the Wilcoxon signed-rank test on your data, reports the medians and z approximation, computes the effect size, and hands you the finished APA 7 sentence and the underlying Python or R code. Upload your spreadsheet, and the report is done in seconds.
Frequently asked questions
Should I report means or medians for a Wilcoxon signed-rank test? Medians. The test works on ranked difference scores, so medians describe the conditions appropriately.
What is the difference between the signed-rank and rank-sum tests? The signed-rank test is for paired or repeated measures. The rank-sum test (equivalent to Mann-Whitney U) is for two independent groups.
What effect size should I report? r = z divided by the square root of N. Report it without a leading zero.
My p value shows as .000. What do I write? Report p < .001. A p value is never exactly zero.