How to Report a Wilcoxon Signed-Rank Test in APA 7 (With Example)

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:

1. The median (Mdn) for each condition. Report medians, not means.
2. The test statistic (T or W, depending on your software) and, for larger samples, the z approximation.
3. The exact p value.
4. 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.

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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:

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.

Run a Wilcoxon signed-rank test yourself, in the browser

sleep ships with R: extra hours of sleep for the same 10 patients on two different drugs, which is exactly the paired design this test is for. Runnable in your browser.

# Wilcoxon signed-rank: two sleep drugs, the same 10 patients.
# Note: paired = TRUE needs the two-vector form, not the formula form.
drug1 <- sleep$extra[sleep$group == 1]
drug2 <- sleep$extra[sleep$group == 2]

wilcox.test(drug1, drug2, paired = TRUE)

Running that gives:

Wilcoxon signed rank exact test

data:  drug1 and drug2
V = 0, p-value = 0.003906
alternative hypothesis: true location shift is not equal to 0

Every number in the write-up above comes from output like this. If you want the mechanics rather than the reporting, the free R lesson on this walks through it step by step, and the playground is there whenever you want to try something.

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.

What about three or more time points, or two separate groups? For three or more related conditions, use the Friedman test; for two independent groups, the Mann-Whitney U test; for three or more independent groups, the Kruskal-Wallis test. If the paired differences turn out roughly normal (Shapiro-Wilk will tell you), the paired t-test has more power.

Which related guides might I need? Often these: McNemar's test, descriptive statistics and p values.