How to Report a Wilcoxon Signed-Rank Test in APA 7

“A Wilcoxon test was conducted” is a sentence a reviewer cannot act on, because it does not say which of the two it was: the signed-rank test, which compares two measurements from the same person, or the rank-sum test, which is Mann-Whitney U wearing a different name. This is the write-up for the paired one, number by number, with the italics APA expects. The wider picture is in how to report non-parametric tests.

Which numbers go in

Four things plus one sample figure: the statistic (the signed-rank T, or whatever your software calls it), the normal-approximation z, the p value and an effect size. The sample figure is the number of pairs that entered the test, which need not match the number of participants.

That last detail is the one most often left out. The test works on within-person difference scores, and a difference of exactly zero carries no sign and takes no rank: most packages drop it. If you measured 39 people and three scored identically at both time points, your test ran on 36 pairs. Write that 36 down, because it is the n holding up the p value and, a section later, the effect size.

With small samples, below roughly 20 to 25 pairs, many packages return an exact p rather than the asymptotic one, and z stops meaning much. Say so explicitly: an exact test was used given the sample size. If you report the exact p and have no z, you will need another route to the effect size, and there is one below.

Italics: T, z, p, r, n, N and Mdn are all italicized. The leading zero depends on whether the statistic can exceed 1: T and z can, so a z = −0.87 keeps its zero; p and r cannot and go without it, p = .002, r = .36. Two decimals for T, z and r. IQR stays in roman type, because it is an abbreviation, not a statistic.

T, V, W or z: your software does not call it the same thing

The classic T from tables of critical values is the smaller of the two rank sums: add the ranks of the positive differences, add the ranks of the negative ones, and keep the smaller total. That is what the textbooks teach and what a reviewer trained before SPSS existed expects to see.

SPSS will not hand you that T. It gives you two tables: Ranks, with mean ranks and the sums of negative and positive ranks, and Test Statistics, with Z and the asymptotic two-tailed significance. The T comes out of the first table by hand, by taking the smaller sum. R calls V the sum of the positive ranks, which is not necessarily the smaller of the two. jamovi and JASP report a W and throw in the matched-pairs rank-biserial correlation.

The working rule is short: name the statistic and say where it came from. “T = 138.00, the smaller of the two rank sums” leaves nothing to argue about; a bare “W = 528” forces the reader to guess whether that is the positive sum, the negative sum or the smaller one, and those three numbers tell different stories. Always give z when you have it, because that is what feeds the effect size.

Medians and interquartile ranges, not means

This is the error I flag most often. If you reached for a rank test, it is because the mean does not describe your data well: skew, outliers, an ordinal scale with five anchors. Describing the two time points with M and SD straight afterwards contradicts you in the very next sentence, and reviewers notice.

What goes in is the median with the interquartile range for each condition: Mdn = 17.0, IQR = 14.0–20.0. Then add something almost nobody includes: the median of the individual difference scores with its IQR. That is what the test analyses. One participant improving by six points and another worsening by six cancel out when you compare group medians, but not in the signs, and signs are where Wilcoxon looks.

One precision that heads off a fussy reviewer: the test does not compare the two medians. If you are willing to assume the difference scores are symmetrically distributed, it tests whether the median of those differences is zero; without that assumption, it tests whether differences tend to fall on one side rather than the other. Writing that the medians differed significantly is a widespread shorthand, but it is still shorthand.

The effect size, and which N goes under the square root

APA 7 asks for an effect size every time, non-parametric tests included. The standard one here is r = |z| / √N, which reads like a correlation and uses Cohen’s (1988) benchmarks: around .10 small, .30 medium, .50 large. They are conventions for orienting the reader, not legal thresholds.

Here is the trap almost nobody declares. What is that N? The most widespread convention, from Rosenthal and the textbooks that followed him, counts observations: in a paired design each participant contributes two, so 36 pairs give N = 72. Other authors plug in the number of pairs. The same z = −3.06 yields r = .36 one way and r = .51 the other, which is the difference between publishing a medium effect and a large one. Neither is wrong; failing to say which one you used is.

If you would rather sidestep the ambiguity altogether, the matched-pairs rank-biserial correlation is a clean alternative, and jamovi and JASP produce it without being asked. It needs no translation: it is the sum of the ranks pointing one way minus the sum of those pointing the other, divided by the total rank sum, so a .60 says the weight of the change splits 80/20 in favor of improvement. It is bounded between −1 and 1, and it does not depend on what you decide to count.

If the result is already written up and you just want the number, the effect size from text tool pulls it out of the sentence you paste in.

A worked example for the Results section

“Insomnia severity decreased from baseline (Mdn = 17.0, IQR = 14.0–20.0) to post-program (Mdn = 11.0, IQR = 8.0–14.0). Three participants showed no change and their zero differences were excluded, so the Wilcoxon signed-rank test was computed on 36 pairs. The reduction was significant, T = 138.00, z = −3.06, p = .002, with a medium effect, r = .36, computed as |z| / √N with N = 72 observations. The median individual change was −5.0 points (IQR = −8.0 to −2.0). A rank test was used because the difference scores were markedly skewed.”

That paragraph has five moving parts and none of them is padding: the two conditions described, what happened to the pairs that dropped out, the test itself, the effect size with its formula declared, and the justification for not running a paired-samples t test. The last one is missing from nine manuscripts out of ten.

If you are staring at the two SPSS tables and cannot tell which row to copy or which rank sum is yours, paste the output into the results interpreter and it comes back written in APA style.

Wilcoxon or Mann-Whitney: paired versus independent

The confusion has a historical root. Wilcoxon published two tests in the same 1945 paper: the signed-rank test for paired measures and the rank-sum test for independent groups, and the second is mathematically equivalent to Mann-Whitney U. So when someone writes “the Wilcoxon test”, they often mean Mann-Whitney. Always use the full name.

To decide, look at one row of your spreadsheet. If a row is a person with two score columns — before and after, condition A and condition B, right eye and left eye — it is the Wilcoxon signed-rank test. If a row is a person with one score and a group label, it is Mann-Whitney U. Deliberate pairing counts as paired too: twins, patient and carer, cases matched on age and sex.

With three or more time points, neither applies: that is Friedman’s test, or a mixed model if you have missing data you would rather not throw away. The parametric version of that design is covered in how to report a repeated measures ANOVA.

A closing word on power. Abandoning the paired-samples t test just in case costs you sample size, and with reasonably symmetric differences the t holds up well. The decision is made by looking at the distribution of the difference scores, not at the raw scores at each time point, which is the classic mistake: you can have two badly skewed distributions and perfectly symmetric differences between them.

Frequently asked questions

What do you report for a Wilcoxon signed-rank test in APA 7?

The statistic (the signed-rank T, or whatever your software returns), the normal-approximation z, the p value, an effect size — usually r = |z| / √N — and the number of pairs that entered the test. Describe each condition with a median and an interquartile range, and close with one sentence explaining why a rank test rather than a paired-samples t test.

What is the difference between the Wilcoxon signed-rank test and Mann-Whitney U?

The signed-rank test is for paired measures: the same person measured twice, or two conditions within the same participant. Mann-Whitney U compares two independent groups. The confusion comes from Wilcoxon also publishing a rank-sum test that is equivalent to Mann-Whitney, which is why you should always write signed-rank when you mean the paired one.

How do you calculate the effect size for a Wilcoxon signed-rank test?

With r = |z| / √N. The argument is about N: the most widespread convention counts observations, so 36 pairs give N = 72, while other authors use the number of pairs. With z = −3.06 that is .36 one way and .51 the other, so you have to declare which you used. jamovi and JASP also give the matched-pairs rank-biserial correlation.

Do you report means or medians with a Wilcoxon signed-rank test?

Medians with interquartile ranges. If you chose a rank test it is because the mean does not describe your data well, so describing the conditions with means and standard deviations afterwards is incoherent. Add the median of the individual difference scores with its interquartile range as well, since that is what the test analyses.

Should I report T, W or z for a Wilcoxon test?

Both the statistic and z if you have them. T is the smaller of the two rank sums and is what textbooks use; z is the normal approximation your software prints, and it is what feeds the effect size. With small samples and an exact p value, z stops being meaningful and the statistic, the number of pairs and the exact p are enough.

What happens to zero differences in a Wilcoxon signed-rank test?

They are dropped, because a difference of zero has no sign and cannot be ranked. That reduces the effective n: if you measured 39 people and three did not change, the test runs on 36 pairs. Report both numbers, participants and pairs analyzed, and compute the effect size from the 36 that entered rather than the 39 you started with, saying whether you are counting pairs or observations.

With the statistic and its z, the p value, an effect size whose N is declared, and medians instead of means, your Wilcoxon test is properly reported. If you are weighing a rank test against a paired-samples t test with your own data in front of you, that is what my statistical consulting is for.