Does the Wilcoxon signed-rank test compare medians?

Only when the distribution of the paired differences is symmetric. The test's null hypothesis is that the differences are distributed symmetrically around zero, so without that symmetry it detects a rank-based shift rather than a change in the median specifically.

What assumption does the Wilcoxon signed-rank test actually require?

Symmetry of the paired differences, not normality of the raw scores. That is weaker than the paired t-test's normality requirement, but it is a real assumption and is rarely reported as checked.

When should you use the Wilcoxon signed-rank test instead of a paired t-test?

When the paired differences are not close enough to normally distributed for the paired t-test to be defensible. Both tests use the same paired design; the Wilcoxon version ranks the differences instead of assuming their distribution.

Wilcoxon Signed-Rank Test: How to Report It

The rank sum answers a question about the whole distribution of differences, not the number in Table 2.

The sentence that's in half the Methods sections

Open almost any paper that ran a Wilcoxon signed-rank test on paired data — pre- and post-operative scores, two raters on the same patients, a symptom scale before and after an intervention — and the Results sentence is nearly always some version of: "the median [outcome] decreased from X to Y (Wilcoxon signed-rank test, P = .0##)." That phrasing treats the test as a direct analogue of the paired t-test with medians swapped in for means: same logic, same one-number summary, just rank-based instead of mean-based.

It isn't quite that. The paired t-test asks whether the mean of the differences is zero, under an assumption that the differences are approximately normal. The Wilcoxon signed-rank test's actual null hypothesis is about the whole distribution of the paired differences — specifically, whether that distribution is symmetric around zero.¹ The test becomes a clean test of the median of the differences only when that distribution is symmetric to begin with. If it isn't, the test can still be perfectly valid and still reject the null, but "the median differed significantly" is no longer the sentence the P-value actually licenses.

What the test is actually built from

Mechanically, it's the rank-based counterpart of the paired t-test: same paired design, but built from the order of the differences rather than their raw values, which is what lets it drop the normality requirement.³ The test takes the difference between each pair of measurements, ranks the absolute values of those differences (discarding any exact zero), then sums the ranks separately for the positive and negative differences. The smaller of those two rank sums is the test statistic. Reviewers who are used to seeing a "W" or "T" statistic alongside a P-value are looking at that sum. The Mann-Whitney U test — its unpaired sibling, covered separately¹ — does the same ranking logic across two independent groups instead of within pairs, and carries an almost identical reporting problem: it's routinely written up as a test of medians when what it actually reflects is the probability that a randomly chosen observation from one group exceeds one from the other.² The signed-rank test's median caveat is the paired-data version of that same story.

The assumption that matters here is symmetry, not normality. The paired t-test needs the differences to be roughly normally distributed. The Wilcoxon signed-rank test relaxes that to a weaker requirement — that the distribution of the differences is symmetric about its centre — but it doesn't drop the requirement altogether.¹ A batch of differences with a long tail in one direction (a handful of large responders alongside a cluster of small changes) can be exactly the case where the test is still appropriate to run, and exactly the case where reporting the plain median as "what the test showed" stops being accurate.

Why the mismatch is easy to miss

It's easy to miss because nothing in SPSS, R, or any other package stops you from running the test on asymmetric differences, and nothing forces you to report the assumption you didn't check. A review of Wilcoxon procedures aimed at clinical researchers makes the point directly: a rank-based test and a simple comparison of medians can disagree — groups can look identical on their medians while the rank-based test still finds a significant shift, because the test is responding to the shape of the whole distribution, not just its middle value.² That's not a flaw in the test. It's a mismatch between what the test evaluates and the one-line summary most Results sections give it credit for.

A worked (illustrative) example

Say a small pilot study measures a 0–10 pain score in fourteen patients before and one week after a procedure. Twelve patients improve by 1–2 points. Two patients — for reasons unrelated to the intervention, perhaps a flare in a comorbid condition — get worse by 5–6 points. The median difference across all fourteen patients might land close to zero once those two outliers are counted, even though the overwhelming majority of patients improved. A Wilcoxon signed-rank test run on the signed ranks of those differences can still return a significant result, driven by the consistent small positive ranks outweighing the two large negative ones in the rank sum — while the raw median of the differences tells a much flatter story. Reporting "the median pain score improved significantly" in that scenario overstates what the median itself shows and understates what the test is actually responding to: a consistent rank-based shift, not a change in the midpoint value. (This is an illustrative scenario to show the mechanism, not a real published dataset.)

The fix in the Methods and Results isn't to stop using the test — it's usually the right test once a paired t-test's normality assumption is untenable. It's to plot or at least visually check the distribution of the differences before deciding whether "median difference" is a safe phrase, and to consider reporting the Hodges-Lehmann estimate of the shift or a rank-based effect size (such as matched-pairs rank-biserial r) alongside the P-value, rather than leaning on the raw median as if it were the test's direct output.

How to run it — SPSS vs StatsPlease

In SPSS Statistics⁴ (version 32.0, the current release), the paired Wilcoxon signed-rank test sits under Analyze ▸ Nonparametric Tests ▸ Legacy Dialogs ▸ 2 Related Samples. Move the two paired variables into the Test Pair(s) List, and leave "Wilcoxon" ticked under Test Type — the same dialog also offers the Sign test, McNemar's test, and Marginal Homogeneity, so it's worth confirming Wilcoxon is the one actually selected before running it. The output produces two tables: a Ranks table (breaking the sample into negative ranks, positive ranks, and ties, with the mean rank and rank sum for each) and a Test Statistics table, which is where the number that matters lives — the Z value and the two-tailed asymptotic significance. The most common misread is treating the medians shown elsewhere in the descriptive output as the quantity the Test Statistics table just tested, which, per the assumption above, is only literally true when the differences are symmetric.

Upload the dataset (or the relevant paired columns). StatsPlease's deterministic engine identifies the appropriate test from the variable type and study design, checks the relevant assumptions, computes the result using fixed, non-LLM algorithms, and drafts the Methods/Results sentence in AMA format — the same number a reader would get running the test by hand in SPSS.

You might also read

References

Hollander M, Wolfe DA, Chicken E. Nonparametric Statistical Methods. 3rd ed. Hoboken, NJ: John Wiley & Sons; 2014.
Divine GW, Norton HJ, Hunt R, Dienemann J. Statistical grand rounds: a review of analysis and sample size calculation considerations for Wilcoxon tests. Anesth Analg. 2013;117(3):699-710.
Nahm FS. Nonparametric statistical tests for the continuous data: the basic concept and the practical use. Korean J Anesthesiol. 2016;69(1):8-14.
IBM Corp. IBM SPSS Statistics for Windows, Version 32.0. Armonk, NY: IBM Corp; 2026.

The gap between "the test found a shift" and "the median changed" is exactly the kind of distinction that gets lost between a dataset and a Results sentence.

StatsPlease's deterministic engine checks whether your paired differences meet the paired t-test's normality requirement, routes to the Wilcoxon signed-rank test when they don't, and drafts the Results sentence to match what that test actually supports — a shift in the differences, not an unqualified claim about the median, unless the symmetry the sentence implies is really there.

Try StatsPlease free