The Wilcoxon signed-rank test compares two related measurements (before and after, or two conditions from the same participants) when the differences are not normally distributed. It ranks the absolute differences and tests whether positive and negative changes balance out. SPSS prints the ranks in one table and the test statistic in another, leaving the effect size and medians for you to compute or extract. This guide reads both tables column by column using a worked example, covers the newer Nonparametric Tests output, lists the misreadings, and gives the APA 7 write-up. The reporting format alone is in the Wilcoxon signed-rank APA guide.
What SPSS gives you
Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples, with Wilcoxon ticked, produces:
- Ranks: the count of negative (improvement) and positive (worsening) ranks, their mean ranks and sum of ranks, plus ties (zero differences).
- Test Statistics: the Z statistic (normal approximation) and the two-sided p value.
Analyze > Nonparametric Tests > Related Samples (the newer procedure) gives the same test in a different layout; see the section on it below.
Neither procedure prints the medians you report or the effect size. Get medians from Analyze > Descriptive Statistics > Explore, placing both variables in the Dependent List (paired data has no grouping variable), or from Analyze > Descriptive Statistics > Frequencies or Descriptives.
The worked example
Twenty-three employees completed an anxiety scale (1 to 10, higher is more anxious) at the start and end of a 3-day training programme. In the dialog, anxiety (start) was entered as Variable 1 and anxiety (end) as Variable 2. The difference scores had some skewness, so a Wilcoxon signed-rank test was chosen over a paired t-test. All numbers below come from one dataset.
From Explore, or examining the data: start Mdn = 6.0; end Mdn = 5.0.
Table 1: Ranks
| N | Mean Rank | Sum of Ranks | ||
|---|---|---|---|---|
| Anxiety (end - start) | Negative Ranksᵃ | 17 | 11.00 | 187.00 |
| Positive Ranksᵇ | 4 | 11.00 | 44.00 | |
| Tiesᶜ | 2 | |||
| Total | 23 |
ᵃ. end < start ᵇ. end > start ᶜ. end = start
- Negative Ranks: 17 employees showed improvement (end < start). SPSS computes differences as the second variable minus the first (end − start), so negative differences appear here. Mean rank is 11.00; sum is 187.00.
- Positive Ranks: 4 employees showed decline (end > start). Mean rank is 11.00, sum is 44.00.
- Ties: 2 employees had identical scores at both time points (end = start, zero difference). They are excluded from the test but counted in the Total.
- Total: 23 people (17 + 4 + 2).
SPSS ranks the absolute values of all non-zero differences from smallest to largest, assigns tied absolute values the average of their ranks, then sums the ranks within each direction. Mean rank is the average position in the ranking, not a value on the original scale.
Table 2: Test Statistics
| Anxiety (end - start)ᵃ | |
|---|---|
| Zᵇ | -2.520 |
| Asymp. Sig. (2-tailed) | .012 |
ᵃ. Wilcoxon Signed Ranks Test ᵇ. Based on positive ranks.
- Z = −2.520: the test statistic, the sum of positive ranks (44.00, the smaller of the two sums) converted to a standard normal score, corrected for ties. The sign reflects which sum was smaller; the magnitude measures how far from symmetry the ranks fall. A Z near zero means equal numbers of improvements and worsenings; large |Z| means one direction dominates.
- Asymp. Sig. (2-tailed) = .012: the two-sided p value from the normal approximation, obtained by comparing |Z| to the standard normal distribution. This is the p value you report. For small samples, SPSS can add an Exact Sig. (2-sided) row, which is more accurate than the asymptotic approximation; say which you report.
Note: SPSS prints Z based on the smaller sum of ranks; the footnote or label will tell you which direction that is.
The effect size SPSS does not print
Compute r from Z and the total sample size: r = |Z| / √N. Here, N = 23 (number of pairs), so r = 2.520 / √23 = .53. By common benchmarks (.10 small, .30 medium, .50 large), that is a large effect. Some fields use the count of non-zero pairs (21) instead: 2.520 / √21 = .55. Others use total observations (46): 2.520 / √46 = .37. State which you used.
The newer Nonparametric Tests output
The Related Samples procedure (not Legacy Dialogs) starts with a Hypothesis Test Summary that states the null hypothesis and says "Reject the null hypothesis" or "Retain the null hypothesis". Its detail view has a Related-Samples Wilcoxon Signed Rank Test Summary with:
- Total N: the sample size (23).
- Test Statistic: the sum of ranks from the smaller group (here 44.00, the positive ranks).
- Standard Error: the standard deviation of the test statistic under the null hypothesis (28.377).
- Standardized Test Statistic: the Z you use for r (−2.520).
- Asymptotic Sig. (2-sided test): the p value (.012).
The newer procedure calls the null distribution "the distribution of differences is symmetric about zero", which is clearer than "no difference between the two variables". Both are the same test.
Misreadings that cost marks
- Reporting mean ranks as if they were medians. Report medians (from Explore or the data) on the original scale; use mean ranks only for direction.
- Leaving out the effect size. SPSS does not print one, so compute r = |Z| / √N.
- Reading direction from the sign of Z. It depends on which sum SPSS picked. The count of negative vs positive ranks, or the medians, tells you the direction.
- Including ties in the ranking. SPSS excludes zero differences from the test but counts them in the Ties row and the Total. The rank sums do not include them.
- Writing p = .000. Write p < .001 if p is below .001.
- No leading zero on r or p. APA 7 drops it.
- Applying it to independent groups. For two separate groups use the Mann-Whitney U test instead. The signed-rank test is for paired or repeated measures.
The APA 7 format template
A Wilcoxon signed-rank test showed that [dependent variable] was significantly higher/lower at [time 2] (Mdn = X.XX) than at [time 1] (Mdn = X.XX), z = X.XX, p = .XXX, r = .XX.
Report medians for each condition, not means and SDs. The effect size r is optional but recommended.
The write-up for this example
A Wilcoxon signed-rank test showed that anxiety at the end of the programme (Mdn = 5.0) was significantly lower than anxiety at the start (Mdn = 6.0), z = −2.52, p = .012, r = .53.
Or, focusing on the direction and count:
A Wilcoxon signed-rank test showed that 17 of 23 employees reported lower anxiety after the programme than before, a statistically significant improvement (start Mdn = 6.0, end Mdn = 5.0), z = −2.52, p = .012, r = .53.
The direction comes from the Ranks table and the medians, not from the sign of Z: 17 employees reported lower anxiety at the end and 4 reported higher, and the median fell from 6.0 to 5.0. The p value (.012) indicates that a difference this large would be unlikely if there were no true change from before to after. The second form is especially useful when direction matters more than whether medians differ on the scale.
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 spreadsheet, extracts the medians, computes the effect size r, and writes the APA 7 sentence, table and plot, with the Python or R code behind every number.
Also useful for the write-up (affiliate links): Proofreading for your thesis or paper (20% off with code PAP20): Paperpal
Frequently asked questions
What do I report for a Wilcoxon signed-rank test? The medians of both conditions, the z statistic, the p value and the effect size r. Report the count of improvements and worsenings if it matters to your story.
Do I report mean ranks or medians? Medians. Mean ranks are the average rank of the absolute differences in each direction; they are not on the scale and are harder for readers to understand. Use mean ranks only to check direction; report the medians.
How is the effect size r computed for a Wilcoxon test? r = |Z| / √N, where N is the total sample size. Some authors use the count of non-zero pairs instead; state which you used.
What if I have no effect size in the output? SPSS does not print one. Divide the absolute value of Z by the square root of N.
What does Ties mean? Zero differences (people with identical scores at both time points). They are excluded from the ranking and the test but counted in the Ties row and the Total. A high proportion of ties can weaken the test.
Should I report Asymp. Sig. or Exact Sig.? Asymp. Sig. (the normal approximation) is the default. For small samples with few ties, the Exact Sig. is more accurate; name whichever you report.
Why do the two procedures (Legacy and Nonparametric Tests) show different layouts? They are the same test, just presented differently. Legacy Dialogs use the older SPSS interface; Nonparametric Tests is the newer menu. Both produce the same Z and p-values.
When should I use this test instead of a paired t-test? Use it when the difference scores are badly non-normal (especially in small samples), or when the outcome is ordinal. If the differences are approximately normal, the paired t-test is more powerful. See our guide on reporting a paired t-test.
Which related guides might I need? Often these: Wilcoxon signed-rank APA format, paired t-test output, Mann-Whitney U for independent groups, and effect size r.