METHOD GUIDE
Wilcoxon Signed-Rank Test in SPSS
Symmetry of Differences and the Effect Size r
The test works on the differences within pairs, and what it says about them depends on their shape. SPSS prints counts of ranks, ties and a Z, but no effect size, so r has to be added to the write-up.
IN SHORT
What the Test Says About Paired Differences
A Wilcoxon signed-rank test analyzes the differences between two linked measurements by ranking their absolute size and comparing the ranks of the positive and negative differences. It fits an ordinal or continuous outcome measured twice on the same cases or in matched pairs. To run the Wilcoxon signed-rank test in SPSS, open Analyze, Nonparametric Tests, Related Samples (Legacy Dialogs, 2 Related Samples in the older layout), pair the two variables, choose the Wilcoxon test, and plot the differences before making any statement about their center. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, carries out and reviews this analysis through an in-house PhD-level statistician.
ANALYSIS SUPPORT
Analysis Support for This Method
The signed ranks show whether changes lean one way. When the size of the mean change is what matters instead, the paired t-test is the better match, and both analyses can be carried out for your study.
Wilcoxon Signed-Rank Test
The paired rank-based analysis carried out within your study design, with the check on the differences, the effect size with an interval and the reporting agreed for your data.
Paired Samples t-Test
The comparison of two linked measurements through the mean of the differences, for a continuous outcome when the mean change is what the research question asks about.
BEFORE YOU RUN IT
Questions to Settle About the Differences
The test acts on the differences, so four questions about them are answered before SPSS is opened, and each one changes how the result may be worded.
Linked Measurements Each case has two measurements, or one member of a matched pair sits in each condition. Independent groups need a rank test for independent samples, and three or more occasions need another test.
Differences That Can Be Ranked Ranking the size of differences assumes that a change of two points means more than a change of one. That suits scores and counts better than a single coarse ordinal item with a few categories.
Shape of the Differences Plot the differences. If they are roughly symmetric around their center, the result reads as a shift in location. Clear skew in the differences calls for wording about ranks of changes.
Zeros and Ties Unchanged pairs, which SPSS lists as Ties, are dropped before ranking, while equal nonzero differences share an average rank. Report how many pairs entered the test, not only how many took part.
IN SPSS
How to Run the Wilcoxon Signed-Rank Test in SPSS
The outline is for IBM SPSS. The SPSS related samples test dialog and the legacy dialog print different tables, so the layout used is noted for the write-up.
- Confirm the design: one outcome measured twice per case, or matched pairs, in two columns on one row per pair.
- Compute the difference for each pair and plot it in a histogram to judge symmetry and extreme values.
- Open Analyze, Nonparametric Tests, Related Samples (Legacy Dialogs, 2 Related Samples in the older layout), and select the two variables as a pair.
- Choose the Wilcoxon signed-rank test, and in the legacy dialog confirm that Wilcoxon is ticked under Test Type.
- Read the number of positive, negative and tied differences before the test statistic.
- Calculate the effect size r from the standardized statistic and the sample size, and record which N was used.
READING THE OUTPUT
What the Ranks, Ties and Z in the Output Mean
The output gives signed counts and a standardized statistic but no estimate of the change itself, and the footnote naming the ranks behind Z is the element most often misread.
| Output element | What it tells you | What to check |
|---|---|---|
| Hypothesis Test Summary | The null hypothesis and the decision at the default .05 | That the Reject or Retain wording is replaced in the text by Z, p and the direction of change |
| Ranks: Negative Ranks, Positive Ranks, Ties | The number of pairs that fell, rose or stayed equal, with mean rank and sum of ranks | That the direction labels follow the order of the two variables in the pair, and that ties are counted |
| Footnote under Test Statistics | Whether Z is based on the positive or the negative ranks | That the sign of Z is read with this footnote and not as the direction of change |
| Z (Standardized Test Statistic) | The normal approximation of the signed-rank statistic, corrected for ties | That it is the input for r and is reported with the number of pairs |
| Asymp. Sig. (2-tailed) (Asymptotic Sig. (2-sided test) in the Related Samples dialog) | The p-value from the normal approximation | That small samples are checked against exact significance where your license offers it |
| Related-Samples Wilcoxon Signed Rank Test view (recent layouts) | A histogram of positive and negative differences with counts and ties | That symmetry is judged from this plot, and not from the p-value |
| Descriptive Statistics (optional) | The median and quartiles of each measurement | That these describe each occasion, while the test acts on the differences |
REPORTING
Reporting the Test With r and the Pairs Used
Every blank in the frame below is filled from your output or your own calculation, and the frame itself states no finding.
Write the core as Z = ___, p = ___, with the number of pairs that entered the ranking and the number of ties set aside. Add the effect size r = Z divided by the square root of N, and state which N was used, because the number of pairs and the number of observations give different values. SPSS prints no interval for r, so an interval, if the journal wants one, needs a bootstrap or other software. Describe the change with the median and interquartile range of the differences, or of the two measurements, and a plot, and say in words in which direction scores moved. When the differences are symmetric, the result can be worded as a shift in location. When they are not, word it as a tendency for changes to be positive or negative.
COMMON MISTAKES
How Signed-Rank Results Get Over-Read
Six points recur when this test is queried in a thesis or manuscript, and half of them come from the sign and the shape of the differences.
Medians Without Symmetry The differences are reported as a change in the median without checking that they are symmetric. Without symmetry the test compares positive and negative ranks, which is a different statement.
Z Read Without Its Footnote The sign of Z depends on whether it is based on positive or negative ranks. A negative Z beside an increase confuses readers, so the direction is stated in words and checked in the Ranks table.
Ties Not Counted Pairs with zero difference leave the ranking. A study in which many participants did not change has a smaller effective sample than its N, and the text reports the number of ties.
r Without Its N The effect size r is calculated from Z and N, and pairs and observations give different values. The N used is named so that another analyst can reproduce the figure.
More Than Two Occasions Running pairs of occasions one after another inflates the chance of a spurious finding and ignores the structure. Three or more related measurements call for one overall test with adjusted follow-ups.
Independent Groups as Pairs Two groups of equal size placed side by side as if paired give a test that ignores the design. Pairing comes from how participants were measured, and not from the layout of the data file.
Already run this analysis? Independent Statistical Review checks the pairing, the handling of ties and the effect size before you submit.
FREQUENTLY ASKED QUESTIONS
Questions About the Signed-Rank Output
How r is obtained, why Z turns negative when scores rise and which descriptives to give are the points this output raises most often.
How is the Wilcoxon effect size r obtained from SPSS output?
Divide the standardized statistic Z by the square root of N, and state which N was used. SPSS does not print r. With N as the number of pairs or as the number of observations the value differs, so the choice is named. Values of about .1, .3 and .5 are often quoted as small, medium and large, but these are rough guides, and an interval from a bootstrap is more informative than a label.
Why is the Z in my output negative when scores went up?
The sign of Z follows the rank sum the statistic is based on, as the footnote says, and not the direction of the change. Read the direction from the counts of positive and negative ranks and from the order of the two variables in the pair. Then state the direction in words, and leave the sign of Z out of the sentence.
Should I report descriptives for each measurement or for the differences?
Report both, because they answer different questions. The test acts on the differences, while readers also want the level of the outcome at each occasion. The difference between the two medians is generally not the median of the differences, so the summary of the differences is given when the text speaks about the change.
Can a statistician check the pairing and effect size in my signed-rank analysis?
Yes. An in-house PhD-level statistician can confirm that the pairing fits how the measurements were taken, review the handling of ties and the effect size in your output, or carry out the analysis from the start. For the tables and the write-up alone, Results Reporting & Interpretation covers that stage. The interpretation remains yours.
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You share your research question, design and relevant materials, such as the dataset or the output you have, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
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