SPSS command: SPSS NPAR TESTS /WILCOXON

Wilcoxon signed-rank test in your browser

The Wilcoxon signed-rank test compares two measurements on the same cases by ranking the size of each paired difference and checking whether positive and negative changes balance out.

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Free · No account · Files stay on your device · Updated 18 October 2026

Worked example result

Test Statistics — Wilcoxon Signed Ranks Test · after - before

Z = −1.965

p = .049 · Effect size r = |Z|/√N = 0.491

Item	after - before
Z	−1.965
Asymp. Sig. (2-tailed)	.049
Exact Sig. (2-tailed)	.051
Effect size r = \|Z\|/√N	0.491

Test Statistics — Wilcoxon Signed Ranks Test

See the full worked example

What it tells you

Crosstabs runs it as SPSS NPAR TESTS /WILCOXON, with the sign test and McNemar's test for paired yes/no outcomes in the same panel.

How many cases went up, went down or stayed the same (positive ranks, negative ranks and ties), with mean and summed ranks.
Whether the changes lean in one direction more than chance allows: tie-corrected Z with asymptotic and, where available, exact two-tailed significance.
The size of the change as r = |Z|/√N, where N counts every analysed pair.
For coarse data, whether pluses and minuses balance (sign test), and for two binary variables, whether the share of “yes” changed (McNemar).

When to use it

Use it when

Before/after or pre/post measurements on the same people where the differences are skewed or contain outliers.
Two ratings given by the same respondent, such as importance and satisfaction on a 1–5 scale.
Matched pairs (twins, matched stores) compared on an ordinal outcome.
A yes/no item asked twice of the same people: use McNemar to test whether the proportion changed.

Use something else when

Two independent groups: use the Mann-Whitney U test.
Three or more measurements of the same cases: use the Friedman test or repeated-measures ANOVA.
Roughly normal differences and a need for a confidence interval for the mean change: the paired-samples t test is more informative.

How to run it in Crosstabs

01
Choose Two related samples
In Statistics mode open Nonparametric tests → Two related samples (NPAR TESTS /WILCOXON).
02
Build the test pairs
Under Test pairs choose Variable 1 and Variable 2, then click Add pair. Repeat for more pairs. Differences are computed as Variable 2 − Variable 1.
03
Choose the tests
Under Test type tick Wilcoxon (the default), Sign and/or McNemar. McNemar needs exactly two values across both variables, such as 0/1.
04
Set missing values and run
Exclude cases test-by-test drops a case only from pairs where it is missing; Exclude cases listwise drops it from every pair. Click Run test.

Run Wilcoxon Signed-Rank Test in your browser

Worked example

Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.

Try with example data

Data

16 synthetic users with weekly active minutes measured before and after a feature launch. Baseline usage is log-normal and each user's change is a random multiplicative shift, so differences are skewed.

Ranks — Wilcoxon Signed Ranks Test

after - before	N	Mean Rank	Sum of Ranks
Negative Ranks	4	7.50	30.00
Positive Ranks	12	8.83	106.00
Ties	0
Total	16

Negative ranks: after < before. Positive ranks: after > before.

Test Statistics — Wilcoxon Signed Ranks Test

Item	after - before
Z	−1.965
Asymp. Sig. (2-tailed)	.049
Exact Sig. (2-tailed)	.051
Effect size r = \|Z\|/√N	0.491

Based on negative ranks.

How to read it

12 of 16 users used the product more after the launch and 4 used it less. The positive ranks sum to 106.0 against 30.0 for the negative ranks, giving Z = −1.96, exact p = .051 and r = 0.49. The asymptotic p (.049) falls on the other side of .05; with only 16 pairs, report the exact value.

Output tables explained

Ranks — Wilcoxon Signed Ranks Test: Negative ranks (second < first), positive ranks (second > first) and ties, each with N, mean rank and sum of ranks.
Test Statistics — Wilcoxon Signed Ranks Test: Z (based on the smaller rank sum), asymptotic and exact two-tailed significance and r = |Z|/√N. The exact value appears when there are no tied absolute differences and at most 50 non-zero differences.
Test Statistics — Sign Test: Counts of negative and positive differences and ties (in Frequencies — Sign Test), with an exact binomial significance for up to 25 non-tied pairs and a continuity-corrected Z above that.
Test Statistics — McNemar Test: N, chi-square and significance for the paired 2 × 2 table shown above it; exact binomial for up to 25 discordant pairs, continuity-corrected chi-square otherwise.

Assumptions and notes

Pairs are independent of each other, and both values in a pair belong to the same case or matched unit.
Differences can be ordered by size; the signed-rank test also assumes they are roughly symmetric around their median. If not, use the sign test.
Zero differences are dropped from the ranking but still counted as ties and in N for r.

How the results are validated

The paired engines are tested against independent reference values computed with SciPy 1.18.1, statsmodels 0.15.0, pingouin 0.7.0 and scikit-posthocs 0.17.1: Wilcoxon statistics, Z and exact and asymptotic p-values match scipy.stats.wilcoxon, the sign test matches scipy.stats.binomtest for up to 25 pairs and the SPSS normal formula above, and McNemar matches statsmodels mcnemar in exact and continuity-corrected forms, all within 1e-9 (relative to the larger of 1 and the reference value). Validation evidence

Questions

Which direction is a positive rank?

Differences are Variable 2 − Variable 1, so a positive rank means the second variable is higher. Put the “before” measure as Variable 1 to read positive ranks as increases.

Why is there no exact p value in my output?

The exact signed-rank distribution is used only when no absolute differences are tied and there are at most 50 non-zero differences. Otherwise the tie-corrected asymptotic value is the one to report.

When should I use the sign test instead?

When only the direction of change is trustworthy, for example coarse ratings where a 1-point and a 3-point change should not be weighted differently, or when the differences are clearly asymmetric.

Can McNemar handle answers coded 1/2 instead of 0/1?

Yes. Any two codes work as long as exactly two distinct values appear across both variables; value labels are used for the 2 × 2 table.

Run Wilcoxon Signed-Rank Test on your own data

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