What is the difference between Wilcoxon and Mann-Whitney?

The Wilcoxon signed-rank test is for paired data from the same people. The Mann-Whitney U test is for two independent groups of different people.

What happens to zero differences?

Pairs with no change are dropped before ranking, as in SPSS and R. The number of pairs used is shown in the result.

Can I use it for Likert scale data?

Yes. It is a standard choice for comparing two paired Likert ratings, such as before and after an intervention.

WILCOXON SIGNED-RANK TEST CALCULATOR

Wilcoxon signed-rank test calculator for paired data.

Compare two related measurements, such as pre-test and post-test scores from the same people, when the differences are not normally distributed. You get T, z, the p value, medians, effect size r, and an APA sentence.

PAIRED DATA

Same participants, two measurements

NON-PARAMETRIC

BEFORE (TIME 1)AFTER (TIME 2)

Keep the same order in both columns: the first value in each column must belong to the same participant.

Wilcoxon signed-rank test: when to use it, steps, and reporting

When to use it

The same participants are measured twice (pre-test and post-test, two conditions)
The differences are skewed or ordinal, such as single Likert items
It is the non-parametric alternative to the paired-samples t-test
For two different groups of people, use the Mann-Whitney U test instead

How it works

T = min(W⁺, W⁻), z = (W⁺ − n(n+1)/4) ÷ √[n(n+1)(2n+1)/24 − Σ(t³−t)/48]

Take each after − before difference, drop zeros, rank the absolute differences (ties share the average rank), then add the ranks of the positive differences (W⁺) and negative differences (W⁻).

Wilcoxon signed-rank vs paired t-test

Check the differences with a Shapiro-Wilk test. If they look roughly normal, the paired t-test has more power. If they are clearly skewed, have outliers, or come from ordinal ratings, use Wilcoxon.

How to report it (APA style)

“A Wilcoxon signed-rank test indicated that post-test scores (Mdn = 16.0) were significantly higher than pre-test scores (Mdn = 14.5), T = 2, z = 2.61, p = .009, r = .83.” Report medians, T, z, p, and r.

References

Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83.
Rosenthal, R. (1991). Meta-Analytic Procedures for Social Research (rev. ed.). SAGE.

Wilcoxon Signed-Rank Test Calculator

The non-parametric alternative to the paired t-test for pre-test/post-test and repeated measurements, with exact p values for small samples.

Compare pre-test and post-test scores from the same students

Analyse paired Likert ratings

Report T, z, p, and r in APA style

KEY FUNCTIONS

Exact p value for small samples without tiesTie-corrected normal approximation (matches SPSS)Zero differences dropped automaticallyMedians and effect size rAPA report sentence

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