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Wilcoxon Signed-Rank Test Calculator

Paired non-parametric test — W statistic, z with tie correction and two-sided p-value for before/after or matched data.

Before (or sample A)

After (or sample B)

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How it works

Rank |dᵢ| ignoring zeros; W = min(Σ ranks of positive d, Σ ranks of negative d); z = (W − n(n+1)/4 + 0.5) ÷ √[n(n+1)(2n+1)/24 − Σ(t³−t)/48]

The signed-rank test is the paired cousin of Mann–Whitney: it ranks the absolute differences between matched observations and checks whether positive and negative changes are balanced. It uses the size of each change, not only its direction (that would be the sign test), and does not assume normal differences. The normal approximation is standard from about 10 pairs; for very small n exact tables give the same answer within rounding.

Worked example

Ten before/after pairs with one zero difference: W = 5 over 9 pairs, z = −2.31, p = 0.021 — the after values are significantly lower.

Frequently asked questions

Why drop zero differences?

A zero carries no evidence of direction; the classic Wilcoxon procedure discards them and reduces n.

Paired t-test or Wilcoxon?

Use the t-test when differences look roughly normal; use Wilcoxon for skewed, ordinal or outlier-prone data.

Related calculators

Mann–Whitney U Test Calculator

Compare two independent samples without assuming normality — U statistic, tie-corrected z, two-sided p-value and the rank-biserial effect size.

Sign Test Calculator

The simplest paired test — count improvements versus declines and get the exact binomial one- and two-sided p-values, with the normal approximation.

Paired t-Test Calculator

Paste before-and-after (paired) data or summary statistics and get the paired t-test: mean difference, t statistic, degrees of freedom, one- or two-tailed p-value, confidence interval, effect size, a Shapiro–Wilk normality check and every step worked out.

For education — check assumptions (sample size, distribution, independence) before using a test result in a real decision.