Wilcoxon Signed-Rank Test Calculator
| # | A | B | Adjusted difference | |difference| | Rank | Sign |
|---|
How this is calculated
Interpretation and assumptions
The Wilcoxon signed-rank test is designed for paired or matched observations. It tests whether the distribution of paired differences is symmetric about the hypothesized difference Δ₀. It is commonly used as a nonparametric alternative to the paired t-test when the paired differences are not suitably modeled as normal.
Important assumptions include paired observations, independence between pairs, an outcome that can be meaningfully ordered, and a roughly symmetric distribution of differences when the test is interpreted as a location-shift or median comparison. The sign of the effect in this calculator is based on A − B.
The rank-biserial correlation is reported as a signed effect-size summary. Positive values favor A over B; negative values favor B over A. Its magnitude ranges from 0 to 1 in absolute value.
Method notes and references
Exact sign-permutation: this calculator enumerates the signed-rank null distribution efficiently with dynamic programming rather than generating every sign pattern explicitly. With distinct non-zero differences, it matches the classical exact Wilcoxon distribution. With ties or zeros, it conditions on the observed absolute ranks and applies the selected zero convention; this is the sign-permutation approach recommended when ties or zeros affect the classical exact distribution.
Auto: exact sign-permutation is used for up to 50 non-zero differences; larger samples use the tie-adjusted normal approximation. Exact mode is capped at 80 non-zero differences for browser performance.
