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Wilcoxon Rank-Sum Statistic — result sheet
Rank two independent samples, calculate the Wilcoxon rank-sum and U statistics, and show a large-sample normal approximation.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Rank the pooled observations with average ranks for ties; Uₐ = Rₐ − m(m+1)/2, μᵤ = mn/2, σᵤ = √[mn(m+n+1)/12], and z = (Uₐ − μᵤ ± 0.5)/σᵤ when a half-unit correction is selected.
The rank-sum method compares the relative ordering of two independent samples rather than assuming the original measurements are normally distributed. This page reports the statistic and an approximate two-sided normal-tail value; it does not replace an exact small-sample table or a study-design decision.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Sample A values — Enter comma-separated numeric values.
- Sample B values — Enter comma-separated numeric values.
- Normal approximation correction — 2 choices
Worked example
| Input | Value |
|---|---|
| Sample A values | 1, 3, 5, 7 |
| Sample B values | 2, 4, 6, 8 |
| Normal approximation correction | none |
The pooled ranks give Rₐ = 16, Uₐ = 6, expected U = 8, and z ≈ −0.577.
Assumptions and limits
- The two lists represent independent observations and are numeric values measured on a common ordering scale.
- Tied values receive their average rank; the displayed normal approximation uses the no-tie variance and is therefore less reliable with many ties.
- The approximate p-value is a screening aid for sufficiently large samples, not a universal significance decision or effect-size measure.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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