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Mann-Whitney U Statistic Calculator — result sheet
Rank two independent samples, calculate the Mann-Whitney U statistics, and show a normal-approximation z score.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Rank all observations with average ranks for ties; Uₐ=nₐnᵦ+nₐ(nₐ+1)/2−Rₐ; z=(U−nₐnᵦ/2)/√[nₐnᵦ(nₐ+nᵦ+1)/12].
The rank-based statistic compares two independent samples without assuming a normal distribution for the observations.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Sample A values — Comma-separated values.
- Sample B values — Comma-separated values.
Worked example
| Input | Value |
|---|---|
| Sample A values | 1, 2, 3, 4, 5 |
| Sample B values | 4, 5, 6, 7, 8 |
Uₐ = 23; Uᵦ = 2; normal-approximation z ≈ −2.193.
Assumptions and limits
- The samples are independent and observations are at least ordinal.
- The displayed z approximation does not apply exact small-sample tie corrections.
- A U statistic or z score alone does not determine a practical or scientific conclusion.
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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