Mann Whitney U Statistic Calculator
Compare two independent samples using pooled ranks, U statistics and observed pairwise superiority.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Rank pooled observations with average ties. Derive both U statistics and the signed rank-biserial comparison.
U₁=R₁−n₁(n₁+1)/2; U₂=n₁n₂−U₁; superiority=U₁/(n₁n₂)
Worked example
Samples 1,2,3 and 3,4,5 give U₁=0.5 and U₂=8.5. Of nine cross-sample pairs, sample 1 has zero strict wins and one tie.
Assumptions and input details
Enter 1–200 observations in each independent sample, magnitude at most 1e12. U₁ is explicitly the number of sample-1 wins plus half ties; some references label U in the opposite direction. This page computes statistics and descriptive superiority only, without an exact or asymptotic p-value. It is not a paired signed-rank test or automatically a test of medians.
References: NIST: rank sum test
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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