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Statistics · Hypothesis testing

Mann–Whitney U Test Calculator

Compare two independent samples using pooled ranks, with tie-corrected normal inference.

Statistics · Hypothesis testing

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Private in-browser calculation · explicit assumptions
Rank procedures replace raw magnitudes with ordered positions, then compare rank patterns under the stated design.
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  3. 3VerifyReview the details and units
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Understand the hypothesis test

How rank-based inference works

Mann–Whitney U Test. Rank procedures use relative order instead of the original numerical distances. This changes both robustness and the population statement being tested.

Test statistic and reference model

U derives from each group’s rank sum; variance is corrected for tied ranks.

The test targets stochastic distribution differences; a pure median interpretation needs similarly shaped distributions.

Responsible interpretation

A rank test is not automatically a test of medians. Median language generally needs comparable distribution shapes and a design that supports that interpretation.

Required assumption: Samples and observations must be independent and at least ordinal; this route consolidates the Wilcoxon rank-sum synonym.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the mann–whitney u test calculator works

U derives from each group’s rank sum; variance is corrected for tied ranks.

The test targets stochastic distribution differences; a pure median interpretation needs similarly shaped distributions.

Worked example

Mann–Whitney U Test example

Samples 1, 2, 3 and 4, 5, 6 have complete rank separation and U=0 for the first group.

U derives from each group’s rank sum; variance is corrected for tied ranks.

Supported inputs

Precision and limits

Model and design

Samples and observations must be independent and at least ordinal; this route consolidates the Wilcoxon rank-sum synonym.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

The test targets stochastic distribution differences; a pure median interpretation needs similarly shaped distributions.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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