Mann Whitney U Test Calculator

Work out mann whitney u test instantly with clear inputs, formula shown and shareable results.

About Mann Whitney U Test Calculator

The Mann-Whitney U test ranks all observations together and compares the rank sums. It tests whether one group tends to give larger values than the other, without assuming normality.

Formulas

U statistic

U₁ = R₁ − n₁(n₁ + 1)/2, U = min(U₁, U₂)

Normal approximation

z = (U − n₁n₂/2) / √(n₁n₂(n₁ + n₂ + 1)/12)

Worked example

With the default values below, Mann Whitney U Test Calculator returns Mann-Whitney U of 14.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First group: 12, 15, 18, 21, 24
Second group: 10, 14, 17, 19, 20, 25

Results

Mann-Whitney U: 14.0000
Rank sum of the first group: 31.0000
Normal approximation z: -0.182574
Two-tailed p value: 0.85513216

Step by step

1Values used
2U statistic
3Normal approximation
4Mann-Whitney U= 14.0000
5Rank sum of the first group= 31.0000
6Normal approximation z= -0.182574
7Two-tailed p value= 0.85513216

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For the two sample groups?

The rank sum of the first group is 31, giving U = 16 and a z of about 0.3651 — no significant difference.

When should I use it instead of a t-test?

When the data is ordinal, heavily skewed, or the samples are too small to trust normality.