Mann Whitney U Calculator

Perform a Mann-Whitney U test comparing two independent samples.

About Mann Whitney U Calculator

The Mann-Whitney U test compares distributions without assuming normality, using only the ordering of observations. The effect size r converts the z statistic into a scale-free magnitude. It tests whether one distribution is stochastically larger than the other, which is a broader claim than a difference in means.

Formula

Mann Whitney U

E(U) = n₁n₂/2; SD(U) = √(n₁n₂(n₁+n₂+1)/12); z = (U − E(U)) ÷ SD(U)

U: Count of times an observation from one group precedes one from the other

Worked example

With the default values below, Mann Whitney U Calculator returns Z Statistic of -1.23443. Change any input above and every figure here is recalculated in your browser.

Inputs used

U statisticminimum 0: 60
Sample size of group 1minimum 3: 12
Sample size of group 2minimum 3: 14
Significance levelaccepts 0.1–20 %: 5 %

Results

Z Statistic: -1.23443
Expected U Under the Null: 84.000
Standard Deviation of U: 19.44222
Effect Size: 0.24209
Decision: Fail to Reject H0

Step by step

1Values used
2Mann Whitney U
3Z Statistic= -1.23443
4Expected U Under the Null= 84.000
5Standard Deviation of U= 19.44222
6Effect Size= 0.24209
7Decision= Fail to Reject H0

Assumptions and limits

The result is derived only from the 4 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 5 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

How is Mann Whitney U calculated?

E(U) = n₁n₂/2; SD(U) = √(n₁n₂(n₁+n₂+1)/12); z = (U − E(U)) ÷ SD(U) The Mann-Whitney U test compares distributions without assuming normality, using only the ordering of observations. The effect size r converts the z statistic into a scale-free magnitude.

Why does Mann Whitney U matter?

It tests whether one distribution is stochastically larger than the other, which is a broader claim than a difference in means.

What values do I need to enter?

This calculator takes 4 inputs: U statistic, Sample size of group 1, Sample size of group 2, Significance level. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.