Mann-Whitney U Test — StatReason

U statistic
p-value
Method
Rank-biserial correlation

What this answers

This test answers "do these two independent groups come from the same distribution, or does one tend to produce larger values than the other?" Rather than working with the raw values and their mean, it ranks every observation from both groups combined and compares how those ranks are distributed between the two groups, which makes it far less sensitive to extreme values or a skewed shape than a t-test.

When to use it, and when not to

Use this when your data is skewed, contains extreme values, is ordinal rather than genuinely numeric, or your sample is too small to trust normality. Do not use it as a direct substitute for comparing means: unless the two groups have a similar shape, a significant result tells you the distributions differ, not specifically that one group's typical value is higher, and the effect size here (rank-biserial correlation) describes dominance in ranks, not a difference in means.

How it is calculated

Every value across both groups is ranked together, with tied values receiving the average of their tied rank positions. The U statistic for each group is derived from the sum of its ranks. When there are no ties and the groups are small enough, this calculator computes an exact p-value by enumerating the null distribution of U directly, rather than approximating it. When ties are present, or the groups are too large to enumerate practically, it falls back to a normal approximation with an explicit tie correction and a continuity correction, and the result panel names which method was used.

Worked example

For Group A of 1, 2, 3 and Group B of 4, 5, 6: every value in Group A is smaller than every value in Group B, complete separation between the groups. This gives U equal to 0, the most extreme possible value, and an exact two-sided p-value of exactly 0.1, a known published result for two groups of three with no ties. Try that input above and confirm the calculator returns U = 0 and p = .100 using the exact method.

Assumption audit

Calculated from your data: each group's sample size, whether the combined data contains tied values (which forces the asymptotic method), and the U statistic itself.

Evidence to review: whether the two groups have a similar distribution shape, visible in a histogram of each group. If the shapes are similar, a significant result can reasonably be described as a difference in typical location; if not, describe it only as a difference in distribution.

You must verify: that observations within and between groups are independent, and that group membership was not itself determined by the outcome you are comparing.

What this result does not mean

A significant Mann-Whitney result means the data provide evidence that the two groups' distributions differ, not automatically that their means or medians differ by a specific amount, and not that one group's distribution causes the other's. A nonsignificant result means the analysis was inconclusive at your chosen threshold, not proof that the two groups are identical.

Limitations

Small samples limit this test's power to detect a genuine difference, and the exact method is only available without ties, a fact this calculator states directly in its result rather than silently switching methods without telling you.