Mann-Whitney U Test Calculator

In short The Mann-Whitney U test asks whether one group tends to produce larger values than another, using only the ORDER of the values rather than their sizes. That is what makes it distribution-free. The two groups loaded above give U₁ = 4.5 and U₂ = 31.5 — note they sum to 36, which is n₁ × n₂, an identity that always holds and is the quickest way to check the arithmetic by hand. The z approximation gives −2.0853 and a two-tailed p of 0.0370. U itself has a concrete meaning worth knowing: it counts how many of the 36 possible pairings between the two groups the first group wins, with half a point for a tie. The rank-biserial correlation of 0.75 restates that as an effect size — 87.5% of pairings went one way. Use it instead of a t-test when the samples are small, the data is visibly skewed, the values are ordinal such as satisfaction ratings, or there are outliers you do not want to delete. It costs very little power when the data really is normal, which makes it a safe default when you are unsure. One correction to a common misstatement: it does not test whether the MEDIANS differ. It tests whether one group tends to exceed the other, and those coincide only when the two distributions have the same shape.