Mann-Whitney U Test

Use this test when you want to compare two independent groups but cannot assume normality, when data are ordinal, or when sample sizes are small. For example, comparing patient satisfaction ratings (on a Likert scale) between two hospitals, or comparing reaction times when the data are heavily skewed.

• Observations in each group are independent.
• The dependent variable is at least ordinal (ranks are meaningful).
• The two groups have similarly shaped distributions if you want to interpret the test as a comparison of medians. If shapes differ, the test compares stochastic dominance.

• If Pr > |Z| is less than alpha, the two groups differ significantly in their rank distributions.
• The rank-biserial correlation (r) quantifies the effect size. easyCris interprets it as negligible (<0.1), small (<0.3), medium (<0.5), or large (>=0.5).
• A positive rank-biserial r indicates that Group 1 tends to have higher values than Group 2.
• The median difference provides a practical summary, but remember the test is based on ranks, not medians directly.
• With very small samples, consider using an exact p-value rather than the normal approximation.

• The test does not compare medians unless the two distributions have the same shape. With different shapes, a significant result means one group tends to produce larger values.
• Tied values reduce the precision of the test. The continuity correction helps but does not fully resolve the issue.
• The normal approximation for the p-value becomes less accurate with very small sample sizes (N < 10 per group).

1. Combine all observations from both groups and assign ranks from smallest to largest.
2. Sum the ranks for each group separately.
3. Compute the U statistic as the number of times an observation from Group 1 precedes an observation from Group 2 in the combined ranking.
4. Standardise U to a Z-score using the expected value and standard deviation under the null hypothesis, then compute the p-value from the normal distribution.