Nonparametric statistical test · BEGINNER LESSON
Mann–Whitney U test
The Mann–Whitney U test, also called the Wilcoxon rank-sum test, is a nonparametric test that compares outcomes from 2 independent groups. It asks whether values in one group tend to be higher or lower than values in the other group by ranking all observations together.
What it is and what it measures
The Mann–Whitney U test is used for 2 independent groups, meaning the people or samples in one group are not paired with those in the other group. It is used for ordinal data, which can be put in order, and for continuous data, which can take many numerical values. The test measures whether observations from one group tend to receive higher or lower ranks than observations from the other group, rather than comparing raw values directly.
[1] McNemar and Mann-Whitney U Tests - StatPearls - NCBI - NIH [3] Nonparametric Statistical Methods in Medical Research
How it works
First, all observations from both groups are pooled and ranked from smallest to largest. Then the test compares the rank patterns between the groups. Because it uses ranks, it is less sensitive to extreme outliers than a test that relies on the original numbers. It is often used when data are skewed or when a normal distribution, a bell-shaped pattern often assumed by parametric tests, is not reasonable.
[1] McNemar and Mann-Whitney U Tests - StatPearls - NCBI - NIH [3] Nonparametric Statistical Methods in Medical Research
How to interpret it
The result is sometimes described as a difference in medians, but that is only a limited interpretation. That reading is valid only when the two groups have similar-shaped distributions and mainly differ in location. More generally, the test examines whether the full distributions of the two groups differ in rank patterns. Reports should include group medians, interquartile ranges, the U statistic or standardized z statistic, the P value, and a clear description of the groups compared.
[1] McNemar and Mann-Whitney U Tests - StatPearls - NCBI - NIH
Limitations
The test does not directly compare means, so it is not the same as a t test. It also requires independence of observations, so it is not appropriate for paired measurements, repeated measurements from the same person, matched case-control data, or before-and-after comparisons in the same subjects. If the groups differ in spread or shape, a significant result may reflect general distribution differences rather than a median difference.
[1] McNemar and Mann-Whitney U Tests - StatPearls - NCBI - NIH
When it is useful
It is commonly used for comparing outcomes such as pain scores, functional scores, time to healing, biomarker levels, or hospital length of stay when the data are ordinal, skewed, or not normally distributed. Rank-based nonparametric methods can be a practical alternative when assumptions for parametric tests are not met, though they may have slightly less power when those assumptions are actually true.
[1] McNemar and Mann-Whitney U Tests - StatPearls - NCBI - NIH [3] Nonparametric Statistical Methods in Medical Research
SEE THE IDEA
How the Mann–Whitney U test compares two groups
The samples are separate and not paired.
Every observation gets an order from low to high.
The test checks whether one group tends to have higher ranks.
Results may reflect overall distribution differences, not only medians.
The test moves from separate observations to pooled ranks, then to a comparison of how ranks are distributed between the groups.
A rank-based comparison of two independent groups, with interpretation limited by distribution shape.
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.