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Mann-Whitney U Test Calculator
Compare two independent groups without assuming normality — with the U statistic, the p-value, and the reproducible R command. Read a full interpretation guide below. Validated against R 4.3.3.
In Simple Words
The Mann-Whitney U test (also called the Wilcoxon rank-sum test) asks whether values in one group tend to be larger than values in another, without assuming the data follow a normal distribution. Instead of using the raw numbers, it ranks all observations from smallest to largest and compares the rank totals of the two groups.
It is the non-parametric counterpart to the independent t-test. Reach for it when your outcome is ordinal, or when a continuous outcome is skewed, has outliers, or comes from a small sample where normality is doubtful. A subtle point worth remembering: the test compares whole distributions, not specifically the medians, unless you are willing to assume the two distributions have the same shape.
When to Use the Mann-Whitney U Test
Use it to compare two independent groups on an ordinal outcome, or on a continuous outcome that is clearly non-normal. Typical cases include Likert-type scores, skewed biomarkers, small pilot samples, and data dominated by a few extreme values where the mean is a poor summary.
If your data are paired (before-and-after on the same subjects), use the Wilcoxon signed-rank test instead; for three or more groups, use the Kruskal-Wallis extension. One important caveat: when the two groups have very different spreads (heteroscedasticity), the test can reject the null for reasons unrelated to location, so report what you are actually comparing. Not sure whether a non-parametric test is needed? Our interactive Test Selector can help.
Expected: 2 columns: Group 1 values | Group 2 values
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected: 2 columns: Group 1 values | Group 2 values
g1 <- c({g1})
g2 <- c({g2})
wilcox.test(g1, g2)User guide
When to use. Non-parametric comparison of two independent groups when normality is doubtful.
Assumptions. Independent observations; ordinal or continuous data.
Common mistakes. It compares rank distributions, not means: describe results as a shift in distribution.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Mann HB, Whitney DR. On a test of whether one of two random variables is stochastically larger. Ann Math Stat. 1947;18:50-60.
Worked Examples
Example 1 — A skewed outcome
Group 1 (12, 15, 11, 14, 13) and Group 2 (18, 20, 17, 19, 22) separate cleanly when ranked: every Group 2 value exceeds every Group 1 value. The U statistic is at its extreme and the p-value is small, indicating Group 2 tends to score higher. Report the U value, the p-value, and the group medians with interquartile ranges.
Example 2 — Why ranks beat means here
If one group contains an extreme outlier, a t-test on the raw values can be dragged toward it. Because the Mann-Whitney test uses ranks, that single point counts only as the highest rank, not as an inflated value, giving a more stable comparison of the typical observation.
Assumptions to Check
Independent groups. The two samples must be unrelated. Paired or repeated measurements call for the Wilcoxon signed-rank test instead.
Ordinal or continuous outcome. The outcome must be at least ordinal so that ranking is meaningful. Purely categorical data need a chi-square or Fisher’s test.
Similar shape if interpreting medians. To read the result as a difference in medians, the two distributions should have a similar shape and spread; otherwise it is a test of stochastic dominance, not of medians.
Common Mistakes
Claiming it always compares medians
The test compares whole rank distributions. It equals a median comparison only when the two distributions share the same shape. State your assumption explicitly.
Using it on paired data
For before-and-after measurements on the same subjects, the Wilcoxon signed-rank test is correct, not Mann-Whitney.
Ignoring unequal variances
When the groups have very different spreads, a significant result may reflect that difference rather than a location shift. Consider a Fligner-Policello or Brunner-Munzel test.
Defaulting to non-parametric out of habit
If the outcome is continuous and roughly normal, the t-test is more powerful. Choose the non-parametric test for a reason, not reflexively.
Frequently Asked Questions
Is the Mann-Whitney U test the same as the Wilcoxon rank-sum test?
Yes. They are mathematically equivalent for two independent groups and give the same p-value; the names reflect different but identical formulations.
When should I use it instead of a t-test?
When the outcome is ordinal, or continuous but skewed, with outliers, or from a small sample where normality is doubtful.
What effect size goes with it?
Report the rank-biserial correlation or a probability-of-superiority statistic alongside medians and interquartile ranges.
Does the result match SPSS, R, and Stata?
Yes. The calculator uses the same rank-sum computation as standard software and shows the exact R command so you can reproduce it.
Related Calculators
References
- Kroeger CM, Ejima K, Hannon BA, et al. Persistent confusion in nutrition and obesity research about the validity of classic nonparametric tests in the presence of heteroscedasticity. Am J Clin Nutr. 2021;113(3):501–508. PMID 33515017.
- Dexter F. Wilcoxon-Mann-Whitney test used for data that are not normally distributed. Anesth Analg. 2013;117(3):537–538. PMID 23966647.
- Mann HB, Whitney DR. On a test of whether one of two random variables is stochastically larger than the other. Ann Math Stat. 1947;18(1):50–60.
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