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What Is the Mann-Whitney U Test?
The Mann-Whitney U test is a non-parametric statistical test used to compare two independent groups. It tests whether one group tends to have larger values than the other without assuming that the data follows a normal distribution. It is the non-parametric equivalent of the independent samples t-test.
The test works by ranking all observations from both groups together, then computing the sum of ranks for each group. The U statistic measures the number of times an observation from one group precedes an observation from the other group in the ranking. Under the null hypothesis of no difference, U has a known distribution.
Formula
Assumptions
- Observations are independent between and within groups
- The dependent variable is at least ordinal
- Under H0, the distributions of both groups are identical
- No assumption of normality or equal variances required
Frequently Asked Questions
When should I use U-test instead of t-test?
Use the Mann-Whitney U test when: data is ordinal (not interval/ratio), sample sizes are small and normality cannot be verified, data contains outliers that would distort the t-test, or the data is clearly non-normal (highly skewed or multi-modal).
Is the U-test the same as the Wilcoxon rank-sum test?
Yes. The Mann-Whitney U test and the Wilcoxon rank-sum test are mathematically equivalent tests with different calculation approaches. They always produce the same p-value and conclusion. The names are often used interchangeably.