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Also known as: Wilcoxon Rank-Sum Test
A nonparametric test that compares two independent samples by ranking observations to assess differences in their distributions.
DESCRIPTION
The Mann–Whitney U test evaluates whether two independent groups differ without assuming normality. By ranking combined observations, it tests for shifted distributions, often used when data are ordinal or skewed. It’s robust to outliers and applicable in A/B testing with non-Gaussian metrics. Effect sizes like Cliff’s delta complement p-values. For parametric assumptions, consider the t-test.
ALTERNATIVE DEFINITIONS
NIST Engineering Statistics Handbook
The Wilcoxon rank sum test (also known as the Mann-Whitney test) is used to test the hypothesis that two populations are equal in location.
Frames the test as comparing population locations via ranks.
Penn State Eberly College of Science
The Mann–Whitney test is a nonparametric alternative to the two-sample t-test that compares the distributions of two independent samples.
Highlights nonparametric nature and role as t-test alternative.
GraphPad Prism
The Mann–Whitney test compares the distributions of two unpaired groups, using ranks rather than raw data to determine whether one tends to have larger values.
Practical description emphasizing rank-based comparison and tendency.
RELATED TERMS
Nonparametric Statistics Permutation Test Cliff’s Delta Median Rank-Based Methods A/B Testing Effect Size
COMPETING TERMS
Independent Samples t-Test Kolmogorov–Smirnov Test
KNOWLEDGE AREAS
Mathematics Data Science Testing & Validation
TARGET AUDIENCE
Data Scientist Data Analyst BI Specialist
EXTERNAL SOURCES
- Wikipedia - Mann–Whitney U test
- NIST - Authoritative test overview and guidance
- Penn State - Comprehensive probability and statistics course
TOP QUESTIONS
When should the Mann–Whitney U Test be used?
Use it when two independent samples are ordinal or non-normal. It’s robust to outliers and does not assume equal variances.
Category: Requirements
How does the Mann–Whitney U Test differ from a t-test?
It compares ranks rather than means and avoids normality assumptions. The t-test requires parametric assumptions.
Category: Example
What is a hot topic around the Mann–Whitney U Test?
Reporting effect sizes like Cliff’s delta alongside p-values to convey practical significance in A/B testing.
Category: Topic
What are common mistakes with the Mann–Whitney U Test?
Assuming it tests differences in medians only, ignoring ties, or applying it to paired data instead of using the signed-rank test.
Category: Mistakes
How to interpret Mann–Whitney U Test results?
A significant result suggests one group’s values tend to be larger. Combine with effect size and confidence intervals for context.
Category: Overview
What are the risks of misusing the Mann–Whitney U Test?
Applying it to dependent samples or multi-group comparisons without adjustments can yield invalid conclusions.
Category: Risks
How is the U statistic computed?
Rank all observations, sum ranks for each group, and transform sums into U values; compare to distribution or use asymptotic approximations.
Category: Example
Is the Mann–Whitney U Test suitable for small samples?
Yes. Exact methods exist for small samples; for larger samples, normal approximations are common.
Category: Opinion
What is a competing test to the Mann–Whitney U Test?
The independent samples t-test for parametric data, or the Kolmogorov–Smirnov test when comparing entire distributions.
Category: Alternatives