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The Wilcoxon-Mann-Whitney test under scrutiny.

Morten W Fagerland¹, Leiv Sandvik

¹Ullevål Department of Research Administration, Oslo University Hospital, Norway. morten.fagerland@medisin.uio.no

Statistics in Medicine

|February 28, 2009

Summary

The Wilcoxon-Mann-Whitney (WMW) test is not robust to distributional shape differences. Small variance differences and skewness can cause significant type I error rate deviations, impacting statistical reliability.

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Area of Science:

Statistics
Statistical Methods

Background:

The Wilcoxon-Mann-Whitney (WMW) test is a widely used non-parametric test.
It is employed to compare two independent samples from potentially non-normal distributions.
Its robustness to distributional shape differences is a key consideration.

Purpose of the Study:

To investigate the robustness of the large sample approximate Wilcoxon-Mann-Whitney test.
To quantify the impact of distributional shape differences on the test's type I error rate.
To compare the performance of WMW with other rank-based tests.

Main Methods:

A comprehensive simulation study was conducted.
The study evaluated the type I error rate of the WMW test under various distributional shapes.
Performance was compared against the Fligner-Policello (FP) and Brunner-Munzel (BM) tests.

Main Results:

The WMW test demonstrates significant sensitivity to differences in distribution shapes.
Small variance heterogeneity and moderate skewness led to substantial deviations in the type I error rate.
These deviations were more pronounced when skewness differed between distributions.
The Brunner-Munzel test generally outperformed the WMW and Fligner-Policello tests.

Conclusions:

The robustness of the large sample approximate WMW test is less than commonly assumed.
Users must carefully examine sample symmetry and variance homogeneity before interpreting WMW test results.
Rank transformation properties contribute to the observed lack of robustness.