31 lines
2.1 KiB
Markdown
31 lines
2.1 KiB
Markdown
---
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title: "Brunner Munzel Test"
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chunk: 1/1
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source: "https://en.wikipedia.org/wiki/Brunner_Munzel_Test"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T12:21:43.494907+00:00"
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instance: "kb-cron"
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---
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In statistics, the Brunner Munzel test (also called the generalized Wilcoxon test) is a nonparametric test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.
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It is thus highly similar to the well-known Mann–Whitney U test. The core difference is that the Mann-Whitney U test assumes equal variances and a location shift model, while the Brunner Munzel test does not require these assumptions, making it more robust and applicable to a wider range of conditions. As a result, multiple authors recommend using the Brunner Munzel instead of the Mann-Whitney U test by default.
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== Assumptions and formal statement of hypotheses ==
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All the observations from both groups are independent of each other,
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The responses are at least ordinal (i.e., one can at least say, of any two observations, which is the greater),
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Under the null hypothesis H0, is that the probability of an observation from population X exceeding an observation from population Y is the same than the probability of an observation from Y exceeding an observation from X; i.e., P(X > Y) = P(Y > X) or P(X > Y) + 0.5 · P(X = Y) = 0.5.
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The alternative hypothesis H1 is that P(X > Y) ≠ P(Y > X) or P(X > Y) + 0.5 · P(X = Y) ≠ 0.5
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Under these assumptions, the test is consistent and approximately exact. The crucial difference compared to the Mann–Whitney U test is that the latter is not approximately exact under these assumptions. Both tests are exact when additionally assuming equal distributions under the null hypothesis.
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== Software implementations ==
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The Brunner Munzel test is available in the following packages
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R: brunnermunzel, lawstat, rankFD (function rank.two.samples())
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Python (programming language): scipy.stats.brunnermunzel
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jamovi: bmtest
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== References == |