Add brunner_munzel(): nonparametric test for stochastic equality (Brunner & Munzel 2000)

[hass-nation]

Summary

Adds brunner_munzel(x, y) — the Brunner-Munzel test, a nonparametric test for stochastic equality of two independent groups. It is more robust than the Wilcoxon rank-sum / Mann-Whitney U test under heteroscedasticity (unequal variances), which is its main practical advantage.

Algorithm

Uses a Welch-Satterthwaite degrees-of-freedom approximation and a t-distribution reference. The test statistic is based on within-group and between-group rank differences. p-values are verified to match scipy.stats.brunnermunzel.

Interface

from pingouin import brunner_munzel

brunner_munzel(x, y, alternative='two-sided')
# Returns DataFrame with columns: W-val, dof, alternative, p-val, RBC, CLES
# CLES = P(X > Y), the common language effect size
# RBC  = rank-biserial correlation

New content

• brunner_munzel() function added to pingouin/nonparametric.py and exported from pingouin/__init__.py
• 11 tests added to tests/test_nonparametric.py covering: basic correctness vs scipy, identical groups, clear-difference groups, one-sided alternatives, effect size bounds, all three nan_policy modes, output column names

Reference

Brunner, E. & Munzel, U. (2000). The nonparametric Behrens-Fisher problem: asymptotic theory and a small-sample approximation. Biometrical Journal, 42(1), 17–25.

[codecov]

Codecov Report

❌ Patch coverage is 91.30435% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.26%. Comparing base (2d906c5) to head (42cab22).

Files with missing lines	Patch %	Lines
src/pingouin/nonparametric.py	91.30%	2 Missing and 2 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #515      +/-   ##
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- Coverage   98.36%   98.26%   -0.10%     
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  Files          19       19              
  Lines        3305     3351      +46     
  Branches      488      495       +7     
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+ Hits         3251     3293      +42     
- Misses         32       34       +2     
- Partials       22       24       +2     

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[raphaelvallat]

Hi,

Thanks for opening the PR. Brunner Munzel is already supported by scipy.stats, so I don't see a strong reason to add it to Pingouin (I'm not sure what the value add would be), unless others feel strongly about it.