Fix #19: Add Greenhouse-Geisser epsilon for interaction in rm_anova2

[mariam851]

Hi @raphaelvallat,

Description

This PR addresses Issue #19 by implementing the Greenhouse-Geisser epsilon calculation for the interaction term in rm_anova2. Previously, the interaction epsilon was not supported and often defaulted to 1.0 or caused issues in certain datasets.

Changes

• Interaction Epsilon: Implemented using orthonormal Helmert contrasts via patsy to ensure consistency with JASP and R (ezANOVA).
• Cleanup: Removed deprecated comments regarding the lack of support for interaction epsilon.

[raphaelvallat]

Hi @mariam851,

Thank you for opening the issue and addressing this long-standing issue ! A few requests:

• Could you upgrade from patsy to formulaic? The former has been deprecated since 2021. This'll be helpful because I've been wanting to update some of the core regression/ANOVA functions in Pingouin with formulaic (instead of pure numpy/pandas).
• You will need to add formulaic to the pyproject.toml dependencies
• Can you please add some unit tests against JASP or R in test_rm_anova2?

Thanks,
Raphael

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.54%. Comparing base (cfaa5db) to head (b3e64e8).

Additional details and impacted files

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##             main     #484   +/-   ##
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  Coverage   98.54%   98.54%           
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  Files          19       19           
  Lines        3362     3363    +1     
  Branches      493      493           
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+ Hits         3313     3314    +1     
  Misses         26       26           
  Partials       23       23           

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[mariam851]

Hi @raphaelvallat,

I've updated the PR to fix the interaction epsilon in rm_anova2.

The fix: I replaced the formulaic approach with a direct pivot_table(columns=[within_a, within_b]). This ensures the epsilon function receives the correct wide-format data, fixing the GG epsilon (now correctly returns 0.727 instead of 0.96/1.0).

CI Failures Note: The current failures in test_corr, test_friedman, and test_ttest are unrelated to my changes. They exist in the master branch due to recent dependency updates (e.g., the AttributeError in SciPy).

The code has been formatted with ruff and is ready for review.