Eta for check group variation

[mattansb]

This PR adds an Eta column to the output of check_group_variation() which is a numeric effect size of the grouping variable's predictive association strength: when it is 0 the grouping variable carries no predictive information, when it is 1 the variable is perfectly predicted by the grouping variable.

• For numeric variables it is the sqrt(icc) - also know as $\eta$ (eta).
• For non-numeric variables it is a non-symmetric version of Cramer's V.

performance::check_group_variation(
  mlmRev::egsingle,
  by = c("schoolid", "childid"),
  include_by = TRUE
)
#> Check schoolid variation
#> 
#> Variable | Variation |  Design |     r
#> --------------------------------------
#> childid  |      both |  nested |  .430
#> year     |      both |         |  .171
#> grade    |      both |         |  .185
#> math     |      both |         |  .358
#> retained |      both |         |  .203
#> female   |    within | crossed |  .183
#> black    |      both |         |  .824
#> hispanic |      both |         |  .692
#> size     |   between |         | 1.000
#> lowinc   |   between |         | 1.000
#> mobility |   between |         | 1.000
#> 
#> Check childid variation
#> 
#> Variable | Variation | Design |     r
#> -------------------------------------
#> schoolid |   between |        | 1.000
#> year     |      both |        |  .416
#> grade    |      both |        |  .429
#> math     |      both |        |  .713
#> retained |      both |        |  .478
#> female   |   between |        | 1.000
#> black    |   between |        | 1.000
#> hispanic |   between |        | 1.000
#> size     |   between |        | 1.000
#> lowinc   |   between |        | 1.000
#> mobility |   between |        | 1.000

^{Created on 2026-08-06 with reprex v2.1.1}

[codecov]

Codecov Report

❌ Patch coverage is 57.57576% with 14 lines in your changes missing coverage. Please review.
✅ Project coverage is 64.12%. Comparing base (961ba2e) to head (6ccf55d).
⚠️ Report is 4 commits behind head on main.

Files with missing lines	Patch %	Lines
R/check_group_variation.R	57.57%	14 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #932      +/-   ##
==========================================
+ Coverage   64.07%   64.12%   +0.05%     
==========================================
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  Lines        8321     8355      +34     
==========================================
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[strengejacke]

Nice! Do we have a reference for eta?

[DominiqueMakowski]

Nice one indeed, would its usage be more meaningful in the context of exploratory analysis? Or to to help (mixed) model specification?

[mattansb]

I've renamed the column to a more generic "r" (see updated example above) - the docs still explain that for numeric variables it is the correlation ratio $\eta$ (with reference).

Nice one indeed, would its usage be more meaningful in the context of exploratory analysis? Or to to help (mixed) model specification?

Ideally one already knows the design of their data and so know which variables are within/between/both, but this is useful for validating your assumptions (which is why it is in {performance})! See examples where I use it in teaching group-mean-centering (datawizard::demean()) here.