{
  "abstract": "Rubin's variance ratio (VR) complements the standardized mean difference by detecting covariate imbalance in spread, but no purpose-built omnibus extension exists for more than two groups. We introduce FVR, a size-weighted quadratic combination of pairwise log-variance-ratios that generalizes VR to k groups, together with geometric-mean and maximum pairwise variance-ratio comparators. FVR has an exact relationship to Rubin's VR at k = 2 and a mathematical structure directly parallel to Cohen's f. In Monte Carlo simulations spanning four variance-driven bias mechanisms, k = 3, 4, 6, and sample sizes from 200 to 10,000, FVR and the geometric-mean statistic generally tracked downstream estimation bias at least as well as the maximum statistic. FVR retained substantially more signal when many groups shared a very small sample, while absolute-bias thresholds were unstable at N = 200. Across mechanisms, FVR < 0.10 was reasonably reassuring, values above approximately 0.30 generally indicated concern, and intermediate values were context-dependent. The statistic is implemented for arbitrary analysis weights in the Stata command varatio and illustrated using a multivalued-treatment application.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27772",
  "author_total": 1,
  "authors": [
    {
      "name": "Ariel Linden"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4xhgy4p384b3t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27772",
  "fulltext_url": null,
  "id": "4xhgy4p384b3t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27772",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7214191385",
  "pdf_url": "https://arxiv.org/pdf/2609.27772",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4xhgy4p384b3t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:06Z",
      "native_id": "2609.27772",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27772"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Beyond the Mean: A Weighted k-Sample Omnibus Variance-Ratio Statistic for Covariate Balance Diagnostics",
  "title_text": "Beyond the Mean: A Weighted k-Sample Omnibus Variance-Ratio Statistic for Covariate Balance Diagnostics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/4xhgy4p384b3t",
  "venue": "arXiv",
  "versions": []
}