{
  "abstract": "Levene's test for homoscedasticity is a standard procedure used to evaluate whether multiple groups of independent observations share a common variance. Because Levene's test relies on an Analysis of Variance (ANOVA) applied to transformed absolute or squared deviations, it structurally mirrors the statistical properties of ANOVA itself. Let $μ_j$ and $σ^2_j$ denote the expectation and variance of the observations in group $j$. It was previously established that for a given significance level $α$, ANOVA can result in a logical contradiction: failing to reject the global null hypothesis $H_0: μ_1 = μ_2 = μ_3$ while simultaneously rejecting the localized hypothesis $H_0': μ_1 = μ_2$ with the same or higher confidence. In this paper, we show that Levene's test directly inherits this same ``paradox'' regarding group variances $σ^2_j$. We provide theoretical reasoning and a numerical illustration of this inconsistency, demonstrating how the addition of a well-behaved third group can dilute the test statistic and mask a significant localized variance discrepancy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17746",
  "author_total": 2,
  "authors": [
    {
      "name": "Vladimir Gurvich"
    },
    {
      "name": "Mariya Naumova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1r1hg5gsj90fr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17746",
  "fulltext_url": null,
  "id": "1r1hg5gsj90fr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17746",
  "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 Statistical Methods and Models"
    ]
  ],
  "openalex": "W7213516020",
  "pdf_url": "https://arxiv.org/pdf/2609.17746",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1r1hg5gsj90fr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:10Z",
      "native_id": "2609.17746",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17746"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Subgroup Inconsistency and the Dilution Effect in Levene's Test for Homoscedasticity",
  "title_text": "Subgroup Inconsistency and the Dilution Effect in Levene's Test for Homoscedasticity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/1r1hg5gsj90fr",
  "venue": "arXiv",
  "versions": []
}