{
  "abstract": "Cramer's V and the other chi-square-family effect sizes are positive under exact independence, so a reported value can be smaller than what the same statistic produces on a table with no association at all. The upward bias is classical (Tschuprow 1925; Bartlett 1937; corrected by Bergsma 2013), and reporting the boundary value, the critical effect size, beside the observed one has been recommended in general form (Perugini et al. 2025); we claim neither. Our contribution is two things a general recommendation does not supply. First, an exact per-table reporting gate: the noise floor V_0.95, the value the effect size reaches by chance 5% of the time under independence, computed from the exact margin-conditional law rather than the asymptotic critical value. The asymptotic floor miscalibrates where reporting is riskiest: on heterogeneous tables its false-alarm rate reaches 0.10 against a 0.05 target, while the exact floor holds nominal. Second, a measurement: across 4,129 real two-way tables from 291 public datasets, 21.8% of labeled effects (cluster-robust 95% CI 17 to 27%) sit on tables with no significant association. We recommend reporting V_0.95, in exact form on sparse or heterogeneous tables, beside every association measure and at the design stage.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26128",
  "author_total": 1,
  "authors": [
    {
      "name": "William J. Dwyer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dr0xp5rc1c778.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26128",
  "fulltext_url": null,
  "id": "dr0xp5rc1c778",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26128",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1804|Meta-analysis and systematic reviews"
    ]
  ],
  "openalex": "W7214088998",
  "pdf_url": "https://arxiv.org/pdf/2609.26128",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dr0xp5rc1c778.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:49Z",
      "native_id": "2609.26128",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26128"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "An Exact Noise Floor for Contingency-Table Effect Sizes: A Per-Table Reporting Gate, and How Often It Would Change Reported Magnitudes",
  "title_text": "An Exact Noise Floor for Contingency-Table Effect Sizes: A Per-Table Reporting Gate, and How Often It Would Change Reported Magnitudes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:49Z",
  "url": "https://research.draconitic.com/paper/dr0xp5rc1c778",
  "venue": "arXiv",
  "versions": []
}