{
  "abstract": "Two-way contingency tables are tested for independence throughout applied statistics (genomics, network and text co-occurrence, pharmacovigilance, ecology, survey cross-tabulation), and the routine test reads asymptotic Gaussian tail probabilities off the table cell by cell. On the tables people actually analyze this is badly miscalibrated: across 5,543 real public two-way tables, two-thirds have counts small enough or margins heterogeneous enough that the asymptotic maximum-cell independence scan false-positives at a mean 33% against a 0.05 target, while an exact margin-conditional anchor holds at about 1%. The failure is sharpest when the departure is sparse, the association concentrated in a few cells, where the omnibus chi-square is inefficient and the sharp object is the detection boundary. In three parts we answer where a sparse signal can be seen, which combiner attains that limit, and how to calibrate at small counts. Part I specializes the sparse-detection theory of Ingster (1997), Donoho and Jin (2004), and Chhor, Mukherjee and Sen (2024) to independence: the table is a heteroscedastic Gaussian sequence whose variance profile is the expected-count table, fixed by the margins via CVe^2 = (1 + CVr^2)(1 + CVc^2) - 1, giving an exact signal map and a closed-form separation radius valid under a moderate-deviation growing-count condition. Part II shows higher criticism, with its closed-form Jaeschke-Eicker null, attains that boundary adaptively over unknown sparsity. Part III measures the small-count calibration failure (size 0.3 to 0.6 even under uniform margins, so the driver is the per-cell tail), removes it with exact margin-conditional laws (size 0.003 to 0.009), and gives a routing rule sending large-count tables to the asymptotic gate and small-count tables to the exact anchor. Every claim is reproduced from openly deposited, deterministically seeded code.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07979",
  "author_total": 1,
  "authors": [
    {
      "name": "William J. Dwyer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7g768w33ewmve.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07979",
  "fulltext_url": null,
  "id": "7g768w33ewmve",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07979",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7202174944",
  "pdf_url": "https://arxiv.org/pdf/2608.07979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7g768w33ewmve.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2608.07979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor",
  "title_text": "Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:22Z",
  "url": "https://research.draconitic.com/paper/7g768w33ewmve",
  "venue": "arXiv",
  "versions": []
}