{
  "abstract": "There exist tests calibrated under a null narrower than the one implied by their test statistic -- the detection-null set. The part of the detection-null set not in the null is the test's blind spot. A framework for assessing detection coherence -- whether a test's blind spot is empty -- is introduced, built on new concepts of calibration statistic, detector, detection functional, detection-null set, and blind spot. It is demonstrated that the Wilcoxon--Mann--Whitney, Kruskal--Wallis, Friedman, and logrank tests are detection incoherent as unrestricted tests. Detection incoherent tests may become coherent under restrictions that make the blind spot empty, though domain restriction is not a reliable route to coherence in practice, since the boundary of the coherence-restoring domain is unknown and unverifiable. The Kolmogorov--Smirnov and Zaremba tests, and the Maximum Mean Discrepancy test with a characteristic kernel, are shown to be universally detection coherent. Due to the blind spot, a detection incoherent test misses discoveries when non-rejecting and yields spurious discoveries when rejecting, in both cases regardless of sample size. Detection incoherent tests should be abandoned.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.11177",
  "author_total": 1,
  "authors": [
    {
      "name": "Marian Grendar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7yp98nhegy0e2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.11177",
  "fulltext_url": null,
  "id": "7yp98nhegy0e2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.11177",
  "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|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7202268296",
  "pdf_url": "https://arxiv.org/pdf/2608.11177",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7yp98nhegy0e2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:56Z",
      "native_id": "2608.11177",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.11177"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Detection coherence of tests",
  "title_text": "Detection coherence of tests",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:56Z",
  "url": "https://research.draconitic.com/paper/7yp98nhegy0e2",
  "venue": "arXiv",
  "versions": []
}