{
  "abstract": "The emerging literature on hypothesis testing with data-dependent significance levels relies on a particular extension of the Type-I error. Existing arguments for this extension are heuristic. We show it is uniquely characterized by three axioms: law-invariance, agreement with classical testing on constant levels, and the preservation of (in)validity under independent selection of the level. We find that three analogous axioms characterize the e-value as a multi-decision generalization of a test in a decision-theoretic framework. We recover the p-value by dropping the invalidity half of the independent selection axiom, showing that e-values correspond to those p-values for which a data-independent choice between two invalid p-values cannot produce a valid p-value. Our main technical contribution is to show how e-values emerge in every decision problem with a notion of validity that satisfies law invariance, the independent selection axiom, and an axiom stating that a procedure that selects an invalid procedure with arbitrarily high probability must itself be invalid. In an application to post-hoc decision-making, we justify expectation-based error rates in multiple testing and recover the 'e-closure principle' as a special case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.28429",
  "author_total": 1,
  "authors": [
    {
      "name": "Nick W. Koning"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2kn9dekyp2vep.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.28429",
  "fulltext_url": null,
  "id": "2kn9dekyp2vep",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.28429",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods in Clinical Trials"
    ]
  ],
  "openalex": "W7162654518",
  "pdf_url": "https://arxiv.org/pdf/2605.28429",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2kn9dekyp2vep.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2605.28429",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.28429"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Axioms for validity: e-values, p-values and data-dependent levels",
  "title_text": "Axioms for validity: e-values, p-values and data-dependent levels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/2kn9dekyp2vep",
  "venue": "arXiv",
  "versions": []
}