{
  "abstract": "We introduce a set of consequence-based measures that quantify the misclassification arising from imperfect reliability in multi-item psychometric scales. Particular attention is given to the probability of individuals in extreme latent-trait percentiles being correctly identified from their observed scores. These cost functions provide a principled and interpretable way to characterise how inadequate reliability distorts classification and reduces the informational value of test scores. We also examine methodological issues in estimating reliability under common-factor models, with emphasis on McDonald's omega and the construction of accurate confidence intervals. To address the computational burden of model fitting, especially in small samples, we derive a modified version of Cronbach's alpha that closely approximates omega when the common-factor model holds. This estimator has comparable sampling variability to omega while requiring no parameter estimation, offering a practical and computationally efficient alternative. y",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03006",
  "author_total": 1,
  "authors": [
    {
      "name": "Rose Baker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/409grma2x0ekd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03006",
  "fulltext_url": null,
  "id": "409grma2x0ekd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03006",
  "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",
      "1803|Psychometric Methodologies and Testing"
    ]
  ],
  "openalex": "W7220462311",
  "pdf_url": "https://arxiv.org/pdf/2610.03006",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/409grma2x0ekd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:56Z",
      "native_id": "2610.03006",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03006"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Psychometric Tests: Quantifying the Consequences of Low Reliability and Improving Reliability Estimation",
  "title_text": "Psychometric Tests: Quantifying the Consequences of Low Reliability and Improving Reliability Estimation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:56Z",
  "url": "https://research.draconitic.com/paper/409grma2x0ekd",
  "venue": "arXiv",
  "versions": []
}