Applying and Testing Benford’s Law Are Not the Same

• William M. Goodman ^[1]
  1. [1] Faculty of Business and IT, Ontario Tech University. Canada
• Localización: Spanish journal of statistics, ISSN-e 2695-9070, Nº. 5, 2023, págs. 43-53
• Idioma: inglés
• DOI: 10.37830/SJS.2023.1.03
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• Resumen

  • Most papers on Benford’s Law primarily discuss either (1) the science and mathematics for explaining the law; or (2) how to apply the law, especially for detecting data manipulation and fraud; or (3) suggestions for statistical tests to determine if data conform to a Benford’s distribution. Leonardo Campanelli’s recent paper “Testing Benford’s Law” strongly objects to a descriptive measure I discussed in my paper “The Promises and Pitfalls of Benford’s Law”—as if that measure were intended for Benford’s testing in the Category-3 sense relevant for Campanelli’s paper (SJS, vol. 4, 2022). This reflects a conflation of meanings for “testing” that is common in the Benford’s literature, where many Category-2 papers claim they are applying (directly) conventional or new hypothesis tests as tools to detect fraud. Yet, fraud detection is a forensic and context-sensitive process, for which there is no set formula. In this paper, I clarify the sampling plan I had used earlier to collect and analyze a quasi-random sample of datasets, based on published criteria in the literature, to paint a tentative picture of how far real data vary, and in what ways, from abstract BL expectations. Further, I discuss simulations I have conducted to replicate and expand on my previous results.