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Severe testing of Benford’s law

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  • Roy Cerqueti

    (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

  • Claudio Lupi

Abstract

Benford’s law is often used to support critical decisions related to data quality or the presence of data manipulations or even fraud in large datasets. However, many authors argue that conventional statistical tests will reject the null of data “Benford-ness” if applied in samples of the typical size in this kind of applications, even in the presence of tiny and practically unimportant deviations from Benford’s law. Therefore, they suggest using alternative criteria that, however, lack solid statistical foundations. This paper contributes to the debate on the “large n” (or “excess power”) problem in the context of Benford’s law testing. This issue is discussed in relation with the notion of severity testing for goodness-of-fit tests, with a specific focus on tests for conformity with Benford’s law. To do so, we also derive the asymptotic distribution of the mean absolute deviation (MAD) statistic as well as an asymptotic standard normal test. Finally, the severity testing principle is applied to six controversial large datasets to assess their “Benford-ness”.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Roy Cerqueti & Claudio Lupi, 2023. "Severe testing of Benford’s law," Post-Print hal-04321928, HAL.
    • Handle: RePEc:hal:journl:hal-04321928
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    References listed on IDEAS

    as
    1. Roy Cerqueti & Claudio Lupi, 2021. "Some New Tests of Conformity with Benford’s Law," Stats, MDPI, vol. 4(3), pages 1-17, September.
    2. Tam Cho, Wendy K. & Gaines, Brian J., 2007. "Breaking the (Benford) Law: Statistical Fraud Detection in Campaign Finance," The American Statistician, American Statistical Association, vol. 61, pages 218-223, August.
    3. Block, Henry W. & Savits, Thomas H., 2010. "A General Example for Benford Data," The American Statistician, American Statistical Association, vol. 64(4), pages 335-339.
    4. Alex Ely Kossovsky, 2021. "On the Mistaken Use of the Chi-Square Test in Benford’s Law," Stats, MDPI, vol. 4(2), pages 1-35, May.
    5. Druică, Elena & Oancea, Bogdan & Vâlsan, Călin, 2018. "Benford's law and the limits of digit analysis," International Journal of Accounting Information Systems, Elsevier, vol. 31(C), pages 75-82.
    6. Fewster, R. M., 2009. "A Simple Explanation of Benford's Law," The American Statistician, American Statistical Association, vol. 63(1), pages 26-32.
    7. Micha Kaiser, 2019. "Benford'S Law As An Indicator Of Survey Reliability—Can We Trust Our Data?," Journal of Economic Surveys, Wiley Blackwell, vol. 33(5), pages 1602-1618, December.
    8. C. W. J. Granger, 1998. "Extracting information from mega‐panels and high‐frequency data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(3), pages 258-272, November.
    9. Sitsofe Tsagbey & Miguel de Carvalho & Garritt L. Page, 2017. "All Data are Wrong, but Some are Useful? Advocating the Need for Data Auditing," The American Statistician, Taylor & Francis Journals, vol. 71(3), pages 231-235, July.
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    Cited by:

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    3. Marcel Ausloos & Probowo Erawan Sastroredjo & Polina Khrennikova, 2025. "Note on Pre-Taxation Data Reported by UK FTSE-Listed Companies: Search for Compatibility with Benford’s Laws," Stats, MDPI, vol. 8(1), pages 1-17, February.
    4. Adriano Silva & Sergio Floquet & Ricardo Lima, 2023. "Newcomb–Benford’s Law in Neuromuscular Transmission: Validation in Hyperkalemic Conditions," Stats, MDPI, vol. 6(4), pages 1-19, October.

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