Severe testing of Benford’s law

Roy Cerqueti () and Claudio Lupi
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Roy Cerqueti: La Sapienza University of Rome

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 2, No 13, 677-694

Abstract: 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”.

Keywords: Benford’s law; Data quality; Fraud discovery; Goodness-of-fit; Large n problem; Severity; 62E20; 62F03 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11749-023-00848-z

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