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Benford's law and the limits of digit analysis

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  • Druică, Elena
  • Oancea, Bogdan
  • Vâlsan, Călin

Abstract

We use panel data that consists of aggregated annual bank account balances and analyze the first two digits of each observation to evaluate conformity to Benford's Law. The data spans a period of 14 years, is naturally generated, and meets the “drawing from a sequence” criterion. We conduct a full battery of null hypothesis significance testing, and we also calculate annual mean absolute deviation and excess mean absolute deviation. The results range from marginal conformity to marginal non-conformity to Benford's Law. We concur with previous research and urge caution when approaching auditing and fraud detection using these analytic tools. This finding illustrates the concept of usual level of conformity, that is, a data-specific signature, driven by the idiosyncrasies of the process that generated it. We also examine the time series of annual mean absolute deviation and excess mean absolute deviation. In a couple of cases, the Dickey-Fuller tests suggest trend-stationarity, although the small number of observations renders the reliability of these results questionable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ijoais:v:31:y:2018:i:c:p:75-82
    DOI: 10.1016/j.accinf.2018.09.004
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    References listed on IDEAS

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    1. Leo Egghe & Raf Guns, 2012. "Applications of the generalized law of Benford to informetric data," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 63(8), pages 1662-1665, August.
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    5. Andreas Diekmann & Ben Jann, 2010. "Benford's Law and Fraud Detection: Facts and Legends," German Economic Review, Verein für Socialpolitik, vol. 11(3), pages 397-401, August.
    6. 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.
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    8. Anton K Formann, 2010. "The Newcomb-Benford Law in Its Relation to Some Common Distributions," PLOS ONE, Public Library of Science, vol. 5(5), pages 1-13, May.
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    2. Pei, Duo & Vasarhelyi, Miklos A., 2020. "Big data and algorithmic trading against periodic and tangible asset reporting: The need for U-XBRL," International Journal of Accounting Information Systems, Elsevier, vol. 37(C).
    3. Roy Cerqueti & Claudio Lupi, 2023. "Severe testing of Benford’s law," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 677-694, June.
    4. Arezzo, Maria Felice & Cerqueti, Roy, 2023. "A Benford’s Law view of inspections’ reasonability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    5. Jalan, Akanksha & Matkovskyy, Roman & Yarovaya, Larisa, 2021. "“Shiny” crypto assets: A systemic look at gold-backed cryptocurrencies during the COVID-19 pandemic," International Review of Financial Analysis, Elsevier, vol. 78(C).
    6. Lasse Pröger & Paul Griesberger & Klaus Hackländer & Norbert Brunner & Manfred Kühleitner, 2021. "Benford’s Law for Telemetry Data of Wildlife," Stats, MDPI, vol. 4(4), pages 1-7, November.
    7. Teddy Lazebnik & Dan Gorlitsky, 2023. "Can We Mathematically Spot the Possible Manipulation of Results in Research Manuscripts Using Benford’s Law?," Data, MDPI, vol. 8(11), pages 1-11, October.
    8. Călin Vâlsan & Andreea-Ionela Puiu & Elena Druică, 2024. "From Whence Commeth Data Misreporting? A Survey of Benford’s Law and Digit Analysis in the Time of the COVID-19 Pandemic," Mathematics, MDPI, vol. 12(16), pages 1-20, August.
    9. de Araújo Silva, Archibald & Aparecida Gouvêa, Maria, 2023. "Study on the effect of sample size on type I error, in the first, second and first-two digits excessmad tests," International Journal of Accounting Information Systems, Elsevier, vol. 48(C).
    10. Pankaj C. Patel & Mike G. Tsionas & Maria João Guedes, 2022. "Benford's law, small business financial reporting, and survival," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(8), pages 3301-3315, December.
    11. Tošić, Aleksandar & Vičič, Jernej, 2021. "Use of Benford's law on academic publishing networks," Journal of Informetrics, Elsevier, vol. 15(3).
    12. González Fernando Antonio Ignacio, 2019. "Detecting Anomalous Data in Household Surveys: Evidence for Argentina," Journal of Social and Economic Statistics, Sciendo, vol. 8(2), pages 1-10, December.
    13. Philip E Hulme & Danish A Ahmed & Phillip J Haubrock & Brooks A Kaiser & Melina Kourantidou & Boris Leroy & Shana M Mcdermott, 2024. "Widespread imprecision in estimates of the economic costs of invasive alien species worldwide," Post-Print hal-04633043, HAL.

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