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Not the First Digit! Using Benford's Law to Detect Fraudulent Scientif ic Data

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  • Andreas Diekmann

Abstract

Digits in statistical data produced by natural or social processes are often distributed in a manner described by 'Benford's law'. Recently, a test against this distribution was used to identify fraudulent accounting data. This test is based on the supposition that first, second, third, and other digits in real data follow the Benford distribution while the digits in fabricated data do not. Is it possible to apply Benford tests to detect fabricated or falsified scientific data as well as fraudulent financial data? We approached this question in two ways. First, we examined the use of the Benford distribution as a standard by checking the frequencies of the nine possible first and ten possible second digits in published statistical estimates. Second, we conducted experiments in which subjects were asked to fabricate statistical estimates (regression coefficients). The digits in these experimental data were scrutinized for possible deviations from the Benford distribution. There were two main findings. First, both digits of the published regression coefficients were approximately Benford distributed or at least followed a pattern of monotonic decline. Second, the experimental results yielded new insights into the strengths and weaknesses of Benford tests. Surprisingly, first digits of faked data also exhibited a pattern of monotonic decline, while second, third, and fourth digits were distributed less in accordance with Benford's law. At least in the case of regression coefficients, there were indications that checks for digit-preference anomalies should focus less on the first (i.e. leftmost) and more on later digits.

Suggested Citation

  • Andreas Diekmann, 2007. "Not the First Digit! Using Benford's Law to Detect Fraudulent Scientif ic Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(3), pages 321-329.
  • Handle: RePEc:taf:japsta:v:34:y:2007:i:3:p:321-329 DOI: 10.1080/02664760601004940
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    1. Schraepler, Joerg-Peter & Wagner, Gert G., 2003. "Identification, Characteristics and Impact of Faked Interviews in Surveys: An Analysis by Means of Genuine Fakes in the Raw Data of SOEP," IZA Discussion Papers 969, Institute for the Study of Labor (IZA).
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    Cited by:

    1. Bauer Johannes & Groß Jochen, 2011. "Difficulties Detecting Fraud? The Use of Benford’s Law on Regression Tables," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(5-6), pages 733-748, October.
    2. Bernhard Rauch & Max Göttsche & Gernot Brähler & Stefan Engel, 2011. "Fact and Fiction in EU‐Governmental Economic Data," German Economic Review, Verein für Socialpolitik, vol. 12(3), pages 243-255, August.
    3. Rabeea SADAF, 2016. "Benford’S Law In The Case Of Hungarian Whole-Sale Trade Sector," SEA - Practical Application of Science, Fundația Română pentru Inteligența Afacerii, Editorial Department, issue 12, pages 561-566, December.
    4. Bruno S. Frey, 2010. "Withering Academia," CREMA Working Paper Series 2010-19, Center for Research in Economics, Management and the Arts (CREMA).
    5. Shikano Susumu & Mack Verena, 2011. "When Does the Second-Digit Benford’s Law-Test Signal an Election Fraud?: Facts or Misleading Test Results," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(5-6), pages 719-732, October.
    6. Schräpler Jörg-Peter, 2011. "Benford’s Law as an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP)," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, pages 685-718.
    7. Carsten A. Holz, 2014. "The Quality of China’s GDP Statistics," a/ Working Papers Series 1403, Italian Association for the Study of Economic Asymmetries, Rome (Italy).
    8. Andreas Diekmann & Ben Jann, 2010. "Benford's Law and Fraud Detection: Facts and Legends," German Economic Review, Verein für Socialpolitik, vol. 11, pages 397-401, August.
    9. Jesus R Gonzalez-Garcia & Gonzalo C Pastor Campos, 2009. "Benford’s Law and Macroeconomic Data Quality," IMF Working Papers 09/10, International Monetary Fund.
    10. Chase Thiel & Zhanna Bagdasarov & Lauren Harkrider & James Johnson & Michael Mumford, 2012. "Leader Ethical Decision-Making in Organizations: Strategies for Sensemaking," Journal of Business Ethics, Springer, pages 49-64.
    11. Lin, Fengyi & Wu, Sheng-Fu, 2014. "Comparison of cosmetic earnings management for the developed markets and emerging markets: Some empirical evidence from the United States and Taiwan," Economic Modelling, Elsevier, vol. 36(C), pages 466-473.
    12. Holz, Carsten A., 2014. "The quality of China's GDP statistics," China Economic Review, Elsevier, vol. 30(C), pages 309-338.
    13. Dlugosz, Stephan & Müller-Funk, Ulrich, 2012. "Ziffernanalyse zur Betrugserkennung in Finanzverwaltungen: Prüfung von Kassenbelegen," Arbeitsberichte des Instituts für Wirtschaftsinformatik 133, University of Münster, Department of Information Systems.
    14. Montag, Josef, 2015. "Identifying Odometer Fraud: Evidence from the Used Car Market in the Czech Republic," MPRA Paper 65182, University Library of Munich, Germany.
    15. Brähler, Gernot & Bensmann, Markus & Emke, Anna-Lena, 2010. "Der Einsatz mathematisch-statistischer Methoden in der digitalen Betriebsprüfung," Ilmenauer Schriften zur Betriebswirtschaftslehre, Technische Universität Ilmenau, Institut für Betriebswirtschaftslehre, volume 4, number 42010.
    16. Kundt, Thorben, 2014. "Applying “Benford’s law” to the Crosswise Model: Findings from an online survey on tax evasion," Working Paper 148/2014, Helmut Schmidt University, Hamburg.
    17. Karl-Heinz Tödter, 2009. "Benford's Law as an Indicator of Fraud in Economics," German Economic Review, Verein für Socialpolitik, vol. 10, pages 339-351, August.
    18. repec:eee:trapol:v:60:y:2017:i:c:p:10-23 is not listed on IDEAS
    19. José A. Álvarez-Jareño & Elena Badal-Valero & José Manuel Pavía, 2017. "Using machine learning for financial fraud detection in the accounts of companies investigated for money laundering," Working Papers 2017/07, Economics Department, Universitat Jaume I, Castellón (Spain).

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