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Not the First Digit! Using Benford’s Law to Detect Fraudulent Scientific Data

Author

Listed:
  • Andreas Diekmann

    (ETH Zurich)

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 real data follow the Benford distribution while 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 digit frequencies in published statistical estimates. Second, we conducted experiments in which subjects were asked to fabricate statistical estimates (regression coefficients). These experimental data were scrutinized for possible deviations from the Benford distribution. There were two main findings. First, the digits of the published regression coefficients were approximately Benford distributed. Second, the experimental results yielded new insights into the strengths and weaknesses of Benford tests. At least in the case of regression coefficients, there were indications that checks for digit-preference anomalies should focus less on the first and more on the second and higher-digits.

Suggested Citation

  • Andreas Diekmann, 2005. "Not the First Digit! Using Benford’s Law to Detect Fraudulent Scientific Data," Others 0507001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpot:0507001
    Note: Type of Document - pdf; pages: 25
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/othr/papers/0507/0507001.pdf
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    References listed on IDEAS

    as
    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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    1. Statistical Sleuthing on the Iran Election
      by (author unknown) in The Numbers Guy on 2009-07-01 05:46:58

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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. 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.
    3. 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, vol. 231(5-6), pages 685-718, October.
    4. Jesus R Gonzalez-Garcia & Gonzalo C Pastor Campos, 2009. "Benford’s Law and Macroeconomic Data Quality," IMF Working Papers 09/10, International Monetary Fund.
    5. 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.
    6. 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.

    More about this item

    Keywords

    Benford; Benford's law; falsification of data; fabrication of data;

    JEL classification:

    • C - Mathematical and Quantitative Methods

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