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Difficulties Detecting Fraud? The Use of Benford’s Law on Regression Tables

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  • Johannes Bauer

    ()
    (Uni Muenchen)

  • Jochen Gross

    (Roland Berger Strategy Consultans Holding GmbH)

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    Abstract

    The occurrence of scientific fraud damages the credibility of science. An instrument to discover deceit was proposed with Benford’s law, a distribution which describes the probability of significant digits in many empirical observations. If Benford-distributed digits are expected and empirical observations deviate from this law, the difference yields evidence for fraud. This article analyses the practicability and capability of the digit distribution to investigate scientific counterfeit. In our context, capability means that little data is required to discover forgery. Furthermore, we present a Benford-based method which is more effective in detecting deceit and can also be extended to several other fields of digit analysis. We also restrict this article to the research area of non-standardized regressions. The results reproduce and extend the finding that non-standardized regression coefficients follow Benford’s law. Moreover, the data show that investigating regressions from different subjects demands more observations and hence is less effective than investigating regressions from single persons. Consequently, the digit distribution can discover indications for fraud, but only if the percentage of forgery in the data is large. With a decreasing proportion of fabricated values, the number of required cases to detect a significant difference between real and fraudulent regressions rises. Under the condition that only few scientists forge results, the investigation method becomes ineffective and inapplicable.

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    Bibliographic Info

    Article provided by Justus-Liebig University Giessen, Department of Statistics and Economics in its journal Journal of Economics and Statistics.

    Volume (Year): 231 (2011)
    Issue (Month): 5-6 (November)
    Pages: 733-748

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    Handle: RePEc:jns:jbstat:v:231:y:2011:i:5-6:p:733-748

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    Related research

    Keywords: Benford; first digit law; digital analysis; data fabrication; distribution of digits from regression coefficients; Monte Carlo simulation;

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    References

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    1. 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.
    2. David E. Giles, 2005. "Benford’s Law and Naturally Occurring Prices in Certain ebaY Auctions," Econometrics Working Papers 0505, Department of Economics, University of Victoria.
    3. 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, 08.
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