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Benford's Law As an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP)

  • Jörg-Peter Schräpler

This paper focuses on fraud detection in surveys using Socio-Economic Panel (SOEP) data as an example for testing newly methods proposed here. A statistical theorem referred to as Benford's Law states that in many sets of numerical data, the significant digits are not uniformly distributed, as one might expect, but rather adhere to a certain logarithmic probability function. To detect fraud we derive several requirements that should, according to this law, be fulfilled in the case of survey data. We show that in several SOEP subsamples, Benford's Law holds for the available continuous data. For this analysis, we have developed a measure that reflects the plausibility of the digit distribution in interviewer clusters. We are able to demonstrate that several interviews that were known to have been fabricated and therefore deleted in the original user data set can be detected using this method. Furthermore, in one subsample, we use this method to identify a case of an interviewer falsifying ten interviews who had not been detected previously by the fieldwork organization. In the last section of our paper, we try to explain the deviation from Benford's distribution empirically, and show that several factors can influence the test statistic used. To avoid misinterpretations and false conclusions, it is important to take these factors into account when Benford's Law is applied to survey data.

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File URL: http://www.diw.de/documents/publikationen/73/diw_01.c.349061.de/diw_sp0273.pdf
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Paper provided by DIW Berlin, The German Socio-Economic Panel (SOEP) in its series SOEPpapers on Multidisciplinary Panel Data Research with number 273.

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Length: 56 p.
Date of creation: 2010
Date of revision:
Handle: RePEc:diw:diwsop:diw_sp273
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  1. Andreas Diekmann, 2002. "Diagnose von Fehlerquellen und methodische Qualität in der sozialwissenschaftlichen Forschung [Sources of Bias and Quality of Data in Social Science Research]," ITA manu:scripts 02_04, Institute of Technology Assessment (ITA).
  2. Jörg-Peter Schräpler & Gert Wagner, 1999. "Das "Interviewer-Panel" des Sozio-oekonomischen Panels: Darstellung und ausgewählte Analysen," Discussion Papers of DIW Berlin 184, DIW Berlin, German Institute for Economic Research.
  3. Engel, Hans-Andreas & Leuenberger, Christoph, 2003. "Benford's law for exponential random variables," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 361-365, July.
  4. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-94, September.
  5. Lolbert, Tamás, 2008. "On the non-existence of a general Benford's law," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 103-106, March.
  6. Joerg-Peter Schraepler, 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), Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 231(5-6), pages 685-718, November.
  7. Bredl, Sebastian & Winker, Peter & Kötschau, Kerstin, 2008. "A statistical approach to detect cheating interviewers," Discussion Papers 39, Justus Liebig University Giessen, Center for international Development and Environmental Research (ZEU).
  8. 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.
  9. Gert G. Wagner & Joachim R. Frick & Jürgen Schupp, 2007. "The German Socio-Economic Panel Study (SOEP) – Scope, Evolution and Enhancements," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 127(1), pages 139-169.
  10. 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.
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