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Advanced Statistical Techniques For Testing Benford'S Law


  • Rabeea Sadaf

    () (Karoly Ihrig Doctoral School of Management and Business University of Debrecen, Hungary)


The frequency of accounting data frauds has been increased in corporate environment. As a result of that, the research on detection of such irregularities in accounting and auditing is gaining researchers’ focus. Bedford’s law has been in the literature for the identification of data manipulation in accounting and auditing field. The application of this law in accounting fraud detection started in 1988 after the work of Carslaw (he observed a greater frequency of zeros and less frequency of nines in the second place in the reported earning numbers). The underlying idea about this technique is based on comparison of certain digit frequency to the expected digit pattern proposed by Bedford’s law. Various goodness-of-fit test are used to analyze the data conformity to Benford’s law based on a null hypothesis of conformity of empirical data to expected data pattern. This study addresses some of the most important goodness-of fit tests that can be used to analyze data pattern and digit behavior. Most importantly chi-square, Kolmogorov-Smirnov test (KS), Euclidean distance, Joenssen’s JP-square, Freedman-Watson u-square, Chebyshev distance, Z-statistics and mean absolute deviation tests are discussed with expression to calculate test statistics. Tests like Chi-Square and KS are also sensitive to size of data set, so a combination of various goodness-of fit test is recommended in literature to make more accurate analysis of data conformity.

Suggested Citation

  • Rabeea Sadaf, 2017. "Advanced Statistical Techniques For Testing Benford'S Law," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(2), pages 229-238, December.
  • Handle: RePEc:ora:journl:v:1:y:2017:i:2:p:229-238

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. Bernhard Rauch & Max G�ttsche & Stephan Langenegger, 2014. "Detecting Problems in Military Expenditure Data Using Digital Analysis," Defence and Peace Economics, Taylor & Francis Journals, vol. 25(2), pages 97-111, April.
    4. Rabeea SADAF, 2016. "Benford’S Law In The Case Of Hungarian Whole-Sale Trade Sector," SEA - Practical Application of Science, Romanian Foundation for Business Intelligence, Editorial Department, issue 12, pages 561-566, December.
    5. Domicián Máté & András István Kun & Veronika Fenyves, 2016. "The Impacts of Trademarks and Patents on Labour Productivity in the Knowledge-Intensive Business Service Sectors," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 18(41), pages 104-104, February.
    6. Morrow, John, 2014. "Benford's Law, families of distributions and a test basis," LSE Research Online Documents on Economics 60364, London School of Economics and Political Science, LSE Library.
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    More about this item


    Benford’s Law; accounting and auditing; Goodness-of-fit; Conformity; Digit pattern;

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • M40 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - General
    • M41 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - Accounting


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