Not the first digit! Using Benford’s law to detect fraudulent scientific data. (English) Zbl 1158.62094

Diekmann, Andreas

J. Appl. Stat. 34, No. 3-4, 321-329 (2007).

Summary: 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.

MSC:

62P99

Applications of statistics

Keywords:

Benford; first digit law; digital analysis; data fabrication; distribution of digits from regression coefficients

References:

[1]	DOI: 10.1109/TR.1982.5221273 · Zbl 0485.90043 · doi:10.1109/TR.1982.5221273
[2]	Benford F., Proceedings of the American Philosophical Society 78 pp 551– (1938) · JFM 64.0555.03
[3]	Berton L., Wall Street Journal (1995)
[4]	Carslow C., The Accounting Review 63 pp 321– (1988)
[5]	Hill T. P., Statistical Science 10 pp 354– (1995)
[6]	Hill T. P., Proceedings of the American Mathematical Society 123 pp 887– (1995)
[7]	Hill T. P., American Scientist 86 pp 358– (1998) · doi:10.1511/1998.31.815
[8]	DOI: 10.1080/08989629508573866 · doi:10.1080/08989629508573866
[9]	DOI: 10.1080/08989620212969 · doi:10.1080/08989620212969
[10]	DOI: 10.2307/2369148 · JFM 13.0161.01 · doi:10.2307/2369148
[11]	Nigrini M. J., The Journal of the American Taxpayer Association 18 pp 72– (1996)
[12]	Quick R., Betriebswirtschaftliche Forschung und Praxis pp 208– (2003)
[13]	DOI: 10.1038/scientificamerican1269-109 · doi:10.1038/scientificamerican1269-109
[14]	DOI: 10.2307/2319349 · Zbl 0349.60014 · doi:10.2307/2319349
[15]	Schäfer C., Schmollers Jahrbuch –Journal of Applied Social Science Studies 125 (2005)
[16]	DOI: 10.1007/s101820500188 · doi:10.1007/s101820500188