Not the first digit! Using Benford’s law to detect fraudulent scientific data.

*(English)*Zbl 1158.62094Summary: 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.

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
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\textit{A. Diekmann}, J. Appl. Stat. 34, No. 3--4, 321--329 (2007; Zbl 1158.62094)

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