Not the First Digit! Using Benford’s Law to Detect Fraudulent Scientific Data

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 real data follow the Benford distribution while 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 digit frequencies in published statistical estimates. Second, we conducted experiments in which subjects were asked to fabricate statistical estimates (regression coefficients). These experimental data were scrutinized for possible deviations from the Benford distribution. There were two main findings. First, the digits of the published regression coefficients were approximately Benford distributed. Second, the experimental results yielded new insights into the strengths and weaknesses of Benford tests. At least in the case of regression coefficients, there were indications that checks for digit-preference anomalies should focus less on the first and more on the second and higher-digits.