• J Hein, R Zobrist, C Konrad, and G Schuepfer.
• Institute of Anesthesiology, Kantonsspital Nidwalden, 6000, Stans, Switzerland.
• Anaesthesist. 2012 Jun 1;61(6):543-9.

AbstractData from natural sources show counter-intuitive distribution patterns for the leading digits to the left of the decimal point and the digit 1 is observed more frequently than all other numbers. This pattern, which was first described by Newcomb and later confirmed by Benford, is used in financial and tax auditing to detect fraud. Deviations from the pattern indicate possible falsifications. Anesthesiology journals are affected not only by ghostwriting and plagiarism but also by counterfeiting. In the present study 20 publications in anesthesiology known to be falsified by an author were investigated for irregularities with respect to Benford's law using the χ(2)-test and the Z-test. In the 20 retracted publications an average first-digit frequency of 243.1 (standard deviation SD ± 118.2, range: 30-592) and an average second-digit frequency of 132.3 (SD ± 72.2, range: 15-383) were found. The observed distribution of the first and second digits to the left of the decimal point differed significantly (p< 0.01) from the expected distribution described by Benford. Only the observed absolute frequencies for digits 3, 4 and 5 did not differ significantly from the expected values. In an analysis of each paper 17 out of 20 studies differed significantly from the expected value for the first digit and 18 out of 20 studies varied significantly from the expected value of the second digit. Only one paper did not vary significantly from expected values for the digits to the left of the decimal. For comparison, a meta-analysis using complex mathematical procedures was chosen as a control. The analysis showed a first-digit distribution consistent with the Benford distribution. Thus, the method used in the present study seems to be sensitive for detecting fraud. Additional statements of specificity cannot yet be made as this requires further analysis of data that is definitely not falsified. Future studies exploring conformity might help prevent falsified studies from being published.

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