Difficulties Detecting Fraud? The Use of Benford's Law on Regression Tables

• Published in: Jahrbücher für Nationalökonomie und Statistik 2011-11, Vol.231 (5/6), p.733-748
• Main Authors: Bauer, Johannes, Gross, Jochen
• Format: Article
• Language: English
• Subjects: Benford; Benford, Frank; Coefficients; Constant coefficients; Data analysis; Data collection; data fabrication; Deceit; digital analysis; Distribution economics; distribution of digits from regression coefficients; Empirical evidence; first digit law; Forgery; Fraud; Investigations; Linear regression; Litigation; Logistic regression; Monte Carlo simulation; Regression analysis; Regression coefficients; Research fraud; Scientific method; Scientific research; Statistical analysis; Tax fraud; Western Europe
• ISSN: 0021-4027; 2366-049X
• DOI: 10.1515/jbnst-2011-5-611

The occurrence of scientific fraud damages the credibility of science. An instrument to discover deceit was proposed with Benford's law, a distribution which describes the probability of significant digits in many empirical observations. If Benford-distributed digits are expected and empirical observations deviate from this law, the difference yields evidence for fraud. This article analyses the practicability and capability of the digit distribution to investigate scientific counterfeit. In our context, capability means that little data is required to discover forgery. Furthermore, we present a Benford-based method which is more effective in detecting deceit and can also be extended to several other fields of digit analysis. We also restrict this article to the research area of non-standardized regressions. The results reproduce and extend the finding that non-standardized regression coefficients follow Benford's law. Moreover, the data show that investigating regressions from different subjects demands more observations and hence is less effective than investigating regressions from single persons. Consequently, the digit distribution can discover indications for fraud, but only if the percentage of forgery in the data is large. With a decreasing proportion of fabricated values, the number of required cases to detect a significant difference between real and fraudulent regressions rises. Under the condition that only few scientists forge results, the investigation method becomes ineffective and inapplicable.