Applying Digital Analysis Using Benford's Law to Detect Fraud: The Dangers of Type I Errors

Abstract

At first glance the application of digital analysis using Benford's Law holds great promise as a fraud detection process. However, a closer look at the underlying statistical assumptions reveals that auditors seeking to use Benford's Law must be aware of the costs of the potential Type I errors that can occur during the analysis stage. For example, statistical considerations indicate that there is a far greater chance of making a Type I error if the Benford's Law analysis is completed on a “digit-by-digit” basis, as compared to the “test-by-test” basis typically employed by statisticians. In this paper, we explain the merits of each choice in terms of statistical concepts and practical audit process considerations.

Financial statement errors: evidence from the distributional properties of financial statement numbers

“…Since accounting data are a series of estimations of the true cash flow realizations of the underlying items (for example, cash flows from sales, cash flows from payments 12 While two other statistics, the Z-statistic and the Chi square statistic, were widely used in the early stages of the forensic accounting literature, in this area researchers have progressed to using the MAD statistic (Cleary and Thibodeau 2005;Nigrini 2012). The main deficiency of using the Z-statistic to examine Benford's Law is that it examines conformity of only a single digit at a time, rather than the composite distribution of digits.…”

Detecting Financial Statement Frauds in Malaysia: Comparing the Abilities of Beneish and Dechow Models

“…The findings suggest that Dechow F-score provides higher accuracy in detecting fraud compared to the Beneish model. Furthermore, as suggested by Cleary and Thibodeau (2005), the error rates of the fraud detection models should be examined by considering Type I and Type II errors. A Type I error occurs when the model wrongly classifies a fraudulent company as a non-fraudulent company.…”

A Data Analysis Based Framework to Detect Anomalies in Large Data Sets Using Benford’s Law

“…They also question validity based on the high occurrence of false positives. Research has also noted the potential high results of Type 1 errors (Cleary and Thibodeau, 2005;Rodriguez, 2004); using a Bayesian approach (Geyer and Williamson, 2004). There are also other streams of research aiming for implementing better methodologies for detecting fraud.…”