The effective use of Benford's Law to assist in detecting fraud in accounting data

TLDR

Benford’s law, which predicts that lower digits occur more frequently (e.g., over 30 % of numbers start with 1), is promoted as a simple, effective tool for fraud detection in accounting data. This paper aims to guide auditors on the most effective use of digital analysis based on Benford’s law. The authors review the law’s background, identify data sets likely to follow Benford’s distribution, evaluate statistical test power, outline fraud types detectable or missed, and discuss issues such as small sample sizes and base‑rate effects. An illustrative case shows Benford’s law successfully identified fraud within a real accounting data set.

Abstract

Benford’s law has been promoted as providing the auditor with a tool that is simple and effective for the detection of fraud. The purpose of this paper is to assist auditors in the most effective use of digital analysis based on Benford’s law. The law is based on a peculiar observation that certain digits appear more frequently than others in data sets. For example, in certain data sets, it has been observed that more than 30% of numbers begin with the digit one. After discussing the background of the law and development of its use in auditing, we show where digital analysis based on Benford’s law can most effectively be used and where auditors should exercise caution. Specifically, we identify data sets which can be expected to follow Benford’s distribution, discuss the power of statistical tests, types of frauds that would be detected and not be detected by such analysis, the potential problems that arise when an account contains too few observations, as well as issues related to base rate of fraud. An actual example is provided demonstrating where Benford’s law proved successful in identifying fraud in a population of accounting data.