Benford's Law

This is an advanced digital analysis technique that involves examining the actual frequency of the digits in the data. The law calculates that numbers in sets of data with low first digits, such as 1, occur with more frequency than numbers with high first digits, like 8 or 9. Valid, unaltered data, without exceptional transactions, will follow the projected frequencies.

Benford's law (principle) has been found to apply to many sets of financial data, including corporate disbursements. Audit software can employ digital analyses using Benford's law to identify fraud and other irregularities in accounts payable, income tax forms, claims payments and other disbursements. Audit software, compatible with Excel, is available at no charge to so this analysis.

Conversely, data that meets the principles criteria, but fails to follow the expected frequencies, may include fraudulent items. It is very difficult for people to make up credible numbers, as invented numbers are unlikely to follow the law. Thus, this principle can be tested by the audit staff to spot irregularities, including possible error, fraud detection, or other anomalies. Audit software is available, including both Excel and a command language process for larger volumes.

The technique has been used in a variety of environments, including:

Detecting Irregularities in Insurance Claims
Highlighting Unusual Employee Expense Reports
Detecting possibly fraudulent tax returns
Fraud detection in medical insurance claims

This test provides the internal auditor with an efficient means of fraud detection by measuring an expected population distribution against the actual distribution. By highlighting selected transactions, vendors or other groups, the internal auditor/researcher is better able to isolate and focus on a target group, and therefore potentially be more productive in identifying errors or unusual transactions.

The fraud detection techniques used are based upon mathematical theories which are explained in detail in various referenced articles. Because transaction volumes are often very significant, and needed computations would be tedious if done manually, the use of audit software , especially a command language, is generally recommended for fraud detection.

Suggested Audit Approaches

Analytical Features of the Audit Software

Benford's Law formulae and values in Excel

Articles on Benford's Law

Downloads (audit software and papers)

Limitations and Cautions

Examples of Application of Benford's Law

Example Charts of Accounts Payable Tests

An audit guide is available for tests using this principle. Also available are tests using the internet, which require no software installation or maintenance. Data from any tab separated value source, e.g. Excel spreadsheets can be "pasted" into the application for analysis. View help page.