Statistician’s new role as a detective – testing data for fraud

Abstract

The objective of this paper is to provide the statistician with a method for the challenging task of deciding whether a given data set might have been invented in a fraudulent way or appearing authentic. This is done not by examining the numbers themselves, but surprisingly, rather by investigating the digital language utilized in writing those numbers! What letters are to words, digits are to numbers. The technique relies on Benford’s Law, a statistical law referring to the consistent and predictable relative proportions of digits occurring in typical real-life data, stating that low digits are much more frequent than high digits. The law is immensely useful as a tool to detect fraud, especially tax fraud, since cheaters inventing fake data mistakenly write them with all digits having about the same proportion due to the erroneous intuition that all digits come with equal chances. By comparing theoretical Benford digit distribution to the actual digit distribution within the accounting data provided by companies, the statistician can easily discover fraud relating to fake and invented data. These digital forensic tests are now standard procedures in most of the Tax Revenue Departments of governments worldwide, as well as in large accounting and auditing companies.