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Digital Analysis Using Benford’s Law 
by Mark J. Nigrini  

Book Review 
by Jim Kaplan

Benford's Law, first identified by Simon Newcomb in 1881, states that if you randomly select a number from a table of physical constants or statistical data, the probability that the first digit will be a "1" is about 30%, rather than 10% as we might expect if all digits were equally likely. 

According to Mark Nigrini, the author of Digital Analysis Using Benford’s Law, the audit technology known as Digital Analysis (DA), tests for abnormalities in the digit patterns and abnormal number duplication in corporate data. Mr. Nigrini does a formidable job of explaining how to use digital analysis in performing audit tests of data. The first 8 chapters of the book delve into the background of Benford’s Law and different models for applying it. As someone who struggled though Algebra and Geometry as well as College Statistics I found the discussion way above my head. However after plodding through the technical foundation and starting with Chapter 9 the application of Benford’s law became apparent as well as enlightening. Nigrini goes through case studies with fraudulent data and explains how Benford’s Law is applied from an audit context. Auditors will be able to appreciate the different scenarios and how using digital analysis can ferret out unusual or suspect data. The test discussed range from high-level digit analysis to more in-depth duplication tests (for duplicate payment reviews), round number tests and more.

As a new user to IDEA I was eager to test data for a recent audit of procurement card transactions. As Mark Nigrini analyzed data using the DATAS suite of programs I felt that perhaps I should test it out as well. I ordered a demo of the DATAS 2001 from Audimation Services and used it on a file of over 27000 transactions. After running some of the tests, I don’t see how an auditor would be able to apply Benford’s Law to audit data without having a data analysis package such as DATAS as it would have taken me days (perhaps months) to sort the large volume of transactions based on the digits. On the same note I would expect that if an auditor were using DATAS they would need a reference guide such as Mark Nigrini’s book by their side to understand each of the tests included in the program and their applicability.  From an auditors perspective, Mark’s insight into auditing is also refreshing.  For instance in the section on testing for low value invoices, Mark states “This test will always produce a finding for auditors.”

In my opinion this book should be in the professional library of every audit department that uses computer assisted audit tools and techniques. In this day and age I can’t imagine any modern audit department that is not using CAATTs and therefore every auditor that uses these tools should read (and reread) Digital Analysis Using Benford’s Law by Mark Nigrini.  Coming from a math challenged auditor, get the book and read it.  You won’t be sorry and it will definitely help with your analysis of digital data!

Top Links

More book information and ordering links: http://www.acl.com/benford/index.html

Site with articles on Benford’s Law and Digital Analysis: http://www.auditsoftware.net