Product Description

A powerful new tool for all forensic accountants, or anyone who analyzes data that may have been altered

Benford's Law gives the expected patterns of the digits in the numbers in tabulated data such as town and city populations or Madoff's fictitious portfolio returns. Those digits, in unaltered data, will not occur in equal proportions; there is a large bias towards the lower digits, so much so that nearly one-half of all numbers are expected to start with the digits 1 or 2. These patterns were originally discovered by physicist Frank Benford in the early 1930s, and have since been found to apply to all tabulated data. Mark J. Nigrini has been a pioneer in applying Benford's Law to auditing and forensic accounting, even before his groundbreaking 1999 Journal of Accountancy article introducing this useful tool to the accounting world. In Benford's Law, Nigrini shows the widespread applicability of Benford's Law and its practical uses to detect fraud, errors, and other anomalies.

• Explores primary, associated, and advanced tests, all described with data sets that include corporate payments data and election data
• Includes ten fraud detection studies, including vendor fraud, payroll fraud, due diligence when purchasing a business, and tax evasion
• Covers financial statement fraud, with data from Enron, AIG, and companies that were the target of hedge fund short sales
• Looks at how to detect Ponzi schemes, including data on Madoff, Waxenberg, and more
• Examines many other applications, from the Clinton tax returns and the charitable gifts of Lehman Brothers to tax evasion and number invention

Benford's Law has 250 figures and uses 50 interesting authentic and fraudulent real-world data sets to explain both theory and practice, and concludes with an agenda and directions for future research. The companion website adds additional information and resources.

Product Details

• Amazon Sales Rank: #869111 in Books
• Published on: 2012-04-24
• Original language: English
• Number of items: 1
• Dimensions: 10.30" h x 1.25" w x 7.55" l, 1.63 pounds
• Binding: Hardcover
• 330 pages

From the Inside Flap

There are hidden patterns in the chaos that we know as data. In the 1930s, the physicist Frank Benford found that there were predictable patterns to the digits in the numbers in tabulated data. For many years, this little secret was known to only a few people, made up mainly of mathematicians and the Benford family. In the 1990s, the accountant Mark Nigrini first advocated the use of Benford's Law as a test for fraud and of data integrity. With 250 tables and figures dealing with 50 data sets revealed over 13 chapters, Nigrini takes us on a pioneering journey in Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection. Our adventure starts with the original 1938 paper on the topic and then moves through the leading-edge mathematical discoveries in the early days, finishing with recent examples from the GM, Chrysler, and Lehman bankruptcy filings, as well as an analysis of the numbers invented by students in an experiment designed to trick the researcher.

The applications include:

• U.S. census population numbers

• The Fibonacci numbers

• Corporate payments

• Enron and AIG's financial statement numbers

• General Motors and Chrysler payments data

• Madoff's monthly returns

• Streamflow and lake data

• Taxpayer interest and dividend income

• The tax returns of Bill and Hillary Clinton

• Lehman's charitable gifts

Benford's Law is written to be understood and enjoyed by auditors, forensic accountants, fraud investigators, financial analysts, and others concerned with data integrity and data authenticity. The book is both informative and entertaining, and is aimed at professionals with a basic knowledge of statistics and a love for numbers and figures. Nigrini's passion for the topic is clear, from the first page, where we are reminded that numbers play an integral part in our daily lives, to the final chapter, which includes an evaluation of where we are at the moment with respect to Benford's Law and where we need to go in the future. The inclusion of Excel, Access, and IDEA screenshots means that you can start working on your own data right away.

A companion website has links to many of the data sets used in the book, together with PowerPoint slides for college instructors and conference presentations. The website includes the Nigrini Cycle Excel template and several Access databases with their Benford's Law queries. The tests in the book will focus your attention on the abnormal duplications, biases, and anomalies in your data.

From the Back Cover
Praise for Benford's Law Applications for Forensic Accounting, Auditing, and Fraud Detection

"Mark Nigrini . . . took Benford's original data and developed it into solid analytical methods to detect a variety of white-collar misdeeds: vendor, payroll, and sales tax frauds; fraudulent medical and insurance claims; check fraud and tax evasion among others. In other words, Dr. Nigrini has put Benford's Law on the map. With the passage of time, he and others will find additional useful applications for this powerful tool."
—From the Foreword by Dr. Joseph T. Wells, CFE, CPA

Apply Benford's Law to detect fraud and to test the integrity of your data

Numbers play an important part in our lives from weather forecasts to the stock market, and from street addresses and phone numbers to baseball statistics and casino games. It would be impossible to take numbers out of our daily lives. The secret is out that there are patterns to the numbers that we come across every day, and more importantly, that deviations from these patterns are red flags for fraud, errors, and biases.

Author Mark Nigrini, a pioneer in forensic accounting, describes the mathematical foundations of Benford's Law in a way that is easily understood by accounting and other business-related professionals. He then shows many examples of authentic and accurate data that conformed to Benford's Law—and the fraudulent and invented numbers that did not.

Nigrini goes way beyond the first digits test and outlines a series of digit- and number-based tests called the Nigrini Cycle. With a companion website with data sets and Excel templates, these tests are based on the state-of-the-art tools, thinking, and research related to Benford's Law.

The applications include:

• The Madoff numbers

• GM and Chrysler bankruptcy data

• Numbers reported by Enron and AIG

• Bill and Hillary Clinton's tax returns

• U.S. census population numbers

• Corporate payments data

• The Fibonacci numbers

• Taxpayer interest and dividend income

Benford's Law "gives Professor Nigrini a tool worthy of Sherlock Holmes," said Robert Burton, chief financial investigator for the district attorney's office in Brooklyn, New York. In Benford's Law, Nigrini shares his insights and passion for the topic in a way that is sure to cause fraudsters to have many sleepless nights in the years ahead.

About the Author
MARK J. NIGRINI, PhD, is a professor at The College of New Jersey where he teaches forensic accounting courses. His research involves advanced theoretical work on Benford's Law and the legal process surrounding fraud convictions. Nigrini is also the author of Forensic Analytics (Wiley), which describes tests to detect fraud, errors, estimates, and biases in financial data. He has been published in national media including the Wall Street Journal and has published papers on Benford's Law and accounting in academic and professional journals. Nigrini regularly presents professional seminars for accountants and auditors in North America, Europe, and Asia with recent events in Singapore, Switzerland, and New Zealand.

Customer Reviews

Most helpful customer reviews

9 of 10 people found the following review helpful.
Great insights and practical applications
By Jeremy R Clopton
As a consultant in the area of fraud and forensics for more than six years, much of my work relates to data mining and analytics. Benford's Law is something I regularly use in my work. Nigrini's "Benford's Law" provides great insight into the history, current application and future uses of Benford's Law. If you're into the hardcore mathematics - the first few chapters will provide you just that. A history of Benford, his law and the theorems behind Benford's Law. Good news for those that aren't mathematicians (myself included) - it is written in a way even we can understand it! As the book progresses, it provides discussion about the variations and supplemental tests used in analyzing Benford's Law. Included are screen shots and how-to's on performing the tests in Excel and/or Access. From here there are numerous chapters showing how well-known fraud schemes look through the eyes of Benford's Law. This is not only interesting, but also quite beneficial if you are looking for "real-world" application. Finally, Nigrini touches on the concept of "My Law". This is one of my favorite parts of the book, providing a new way to apply Benford's in a comparative environment. Overall, this book is a great resource on Benford's Law. Whether you enjoy reading on the topic or are trying to figure out how to apply Benford's Law in practice, this book should provide most (if not all) of what you are looking for. For those outside accounting, I think it is interesting reading on the topic of numbers manipulation and creation in data sets.

9 of 11 people found the following review helpful.
Benford's Law Applications for Forensic Accounting, Auditing, and Fraud Detection: Review From a Recent College Graduate
By Ashley Covello
The accompanying website for the book, which is the Benford's Law tab on [...], is interesting even if you haven't bought the book. It has approximately 15 interesting data sets that are made available for download. Some of the data sets agree with Benford's Law, others have less agreement, and the payroll data has no conformity at all. Additionally, the website has about ten other files that are templates and files related to Figures in the book. The accompanying site also has some photos, links to interesting items, and links to a video of the author talking about Benford's Law.

Overall, the book covers a lot of ground. The first few chapters cover the mathematical and statistical aspects of Benford's Law in just the right amount of detail for me, a recent college graduate. The next few chapters talk about the various Benford's Law tests that can be run, with helpful examples. The tests are notably more detailed that the usual first digit test seen in many research papers. The last few chapters have some good examples of detecting financial statement fraud, detecting Ponzi schemes, and other various applications including tax evasion and an analysis of Lehman's benevolent gifts.

The book does a good job of making accountants, auditors, and data analysts aware of the patterns that we should expect in accounting data and how to examine these patterns more closely to identify fraud, errors, or other issues. The book shows how these tests can be run on any data set using either Excel or Access.

4 of 4 people found the following review helpful.
Mathematics, Mystery, and Intrigue
By Grant Babb
It is not common to find a book that you hope covers the topic you are looking for and entertains you at the same time.

Nigrini does a good job of developing the context of the book: some more esoteric math concepts, the challenges of getting new ideas through academia and the business world, and the unfortunate responsibility of catching bad people. My job requires me to communicate math to people who are NOT mathematicians, and I appreciate the help when I get it.