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.
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.
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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.
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.
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.
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