Benford’s Law

There are several different techniques and methods that auditors and forensic accountants use in order to detect fraud. One of the methods for detecting fraud is the Benford’s Law. The Benford’s Law is a mathematical theory that was created in 1938 by Frank Benford (Singleton, 2011). The Benford’s law states that “in numbered lists providing real-life data, the leading digit is one almost 33 percent of the time” while “larger numbers occur as the leading digit with less frequency as they grow in magnitude to the point that nine is the first digit less than 5 percent of the time” (Lynch & Zhu, 2008). The Benford’s law can be applied to the first digit, second digit, first two digits, last digit and other combinations of digits of a data set (Singleton, 2011). The graph at the bottom further demonstrates the Benford’s Law digit distribution . The Benford’s Law can only be used with natural occurring numbers or numbers that arise naturally from real-life sources such as death rates, baseball statistics, or financial transitions (Lynch & Zhu, 2008). The Benford’s law is used by comparing the client’s digit frequency distribution with the Benford’s expected distribution. This will enable the auditors or forensic accountants to spot possible errors or fraudulent transactions that would need further investigation since there would be an unusual amount of transactions for a specific leading number.

There are several different ways that Auditors can use the Benford’s law during their audit plan. Firstly, auditors are able to use Benford’s law in order to detect expense and accounting fraud since expenses and accounting transactions are generally natural occurring numbers. Forensic accountants and auditors can also detect fraud in a client’s disbursement cycle by being able to measure the actual occurrence of leading digits in disbursements compared to the digit’s probability (Singleton, 2011). The Benford’s law can be used to investigate credit card transactions, purchase orders, journal entries, customer balances, and customer refunds in order to determine if fraud has been occurring. Other items that Benford’s law could be to test for accuracy and potential fraud are inventory prices, loan data, stock prices, and accounts payable transactions. Auditors might use the Benford’s law when they are testing a large data set, 1,000 records or greater, since the results will be more reliable. Benford’s law can be used to test for duplicate payments, missing checks, or missing invoices (Durtschi, Hillison, & Pacini, 2004). The Benford’s Law is useful when testing accounts receivable and accounts payable since the numbers come from a mathematical combination of numbers in addition to coming from two distributions (Durtschi, Hillison, & Pacini, 2004). Benford’s Law is applicable to use when testing full year’s transactions since the data set is general lager which creates more observations (Durtschi, Hillison, & Pacini, 2004).

There are several data sets that the Benford’s Law would not be suitable for. Auditors should not use the Benford’s law if they are trying to test data information with 500 or less transactions since the data will not provide accurate distributions. Auditors also shouldn’t use the Benford’s law, if the information was created by formulas such an YYMMDD because the formula causes the numbers to be restricted (Singleton, 2011). Forensic accountants should avoid using the Benford’s law when testing data that has a maximum or minimum number since it limits the data to a specific range. While testing, auditors should avoid using Benford’s law when the data being tested is assigned by either the client or the vendor such as check numbers or invoice numbers since this theory assumes that the data is naturally occurring (Singleton, 2011). Forensic accountants should also avoid using Benford’s law when testing ATM withdrawals since these numbers are influenced by human interactions (Durtschi, Hillison, & Pacini, 2004). Benford’s law will not help auditors find any thefts, kickbacks, contract riggings, or any other illegal activity since this theory only helps auditors determine any indications of fraud.