The Use of Benford's Law as an Aid in Analytical Procedures

Key Words: Analytical procedures, Benford's Law. Data Availability: The data used in the study are confidential current corporate data, and therefore are not available to readers. Contact the first author for software that can be used to duplicate the tests on other data sets. SAS No. 56 requires auditors to use analytical procedures in planning the nature, timing and extent of other auditing procedures (AICPA 1988). This study introduces and illustrates how Digital Analysis could be used as an analytical procedure.(1) Digital Analysis focuses on digit and number patterns, and is based on a mathematical phenomenon known as Benford's Law (Benford 1938). Recent declines in the cost of the computing power of desktop and laptop computers have contributed to the feasibility of using Digital Analysis in analytical procedures. Analytical procedures are defined by SAS No. 56 to be evaluations of financial information made by a study of plausible relationships among both financial and nonfinancial data (AICPA 1988). Analytical procedures are required in planning the examination, and in the overall review of the financial statements during the completion phase of the audit. Akresh et al. (1988) believe that SAS No. 56 places a greater emphasis on the use of analytical procedures than was previously the case, and that auditors will be evaluated and judged more critically on their use of analytical procedures. They state that analytical procedures are used extensively--but inconsistently, in practice--and that the procedures used are generally the less complex procedures. They include in the list of research needs the development of more effective, simple procedures. Internal auditing standards also require analytical procedures. Gauntt and Glezen (1997) summarize the professional standards related to analytical procedures. Their study focuses on identifying and investigating material unexpected variations. Unexplained results or relationships from applying analytical procedures may be indicative of significant conditions such as potential errors, irregularities or illegal acts (Institute of Internal Auditors 1993). Coglitore and Berryman (1988) conclude that analytical procedures are useful to detect overstatements of revenue, fictitious sales and receivables, fictitious and overvalued inventory, understated bad debts and allowances for doubtful accounts, unrecorded purchase liabilities, underaccrual of expenses, and inappropriate expense capitalization. Some of these misstatements require that the auditee invent numbers. SAS No. 56 notes that analytical procedures should use sources such as comparable prior periods, or relationships among elements of financial information. The novelty of Digital Analysis tests is that they analyze the relationships between the elements of an auditee data set, to determine whether they are reasonable. The tests focus on determining whether auditee data contain excesses of (1) specific digits, (2) digit combinations, (3) specific numbers, or (4) rounded numbers. These excesses could signal misstatements. The paper is organized into three sections. The first section reviews Benford's Law, which is the mathematical basis of Digital Analysis. The discussion includes both the theory behind Benford's Law, as well as empirical studies that have utilized the law. The second section describes and illustrates six Digital Analysis tests. A case study is described, from which a large data set was obtained and on which four of the tests were performed. Other data sets on which two digital tests were performed are also described. The third section discusses factors that should be considered by users together with suggestions for future research. BENFORD'S LAW The expected frequencies of the digits in lists of numbers is known as Benford's Law. Benford, a physicist at the GE Research Laboratories, conducted an extensive study of the digit frequencies in tabulated data (Benford 1938). …