DATA DIAGNOSTICS USING SECOND ORDER TESTS OF BENFORD’S LAW by

We wish to thank the management of the restaurant company for allowing the use of their corporate data in the case study and the simulations. In accordance with their requests we have not shown the actual years that the data relates to and we have approximated some of the descriptive statistics. We also wish to thank the AJPT reviewers and the editor, Dan Simunic, for their excellent comments. Summary SAS No. 99 requires auditors to use analytical procedures to identify the existence of unusual transactions, events, and trends. This use of analytical procedures and the effective use of the computer on transaction level data is an efficient means for auditors to partially fulfill their duties with regards to the detection of fraud and material misstatements. Benford's Law gives the expected patterns of the digits in numerical data, and it has been advocated as a test for the authenticity and reliability of transaction level accounting data. To date these tests have been tests of the first digits and first-two digits of accounting data. This paper proposes a new second order test of Benford's Law that has the potential to provide new insights into accounting data. The second order test is an analysis of the digit frequencies of the differences between the ordered (ranked) values in a data set. The digit frequencies of these differences approximates the frequencies of Benford's Law for most distributions of the original data. The second order tests generate few false positives and can detect rounded data, data generated by linear regression, data generated by using the inverse function of a known distribution, and inaccurate ordering. These conditions would not be easily detectable using traditional analytical procedures. Data availability: The accounts payable data of the first case study are available from the authors. (AICPA, 2002), establishes standards and provides guidance to auditors with respect to the detection of material misstatements caused by error or fraud. Auditors are required to explicitly consider the potential for material misstatements due to fraud. Analytical procedures applied to highly aggregated data can however only provide a broad initial indication of the existence of a material misstatement. Computer-assisted audit techniques could be used to inter alia test an entire population instead of a sample, and may be useful in identifying unusual or unexpected relationships or transactions. The effective use of the computer on transaction level data could present an efficient means for auditors to …