Detecting Newcomb-Benford Digital Frequency Anomalies in the Audit Context: Suggested Chi2 Test Possibilities

Abstract

Digital Frequency Testing [DFT] has achieved justifiable currency as a valuable part of the panoply of the auditor. There are a number of inference models, such as the parametric test for proportional differences to entropic screening, that can be used to create information regarding the use of extended procedures to investigate the difference between the Observed digital frequency compared to the Expectation benchmark. One inferential model which seems ideal for DFT in the audit context is the Chi2 model as it is formed as the ratio of the square of the difference between the Observed and the Expectation benchmarked by the Expectation. This Chi2 ratio fits perfectly the usual audit investigation sensitivity imperative developed by the analytic procedures phase of the audit. However, there are Expectation Specification and Sample Size issues that need to be considered in using the Chi2 test in DFT. We present and illustrate in detail three testing models focusing on the Pearson and the Direct Benchmarking expectation differences with suggestions as to sample size control that could be used by the auditor in the certification audit. We offer important audit action information regarding the inference information that is related to the overall Chi2 test as well as to the Chi2 cell contribution signals. Finally, we have a Decision Support System [DSS] that aides in the creation of this Chi2 audit-screening information. The DSS, programmed in Excel-VBA, is available from the corresponding author as a free download without restriction to its use.