An Analysis of the Relative Power Characteristics of Analytical Procedures

Abstract

The overall objective of this study is to analyze the relative effectiveness and efficiency of several analytical procedures. To accomplish this, we test the power characteristics of analytical procedures in simulated business and economic environments. The analytical procedures we test include the Martingale, Census X-11, ARIMA, and stepwise regression expectation models. The power characteristics are measured by both positive and negative testing approaches, with and without accompanying tests of details, and with simple and dispersed error seeding patterns. The results suggest that the stepwise regression model outperforms X-11, ARIMA, and Martingale models in discriminating between the decision risks at zero and material error for both testing approaches. All models seem to perform better in terms of the aggregate slope for higher degrees of economic stability. The stepwise procedure either outperforms the other procedures for the positive approach or comes close to doing so for the negative approach in terms of reducing the risk of incorrectly concluding that an account is not in material error when it is indeed in material error. The stepwise model combined with the negative approach exhibits the lowest risk of rejecting an account that is not materially misstated. The negative approach of testing, compared to the positive approach, seems to offer the auditor superior protection against not detecting a material error, while minimizing excessive audit work by correctly concluding that an account is not in material error if nonmaterial errors are present. When applied in conjunction with tests of details as well as when different error dispersion patterns are considered, all four analytical procedure models provide about the same level of assurance (effectiveness) in detecting material errors. The stepwise model, however, is the most efficient one in both of these scenarios in saving excessive audit work.