The impact of false rejection risk on posterior audit risk measurement

Abstract

This paper investigates false rejection risk, analysing the a priori relationship between the risk of false rejection and the more common risk of false acceptance, of an account balance by a substantive test. The paper uses probability theory to specify the relationship between these two risks and thus generate a model of posterior audit risk. The paper proceeds to investigate the relationship using the power function of basic statistics. This specifies the relationship between (i) the probability of rejecting the account balance and (ii) the size of the error which the balance contains. We argue that unless there is a discontinuity in the power function around the specified value of material error, then posterior audit risk will be unaffected by the substantive tests undertaken. Posterior risk will then be determined entirely by the assessed inherent and control risks. This conclusion is counter-intuitive to the approach to audit risk adopted by many professional pronouncements and results from the adoption of a mathematically rigorous definition of the risks encountered by the auditor. The primary conclusion is that the discontinuity arises under conditions of careful audit planning. If planning is careful, then false rejection risk contributes very little to posterior risk. In addition, there is very little difference between planned risk and posterior risk.