As far as we know, we have never made an undetected error...
In my presentation I will give a survey of my thesis written during my traineeship at the Court of Audit in The Hague (Algemene Rekenkamer). There, I investigated the quality of a statistical model for auditing large populations.
In the Court of Audit, I looked at some statistical aspects of the work of an auditor. In principle, an audit opinion is based on substantive testing (testing of the book-amounts for their correctness) as well as on risk assessment. By risk assessment we mean the assessment of the risk that the financial statement to be audited will contain an unacceptable error.
When an auditor can rely on his risk assessment, he reduces the risk of agreeing wrongly with a financial report. My traineeship played a role in the study of this validity of risk assessment. The data in this study were on account level and consisted, among other things, of
In the validation the likelihood of giving an unjustified unqualified opinion, given the outcome of the audit sample, is used as a criterion. With only the given data, available at the level of the sample, normal evaluation procedures, like the Stringer Bound are not applicable. To solve this problem the assumption was made that p, the mean error rate of the account, given the mean error rate of what is sampled, has a conditional beta distribution.
The goal of my research was to investigate the quality of this model in situations that may be assumed to be similar to prevalent distributions of errors in accounts. I conducted this study both from an analytical and a simulation perspective, using S-Plus. If the detection risk of a material error could indeed be modelled by a beta distribution, then studying the validity of risk assessment was indeed possible using only the data available in the case we study. A convenient by-product would have been that this beta distribution provides auditors with a much simpler way of evaluating statistical samples, if the method would have turned out to be valid.
In my presentation I will briefly discuss the context of my investigation, followed by a discussion of the three models I looked at in my investigation, both from an analytical as from a simulation point of view. Whether or not my findings pleased the Court of Audit is a question hopefully answered after 45 minutes...