Abstract
Problems in statistical auditing are usually one–sided. In fact, the main interest for auditors is to determine the quantiles of the total amount of error, and then to compare these quantiles with a given materiality fixed by the auditor, so that the accounting statement can be accepted or rejected. Dollar unit sampling (DUS) is a useful procedure to collect sample information, whereby items are chosen with a probability proportional to book amounts and in which the relevant error amount distribution is the distribution of the taints weighted by the book value. The likelihood induced by DUS refers to a 201–variate parameter but the prior information is in a subparameter linear function of , representing the total amount of error. This means that partial prior information must be processed. In this paper, two main proposals are made: (1) to modify the likelihood, to make it compatible with prior information and thus obtain a Bayesian analysis for hypotheses to be tested; (2) to use a maximum entropy prior to incorporate limited auditor information. To achieve these goals, we obtain a modified likelihood function inspired by the induced likelihood described by Zehna (1966) and then adapt the Bayes’ theorem to this likelihood in order to derive a posterior distribution for . This approach shows that the DUS methodology can be justified as a natural method of processing partial prior information in auditing and that a Bayesian analysis can be performed even when prior information is only available for a subparameter of the model. Finally, some numerical examples are presented.
Highlights
This paper addresses the statistical problem of estimating the total amount of error in an account balance obtained from auditing
The conclusions drawn from the audit process are commonly based on statistical methods such as hypothesis testing, which in turn is based on compliance testing and substantive testing
Following Hernández et al (1998) [3], we propose a modification of the likelihood to make it compatible with prior information on θ and perform a Bayesian analysis
Summary
This paper addresses the statistical problem of estimating the total amount of error in an account balance obtained from auditing. The conclusions drawn from the audit process are commonly based on statistical methods such as hypothesis testing, which in turn is based on compliance testing and substantive testing The first of these is conducted to provide reasonable assurance that internal control mechanisms are present and function adequately. The taints in a dollar unit sample are recorded and used to draw inferences about the parameter of interest, i.e., the total amount of error. The prior distribution for the total amount of error in the population is commonly asymmetrical and right tailed, and statistically–trained auditors can readily elicit values such as the mean and/or certain quantiles.
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