Mathematical and Statistical Methods of Assessment in Audit

Abstract

In course of an audit, auditor must collect, scrutinize, assess and document a large amount of reliable and acceptable information that will be useful for audit purposes. The article is devoted to use of mathematical and statistical methods in analytical procedures of audit. Because by the requirement of international standards of audit, auditors can use analytical procedures in all the types of auditor services, this is an evidence of the importance of these procedures. Analytical procedures (analytical tests) are comparisons of the actual data with the data which an internal auditor expects to collect in course of an audit. Mathematical and statistical methods are proposed as framework tools for the procedures used for assessment of the collected data. The notions underlying these methods are considered: probability, discrete and continuous random variables, dispersion, standard deviation etc.

In focus of the study is risk assessment that is interpreted as the condition when a probability of unfavorable deviation from the expected result occurs, and uncertainty which is the risk that cannot be assessed. When a decision is being taken with accounting for the factors of risk and uncertainty, the measures of expected profit or expected profitability are used to derive the most probable result from taking this decision. Also, standard deviation of distribution of the probabilities of potential profitability is used as a measure of the risk associated with the taken decision.

The analytical procedures, therefore, aim to help an auditor to form the substantiated and competent judgment, with the complexity of the procedures being compensated by their effectiveness. Apart from the common methods and techniques, mathematical and statistical methods can well be used for audit purposes, allowing an auditor to assess financial data by scrutinizing stochastic dependencies between them.