Efficient Sampling Design in Audit Data

Abstract

Auditors are often faced with reviewing a sample drawn from special populations. One is the special population where invoices are divided into two categories, according to whether or not invoices are qualified. In other words, the qualified amount follows a nonstandard mixture distribution in which the qualified amount is either zero with a certain probability or the same as the known invoice amount with a certain probability. The other is the population where some invoices are partially qualified. In other words, some invoices have a qualified amount between zero and the full invoice amount. For these settings, the typical sample design is stratified random, with the estimation method employing a ratio type method. This paper focuses on efficient sample design for this setting and provides some guidelines in setting up stratum boundaries, calculating sample size and allocating sample size optimally across strata.

Designing Efficient Stratified Mean-Per-Unit Sampling Applications in Accounting and Auditing

“…When stratification is based on recorded values, population elements excluded from the census stratum are sorted in order of recorded value and a stratum BSM is used to classify the elements into two or more mutually exclusive sampling strata. Two methods commonly used in accounting and auditing are the Dalenius and Hodges (1959) method 12 and the EV method (Guy et al, 2002;Liu et al, 2005;New York State Department of Taxation and Finance, 2001;Roberts, 1978;Tennessee Department of Revenue, 2005;Yancey, 2002). Levy and Lemeshow (1999) suggest that two intuitively appealing methods for stratum boundary selection are the Equal-Range-Per-Stratum (ER) and the Equal-Frequency-Per-Stratum (EF) methods.…”

“…Due to their availability, recorded values { x i : x 1 , x 2 , … , x N } are often used as the basis for stratification (Guy et al, 2002; McGrath, 2003; Yancey, 2002). Reliance on recorded values as a basis for stratification works well so long as these values are highly correlated with correct values (Cochran, 1977; Liu et al, 2005). In accounting and auditing, high correlations are common because many of these applications involve large populations with few errors (Durney et al, 2014).…”

Learning Sampling in Financial Statement Audits using Vector Quantised Autoencoder Neural Networks

“…• Systematic or sequential sampling in which the sampling starts by selecting an entry at random and then every n-th journal entry of an ordered sampling frame is selected. • Proportional, block or stratified sampling in which the population is sub-divided into homogeneous groups of journal entries to be sampled from [28]. • Haphazard sampling, in which no explicit or structured selection strategy is employed by the auditor.…”