Stratified Sampling Using a Stochastic Model

Abstract

According to SAS No. 39, planning a statistical substantive test of details requires specifying a tolerable monetary error and an allowable risk of incorrect acceptance. The tolerable error represents the maximum monetary error that can exist in the population (i.e., the account balance or class of transactions) without causing the financial statements taken as a whole to be materially misstated. The risk of incorrect acceptance (beta error) is the risk that the sample will support the conclusion that the total monetary error in the population does not exceed the tolerable error when, in fact, the total monetary error does exceed it. The auditor may also elect to control the risk of incorrect rejection (alpha error), but this is generally assumed to be a less costly risk. This overall audit problem is often formulated as a statistical hypothesis test (first proposed by Elliott and Rogers [1972] and Roberts [1978]), which involves specifying a hypothesis and an alternative. The hypothesis is that the total monetary error in the population exceeds the tolerable error, while its alternative is that the total monetary error in the population is less than or equal to the tolerable error. Quite often, the account balances to be tested are aggregates of individual accounts of quite different magnitudes (sizes). In such cases, it is common to use a stratified random sampling procedure. This entails dividing the recorded amounts into several strata, choosing a random sample from each stratum, and then evaluating the results in terms of an estimate of the total monetary error for the account. An exact statistical solution to this testing problem requires knowing