The CPA Journal

The Mythical Isolated Error

By Neal B. Hitzig

An enduring myth in auditing is that of the isolated error—an auditor’s belief that the one error detected in an audit sample is the only error in the population under examination. This occurs when an auditor, expecting to find no error, selects a small audit sample, such as a discovery sample. If the sample discloses no error, it is not unheard of for an auditor to claim that the population has no error. If the audit procedure has been properly planned, this conclusion, although inappropriate, would not likely have adverse consequences. The same cannot be said for the isolated-error decision, which may be based in part on an auditor’s reluctance to dispense with a prior belief that the population under audit is essentially error-free.

The myth of the isolated error is supported neither by the authoritative literature (SAS 39) nor by the AICPA’s Audit Practice Release, “Audit Sampling.” Nevertheless, the myth persists. Even if collateral information tends to support the unusual nature of a lone error, an auditor’s decision that such an error is isolated is risky without the support of extensive additional work. The extent of work that would be necessary to establish that an error is, in fact, isolated is likely to be greater than the extent necessary to establish that its effect is not material. The appropriate response to the detection of error where none was expected is to interpret that error as a red flag, a warning that conditions have changed and that further investigation is necessary—even if that additional audit effort only confirms the auditor’s earlier judgment. For an auditor to maintain the belief that a single error in a sample is also isolated is risky, and demonstrating that riskiness is not difficult.

Small samples are unlikely to disclose items whose occurrence in the population is rare. Should a sample disclose such an error, the prudent conclusion would be that the detected error is only one of many. If an audit sample has been selected at random (or even haphazardly), the odds against a unique error occurring in a sample is given by the following ratio:

Population Size – Sample Size/ Sample Size

For example, suppose a population of 1,000 items has only one error. If a random sample of 50 items were selected from that population, the odds against finding that one item would be 19 to 1. This fact enables an auditor to apply accepted rules of statistical inference to a situation where such a sample does disclose a single error. That is, the auditor may also conclude that the odds against that error being the only error in the population are also 19 to 1. The larger the population, or smaller the sample size, the longer the odds become. For example, if the 50-item sample is selected from a population of 10,000 items, the odds against uniqueness rise to 199 to 1. The basis for the calculation and the formula for the odds are given in the Sidebar. The Exhibit illustrates the relationship between sample size, population size, and the odds against a single detected error being isolated.

The Exhibit shows that it is extremely unlikely that an isolated error will occur in an audit sample when the sample size is a small percentage of the population. If a single error is detected, the proper inference is that the error is not the only one in the population and that there are more waiting to be found. This is a fundamental reason for the GAAS requirement that errors—even one error— be projected to the population from which a sample was selected.

Just as one is unlikely to find a needle in a haystack, an auditor is unlikely to find a population’s only error in an audit sample. Auditors need to understand the real properties of the procedures they apply. Those who fail to do so run the risk of drawing inappropriate conclusions from otherwise properly executed procedures.

By Neal B. Hitzig, PhD, CPA, a retired partner of Ernst & Young, is a professor at Queens College (CUNY) and a member of the NYSSCPA Auditing Standards and Procedures Committee.

Editor:
Robert H. Colson, PhD, CPA
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