Example: Statistical Sampling in Test of Control | CPA Exam

In this session I work an example for statistical sampling in test of control.
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Explain the concept of representative sampling.
When selecting a sample from a population, the auditor strives to obtain a representative sample. A representative sample is one in which the characteristics in the sample are approximately the same as those of the population. This means that the sampled items are similar to the items not sampled. Assume a client’s internal controls require a clerk to attach a shipping document to every duplicate sales invoice, but the clerk fails to follow the procedure exactly 3 percent of the time. If the auditor selects a sample of 100 duplicate sales invoices and finds three are missing attached shipping documents, the sample is highly representative. If two or four such items are found in the sample, the sample is reasonably representative. If no or many missing items are found, the sample is nonrepresentative.

In practice, auditors never know whether a sample is representative, even after all testing is complete. (The only way to know if a sample is representative is to subsequently audit the entire population.) However, auditors can increase the likelihood of a sample being representative by using care in designing the sampling process, sample selection, and evaluation of sample results. A sample result can lead to an incorrect conclusion due to sampling error or nonsampling error. The risk of these two types of errors occurring is called sampling risk and nonsampling risk.

Sampling risk is the risk that an auditor reaches an incorrect conclusion because the sample is not representative of the population. Sampling risk is an inherent part of sampling that results from testing less than the entire population. For example, assume the auditor decided that a control is not effective if there is a population exception rate of 6 percent. Assume the auditor accepts the control as effective based on tests of the control with a sample of 100 items that had two exceptions. If the population actually has an 8 percent exception rate, the auditor incorrectly accepted the population because the sample was not sufficiently representative of the population.

Auditors have two ways to control sampling risk:

Adjust sample size
Use an appropriate method of selecting sample items from the population
Increasing sample size reduces sampling risk, and vice versa. At one extreme, a sample of all the items of a population has a zero sampling risk. At the other extreme, a sample of one or two items has an extremely high sampling risk.

Using an appropriate sample selection method increases the likelihood of representativeness. This does not eliminate or even reduce sampling risk, but it does allow the auditor to measure the risk associated with a given sample size if statistical methods of sample selection and evaluation are used.

Nonsampling risk is the risk that the auditor reaches an incorrect conclusion for any reason not related to sampling risk. The two causes of nonsampling risk are the auditor’s failure to recognize exceptions and inappropriate or ineffective audit procedures.

An auditor might fail to recognize an exception because of exhaustion, boredom, or lack of understanding of what might constitute an exception. In the preceding example, assume three shipping documents were not attached to duplicate sales invoices in a sample of 100. If the auditor concluded that no exceptions existed, that is a nonsampling error. An ineffective audit procedure for detecting the exceptions in question would be to examine a sample of shipping documents and determine whether each is attached to a duplicate sales invoice.


Both probabilistic and nonprobabilistic sample selection fall under step 2. When using probabilistic sample selection, the auditor randomly selects items such that each population item has a known probability of being included in the sample. This process requires great care and uses one of several methods discussed shortly. In nonprobabilistic sample selection, the auditor selects sample items using nonprobabilistic methods that approximate a random sampling approach.