Examples: Monetary Unit Sampling & Probability Proportion in Size: Upper Bound Misstatement.

In this session I work an example discussing monetary unit sampling and probability proportion to size including upper bound misstatement.
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pply monetary unit sampling.
Now that we have discussed nonstatistical sampling, we will move on to statistical sampling, starting with monetary unit sampling, which is a statistical sampling methodology developed specifically for use by auditors. Monetary unit sampling (MUS) is the most commonly used statistical method of sampling for tests of details of balances because it has the statistical simplicity of attributes sampling yet provides a statistical result expressed in dollars (or another appropriate currency). MUS is also called dollar unit sampling, cumulative monetary amount sampling, and sampling with probability proportional to size.

Differences Between MUS and Nonstatistical Sampling

MUS is similar to using nonstatistical sampling. All 14 of the steps must also be performed for MUS, although some are done differently. Understanding those differences is the key to understanding MUS. Let’s examine these differences in detail.

The Definition of the Sampling Unit Is an Individual Dollar
A critical feature of MUS is the definition of the sampling unit as an individual dollar in an account balance. The name of the statistical method, monetary unit sampling, results from this distinctive feature.

By focusing on the individual dollar as the sampling unit, MUS automatically emphasizes physical units with larger recorded balances. Because the sample is selected on the basis of individual dollars, an account with a large balance has a greater chance of being included than an account with a small balance.

Sample Selection Is Done Using PPS
Monetary unit samples are selected with probability proportional to size sample selection (PPS). PPS samples can be obtained by using computer software or systematic sampling techniques.


The Auditor Generalizes from the Sample to the Population Using MUS Techniques.
Regardless of the sampling method selected, the auditor must generalize from the sample to the population by (1) projecting misstatements from the sample results to the population and (2) determining the related sampling risk. The statistical result when MUS is used is called a misstatement bound. The misstatement bound is an estimate of the likely maximum overstatement at a given ARIA. The discussion and example that follow are limited to overstatements because MUS is designed primarily to test for overstatements. Calculation of misstatement bounds is usually done using audit software or computer templates.

Decide the Acceptability of the Population Using MUS

The auditor compares the calculated misstatement bound to tolerable misstatement. If the bound exceeds tolerable misstatement, the population is not considered acceptable. The options available to the auditor when the population is rejected are the same ones already discussed for nonstatistical sampling .

Now that we have discussed the differences between MUS and nonstatistical sampling for tests of details of balances, we examine the determination of sample sizes and calculation of misstatement bounds in further detail.

Determining Sample Sizes Using MUS

We illustrate the formula for computing sample sizes using MUS based on the AICPA Audit Sampling Audit Guide. We first discuss the factors used in computing sample size.

Acceptable Risk of Incorrect Acceptance

Recorded Population Value
The dollar value of the population is taken from the client’s records. For this example, it is $5 million.

Tolerable Misstatement
Tolerable misstatement is generally the same as performance materiality, but the auditor may decrease the amount of tolerable misstatement if less than 100 percent of the population is tested.
Estimated Population Misstatement
MUS is most often used when no or few misstatements are expected.
Ratio of Estimated Population Misstatement to Tolerable Misstatement.
confidence Factor