## Monetary Unit Sampling

Monetary Unit Sampling (MUS), also known as probability-proportional-to-size (PPS) sampling, is a statistical sampling method used in auditing to test the fairness of financial accounts. The key characteristic of this sampling method is that every dollar in a transaction population has an equal chance of being selected as part of the sample.

In MUS, the sampling selection is weighted towards items with a larger monetary value because the likelihood of an item being selected is proportional to its dollar value. This means that higher-value items have a higher probability of being selected for the audit sample than lower-value items. This is useful because larger-value items pose more financial risk and are more likely to be materially misstated.

To illustrate, let’s consider an example:

An auditor is testing an account payable balance of $500,000 and wants to select a sample of transactions using MUS. If the auditor sets the sampling interval at $5,000, then, theoretically, every $5,000 in the account payable balance has an equal chance of being selected. So a payable of $20,000 is four times more likely to be selected than a payable of $5,000.

One of the advantages of MUS is its simplicity and ease of use, especially with the aid of computerized audit tools. It also automatically provides more coverage of higher-dollar items. However, it might not be as effective when there are many small misstatements that collectively could be material, or when the population has a significant number of zero or negative balances.

## Example of Monetary Unit Sampling

Let’s look at an example of how Monetary Unit Sampling (MUS) might be applied in an auditing context.

Suppose an auditor is conducting an audit of a company, XYZ Corp., and wants to test the company’s accounts receivable, which total $1,000,000. The auditor decides to use MUS to select a sample of individual receivables for testing.

First, the auditor would determine a sampling interval based on the total value of the population and the desired sample size. For example, if the auditor wants a sample size of 100, the sampling interval would be $1,000,000 / 100 = $10,000.

Next, the auditor would select a random start point within the first interval. For instance, if the random start is $3,000, the auditor will select the first individual receivable that, when counted cumulatively from the beginning of the population, reaches or exceeds $3,000.

Then, the auditor would select each individual receivable that meets or exceeds the cumulative total of the sampling interval. So, the auditor would select the receivable that meets or exceeds $13,000 ($3,000 initial point + $10,000 interval), then $23,000, $33,000, and so on.

The selected receivables constitute the audit sample and would be examined in detail to verify their accuracy. Because each dollar in the accounts receivable has an equal chance of being selected, and larger receivables are more likely to be selected than smaller ones, MUS helps to focus the audit effort on the areas of greatest potential financial risk.

Keep in mind that this is a simplified example. In an actual audit, the process might be more complex, and the auditor would use professional judgement to assess the results and conclude whether the accounts receivable are fairly stated.