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Statistical Sampling Methods

There are three basic types of sampling methods that auditors may use. The choice of methods depends on the main purpose of the sample and substantive test.

Probability Proportional-to-Size Sampling (PPS)

This method is used to estimate the total monetary amount of potential misstatement in a population. PPS uses monetary unit sampling (MUS) or dollar unit sampling (DUS). While other methods are based on occurrences or number of records, this method is based on dollar values where the higher monetary value transactions have a higher likelihood of being chosen in a sample. MUS is similar to systematic sampling, but where systematic sampling may sample every thousandth record, MUS will sample every thousandth dollar. It is typically used to determine the accuracy of financial accounts, where size is the most important factor, and where errors are expected to be few and far between. MUS provides a substantive assessment of error or misstatement in dollar figures and is specifically designed to predict overall error. MUS should be used when:

- The process audited is well established and known to be reliable.

- The likelihood of errors (misstatements) is low.

- Obtaining a small sample size is important.

- You want to target larger dollar transactions, and expect to see some spikes in the data. Performing MUS sampling involves the following steps.


- Determine the objectives of the exercise.

- Define the population.

- Define what a misstatement means.

- Determine sample size, using the following:

- Confidence level. A percentage value comfort level that the sample will be representative and that you have the capabilities to interpret the results correctly.

- Tolerable error. The point of no return past which you would no longer have faith in the process audited, nor the validity of the sample.

- Expected error. The amount of errors or misstatements that are reasonably expected in a population.

Performing MUS Sampling Procedures

- Select the samples.

- Perform the audit procedures.

- Record and analyze any errors observed.


- Create a projected misstatement by summarizing errors and extrapolating these across population.

- Compare ranges of the projected misstatement against the tolerable error limit.

- Draw final conclusions.

As seen in Figure 4.7, IDEA will simplify all these steps for you.

Monetary Unit Sampling Feature

FIGURE 4.7 Monetary Unit Sampling Feature

In the example of testing sales, seen in Figure 4.8, we select absolute values as there are a few credit or refund values that are negative amounts in the Total field. We select a confidence level of 95 percent. Confidence levels below 90 percent are not generally recommended for MUS sampling. It should be recognized that the higher the confidence level, the larger the sample size needed.

The tolerable error amount or percentage must be entered. This is the absolute error limit that can be tolerated. The higher the tolerable error, the more errors you can accept and the lower the sample size needs to be. In this example, with sales in excess of $1.7 million, 1 percent or $17,000 was decided as the maximum tolerable error. A 1 percent loss would be material enough to take actions such as to initiate an investigation or redesign the sales system. Since MUS is only to be used for processes where there is a high degree of confidence based on actual experience, significant errors may indicate fraud, embezzlement, or untrained or incompetent staff.

The expected error is the anticipated misstatement that is a realistic estimate of likely errors expected to found in the process. It is historical experience that dictates the estimate amount. Both the expected error and tolerable error can be entered either as an amount or percentage. In this example, management estimates that approximately 10 percent or $1,700 is the expected error.

When the Estimate button is selected, IDEA's MUS calculation determines that in order to be 95 percent confident, it is necessary to set the sample size at 363 records and that there should be no more than 36.25 percent tainting or total percentage of errors found.

Once the Accept button is selected, the Monetary Unit Sampling—Extract screen appears as displayed in Figure 4.9.

Monetary Unit Sampling Planning

FIGURE 4.8 Monetary Unit Sampling Planning

Extracting the Sample Records for Monetary Unit Sampling

FIGURE 4.9 Extracting the Sample Records for Monetary Unit Sampling

Three hundred sixty-three records are then extracted and an AUDIT_AMT field is created as in Figure 4.10. The value of this field is equal to the field being audited but can be changed to reflect the proper amount determined during the execution of the audit procedures.

Random Record Selection Results for Monetary Unit Sampling

FIGURE 4.10 Random Record Selection Results for Monetary Unit Sampling

Suppose three discrepancies were found, including the one in record number 250 where the actual amount was $60.00 instead of the $55.32 recorded in the sales system as shown in Figure 4.11. To evaluate the MUS sample, select the Single Sample option.

Audit Results of the Sampled Records

FIGURE 4.11 Audit Results of the Sampled Records

The screen in Figure 4.12 appears

Evaluating Single Sample Results in Monetary Unit Sampling

FIGURE 4.12 Evaluating Single Sample Results in Monetary Unit Sampling

Once OK is selected, the summary shown in Figure 4.13 appears displaying:

- Zero overstatements were discovered.

- Three understatements were discovered. - The net most likely error is $1,512.47.

- Both the gross and net upper error limits are less than materiality (tolerable error) of $17,000.

The conclusion is that with 95 percent certainty the projected total errors based on errors found in the sample is within the accepted range and will not exceed the tolerable error of $17,000. That is, you are 95 percent assured that the sample is representative of the population and that no actions to investigate or redesign the sales system are needed.

Summary and Conclusion of Audit Results of MUS

FIGURE 4.13 Summary and Conclusion of Audit Results of MUS

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