When and How to Use Classical Variable Sampling

Classical variables sampling (CVS) is a statistical method used by auditors to form a conclusion about an account balance or class of transactions. It relies on normal distribution theory to evaluate the characteristics of an entire population based on a smaller sample. The primary purpose is to estimate the total monetary value of an account or the amount of monetary misstatement within it. This approach treats every item in a population as a distinct sampling unit with an equal chance of being selected. The process allows an auditor to state with a certain confidence level that the account’s true value is within a specific calculated range.

Appropriate Uses for Classical Variables Sampling

An auditor’s decision to use classical variables sampling is influenced by the account’s characteristics and the audit’s objectives. This method is effective when an auditor expects to find a moderate to high number of misstatements within the population. If preliminary assessments or historical data suggest that errors are likely, CVS provides a robust framework for estimating the total impact of those errors, as it is designed to handle such situations.

CVS is well-suited for populations where misstatements could be either overstatements or understatements. This is an advantage over techniques primarily designed to detect overstatements. Because CVS evaluates the audited value of each item in the sample, it can identify both positive and negative discrepancies, providing a comprehensive view of the account’s accuracy.

This method is also effective for testing accounts where understatements or zero balances are a concern. For example, when testing accounts payable, an auditor is often concerned that liabilities are understated. CVS can identify omissions or balances improperly recorded as zero because it does not rely on an item’s monetary value for selection.

Situations that require a precise estimate of an account’s true value often call for CVS. The goal may extend beyond simply accepting or rejecting a recorded balance. An auditor might need to develop a reliable estimate of the correct value, and CVS provides the tools to do so by calculating a range of likely values.

Information Required for the Sampling Plan

Executing a classical variables sampling plan requires gathering several pieces of information. These inputs directly influence the sample size and the subsequent evaluation of the results. The primary requirements include:

• Tolerable misstatement: This represents the maximum amount of misstatement an auditor can accept in the account balance without it being considered materially misstated. It is established in the context of the overall audit plan and materiality.
• Acceptable risk of incorrect acceptance: This is the risk that the auditor will conclude the account balance is not materially misstated when it is. A 5% risk of incorrect acceptance corresponds to a 95% confidence level and is based on the assessed level of control and inherent risk.
• Population characteristics: This includes knowing the population size, which is the total number of records in the account. A unique input for CVS is the population’s variability, measured by its standard deviation. Auditors often estimate this by examining prior year data or testing a small pilot sample of 30-50 items.
• Expected misstatement: This is an estimate of the total error the auditor anticipates finding in the population. This expectation is formed based on prior audit experience, the results of related audit procedures, and the assessment of internal controls.

Executing the Sampling Plan and Evaluating Results

Once the planning inputs are established, the auditor calculates the necessary sample size. This is accomplished by entering the tolerable misstatement, risk of incorrect acceptance, population size, and estimated standard deviation into a statistical formula. This calculation ensures the resulting sample will be sufficient to meet the objectives of the test.

With the sample size determined, the auditor selects the specific items to be examined from the population using a random selection method, such as a random number generator. This unbiased selection is necessary for the results to be projectable to the entire population. Following selection, the auditor performs the planned audit procedures on each item to determine its correct “audited” value and identifies any differences from the client’s recorded book value.

After auditing all the selected items, the misstatements found in the sample are used to project the total misstatement for the entire population. CVS utilizes three primary estimation techniques for this projection.

Estimation Techniques

The Mean-Per-Unit (MPU) estimation calculates the average audited value of the sample items and multiplies it by the total number of items in the population to estimate the total population value. This method is useful when the book values of individual items are unavailable or unreliable.

Two other techniques, ratio and difference estimation, are often more precise if a correlation exists between the audited values and book values. Ratio estimation calculates the ratio of the total audited value of the sample to its total book value and applies this ratio to the total book value of the entire population. Difference estimation calculates the average difference between the audited and book values in the sample and projects this average difference across all items in the population.

The final step is to evaluate the results. The auditor compares the projected misstatement from the sample, plus an additional allowance for sampling risk, to the tolerable misstatement defined during the planning phase. If the total estimated misstatement range is less than the tolerable misstatement, the auditor can conclude that the account balance is fairly stated. If the range exceeds the tolerable misstatement, it indicates a material misstatement, requiring further investigation or an adjustment.