# How Does Classical Variables Sampling Work?

When using classical variables sampling, auditors treat each individual item in the population as a sampling unit. This method is most like the statistics classes you had to take in high school and college. You use this method to evaluate your entire population based on your sample data. You can use three common types of classical variables sampling estimators: mean-per-unit, ratio, and difference.

Mean-per-unit uses the familiar statistical concept of mean. For instance, if you add 10 + 30 + 50 to get 90, and then divide 90 by 3 (the number of values in this example), you get 30, which is the mean. As an auditor, you apply this statistical concept to evaluate characteristics of your total population. Taking the average value (mean) of items in your sample, you can estimate the true population value.

For example, you have a total population of 3,000 items in accounts receivable, and your sample size is 50. Adding up the individual values of the 50 items, you get a total of $2,000; therefore, your mean is $40 (2,000/50). Your mean estimate of the true value of accounts receivable is $120,000 ($40 x 3,000).

Considering this data with your sampling risk, confidence level, and error rate, if your confidence level is 95 percent and your error rate is 10 percent, you can say that you’re 95 percent confident that the total value of accounts receivable is $120,000, plus or minus $12,000 ($120,000 times your error rate of 10 percent).

The mean-per-unit method is a very good one to use if you don’t have the underlying documents that support the account balance — if, for instance, your client’s balance sheet shows a total for accounts receivable, but the individual invoices supporting the balance aren’t available.

Another method of classical variables sampling is ratio estimation*,* which applies the sample ratio to an entire population. If your sample for any of your client’s accounts shows errors of $1,000 in a total sample of $10,000, your misstatement ratio is 10 percent (1,000/10,000).

You would then apply this ratio to the entire population. If the entire population totals $50,000, your projected misstatement, which is an estimation of the misstatement in the entire population, is $5,000 ($50,000 x 10 percent).

For sampling risk, if projected misstatement doesn’t exceed expected error, you can reasonably conclude that actual misstatement doesn’t exceed your tolerable misstatement.

Lastly, difference is another classical variables sampling method. It’s similar to ratio estimation, except it incorporates the items in the population. For example, your population consists of 5,000 items and your sample consists of 1,000 items. Your audit procedures find errors totaling $500. The projected misstatement is $2,500 [($500/1000) x 5,000 items].