Ratio estimation uses the known population totals for variables to improve the weighting from sample values to population estimates. It compares the sample estimate of the variable with the population total. The ratio of the sample estimate to its population total is used to adjust the sample estimate for the variable of interest.
Ratio estimation is frequently used by the auditors. The auditors use ratio estimation as a method of classical variables sampling. This type of sampling is usually referred to as estimation sampling. Estimation sampling is used to estimate the actual value of a population characteristic within a range of tolerable misstatement.
In audit sampling, the ratio estimation is a ratio of proportion of error in the sample applied to the population value to estimate total error. This method applies the sample ratio to the entire population.
Let's try to understand ratio estimation with the help of an example. Suppose you are auditing a company and you want audit evidence regarding the accounts receivable. Let's assume that the total accounts receivable of the company are $50,000. You choose a sample of $10,000 and apply auditing procedures to this sample. As a result of auditing procedures, you find out that there were errors or misstatements of $1,000. This means that your error or misstatement ratio is 10% (i.e. $1,000/$10,000).
With the help of this error or misstatement ratio, you can estimate the value of errors or misstatements in the entire population. For estimating the errors or misstatements in the entire population, you simply have to apply the above ratio to the entire population. As we have assumed that the entire population total is $50,000, your projected error or misstatement for the whole population will be %5,000 (i.e. $50,000 x 10 per cent). $5,000 is the ratio estimation of the errors or misstatements in the entire population.
Ratio estimation and estimation sampling are important tools that the auditors can apply in their auditing assignments to gather audit evidence, estimate the amount of errors or misstatements, and to form an audit opinion about the financial statements of an organization to see whether they present true and fair view.