Auditors perform tests of controls and substantive tests of transactions to determine: Whether the exception rate in the population is sufficiently low. To reduce assessed control risk and thereby reduce tests of details of balances. For larger public companies to conclude that the control is operating effectively for purposes of auditing internal control over financial reporting.
Because audit sampling for tests of details of balances measures monetary misstatements, a misstatement exists whenever a sample item is misstated.
Auditors use tolerable misstatement for determining sample size and evaluating results in non-statistical sampling. The auditor starts with a preliminary judgment about materiality and uses that total in deciding tolerable misstatement for each account. ARIA is the amount of risk an auditor is willing to take of accepting a balance as correct when the true misstatement in the balance exceeds tolerable misstatement. The planned sample size increases as the amount of misstatements expected in the population approaches tolerable misstatement.
It is essential for auditors to evaluate the nature and cause of each misstatement found in tests of details of balances. The auditor will determine why that type of misstatement occurred and then determine the implications on other auditor areas.
MUS is the most commonly used statistical method of sampling for tests of details of balances because it has the statistical simplicity of attributes sampling yet provides a statistical result expressed in dollars.
The population is the recorded value of the account tested. The auditor’s preliminary judgment about materiality should be the amount used as tolerable misstatement in all applications of MUS.
PPS samples can be obtained by using computer software random number tables or systematic sampling techniques. The problem with PPS selection is that population items with a zero recorded balance have no chance of being selected with a PPS sample.
Auditor wants to be 95% confident that no more than 3% of the dollar units in the population are misstated. Thus, the dollar value of the misstatement is not likely to exceed $36,000.
The assumption is that on average, those items that are misstated are misstated by no more than 10%. The change from 100% to 10% significantly affects the misstatement bounds.
The auditor must set these percentages based on professional judgment in the circumstances. In the absence of convincing information to the contrary, most auditors believe that it is desirable to assume a 100% amount for both overstatements and understatements unless there are misstatements in the sample results.
First upper and lower misstatement bounds are calculated separately for overstatement and understatement amounts. When there were no misstatements in the sample, an assumption was required as to the average percent of misstatement for the population items misstated.
The adjustment of bounds for offsetting amounts is made as follows: A point estimate of misstatements is made for both overstatement and understatement amounts. Each bound is reduced by the opposite point estimate.
The method used to determine sample size for MUS is similar to that used for physical unit attributes sampling, using the attributes sampling tables. The preliminary judgment about materiality is normally the basis for the tolerable misstatement amount used. There may be a separate assumption for the upper and lower bounds. The auditor’s judgment should be based on knowledge of the client and past experience. ARIA is auditor judgment. The population value is taken from the client records.
Normally, the estimate of the population exception rate for MUS is zero, as it is most appropriate to use MUS when no misstatements or only a few are expected. When misstatements are expected, the total dollar amount of expected population misstatements is estimated and then expressed as a percent of the population recorded value.
Variable sampling is a statistical method that auditors use for tests of details of balances. The use of variable methods shares many similarities with non-statistical sampling. All 14 steps must be performed for variable methods.
After calculating the mean for each sample, the auditor plots them into a frequency distribution. As long as the sample size is sufficient, the frequency distribution of the sample means will appear much like the curve above.
Auditors use difference estimation to measure the estimated total misstatement amount in a population when both a recorded value and an audited value exist for each item in the sample. Ratio estimation is similar to difference estimation except that auditor calculates the ratio between the misstatements and their recorded value and projects this to the population to estimate the total population misstatement. Ratio estimation can result in sample sizes even smaller than difference estimation if the size of the misstatements in the population is proportionate to the recorded value of the population items. Mean per unit estimation requires the auditor to focus on the audited value rather than the misstatement amount of each item in the sample. The point estimate of the audited value equals the average audited value of items in the sample times the population size.
ARIA is the risk that the auditor has accepted a population that is materially misstated. ARIA is a serious concern to auditors because of the potential legal implications of concluding that an account balance is fairly stated when it is misstated by a material amount. ARIR is the statistical risk that the auditor has concluded that a population is materially misstated when it is not. This causes the auditor to perform more audit work than should be necessary.
For purposes of the example in the test, the objective is to determine whether accounts receivable is materially misstated. Audit sampling applies in the confirmation of accounts receivable because of the large number of accounts. The misstatement condition is a client misstatement determined by the confirmation of each account. The population size is determined by count as it was for attribute sampling. The sampling unit is an account on the list of customer accounts. The amount of misstatement the auditor is willing to accept is a materiality question.
ARIA is the risk of accepting accounts receivable as correct if it is actually misstated by more than a material amount. ARIR is the risk of rejecting accounts receivable as incorrect if it is not actually misstated by a material amount.
Auditors need an advance estimate of the population point estimate for difference estimation much as they need an estimated population exception rate for attribute sampling. To determine the initial sample size, auditors need an advance estimate of the variation in the misstatements in the population as measured by the population standard deviation.
The auditor must use one of the probabilistic selection methods discussed earlier to select the sample items for confirmation. For confirmations, a misstatement is the difference between the confirmation response and the client’s balance after the reconciliation of all timing differences and customer errors.
The point estimate is a direct extrapolation from the misstatements in the sample to the misstatements in the population. The population standard deviation is a statistical measure of the variability in the values of the individual items in the population. The precision interval is calculated by a statistical formula. The results are a dollar measure of the inability to predict the true population misstatement because the test is based on a sample rather than on the entire population. Auditors calculate the confidence limits which define the confidence interval by combining the point estimate of the total misstatements and the computed precision interval at the desired confidence level.
If the actual standard deviation is larger than the advanced estimate and the actual point estimate is larger than the advanced estimate, it may seem surprising that the population was accepted; however, the use of a reasonably small ARIR caused the sample size to be larger than if the ARIR had been 100 percent.