Tests of Controls

The Upper Error Limit (UEL) is similar to the upper confidence limit of a statistical confidence interval.

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If UEL is greater than the tolerable deviation rate, you can conclude that the population deviation rate is low enough to meet your tolerable rate decision criterion, and you can assess the control risk at the level associated with the tolerable deviation rate.

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GAAS requires that independent auditors disclose all information about their audit sampling applications in their reports on audited financial statements.

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Decisions concerning materiality and audit risk are the most significant made in the course of an audit because they form the basis for determining the extent of the auditing procedures to be undertaken.

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If we consider the statement "there exists a material misstatement in the total amount recorded for the accounting population" as the null hypothesis, then we are using the negative approach to hypothesis testing.

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Define the projected likely misstatement. What is its significance?
The projected likely misstatement is the auditors' best estimate of misstatement based on the errors found in the sample (that is, to extend the findings from the sample to the entire population). Auditors are supposed to think about the PLM in relation to the material misstatement (MM) and consider whether there may be "further misstatement remaining undetected". The PLM plays a significant role in the auditors' problem of deciding upon an amount to recommend for adjustment when they have made a "rejection" decision.
If you have sampled a population of A/R and the projected likely misstatement is material, what is the first step you should take as the auditor?
Increase the sample size. It can be shown that for any amount of error, sample size can be increased sufficiently so that adjusting for projected misstatements will always reduce the remaining error to less than a material amount at the stated confidence level. Of course, if the auditor cannot increase the sample size sufficiently, then the theoretically best available adjustment is not an option and the auditor may have to rely on other audit procedures to determine the amount of adjustment or to make the appropriate reservation in the auditor's report.
According to the CICA Handbook, how should the auditor estimate a likely aggregate misstatement?
Section 5130.37 of the CICA Handbook suggests that the auditor should estimate a likely aggregate misstatement by aggregating:
Known errors on other than representative samples,
Projection of misstatements on representative (i.e. statistical) samples
Disagreements with accounting estimates,
Net effect of uncorrected misstatements in opening equity.
As noted in Handbook Section 5130.35, the above types of errors are aggregated in stages: in each stage the auditor determines whether the misstatement for each balance or class of transactions is material. If not, the auditor proceeds until the highest level of aggregation (net income, net assets) is reached.
What is "Discovery Sampling"? What is its typical application?
Discovery sampling is essentially another kind of sampling design directed toward a specific objective. In substance, the auditor is trying to arrive at a sample size which provides assurance of finding at least one example of deviation. Ordinarily, discovery sampling is used for designing procedures to search for forged cheques or other management improprieties (i.e. forensic applications).
What are the advantages of utilizing Dollar Unit Sampling (DUS)?
An accurate estimate of a normal distribution standard deviation is required for classical sampling. DUS does not require this estimate because the statistical basis is the binomial distribution.
Classical statistics estimators suffer problems of bias because a sufficient number of errors may not be found in a sample to permit proper use. DUS imposes no requirements for a minimum number of errors.
Large sample sizes: DUS sample sizes are generally smaller than classical sampling sample sizes. (Smaller sample sizes are considered more efficient in most situations.)
Complicated stratification plans: DUS sample selection methods accomplish stratification by automatically selecting a large proportion of high-value items.
80/20 "rule":
the rule of thumb about population skewness that 80 percent of the value tends to be in 20 percent of the units.

accounting estimate:
an approximation of a financial statement element, item, or account made by an organization's management.

average sampling interval (ASI):
the recorded dollar amount of a population being sampled divided by the sample size.

computed upper limit (CUL):
a statistical estimate of the population deviation rate computed from the test of controls sample evidence.

decision criteria:
standards for decision and evaluation in specific circumstances.

dollar-value estimation objective in statistical sampling:
the job of helping a client obtain an estimate of an amount.

finitely corrected:
sample size calculation that incorporates the population size in such a way that sample sizes larger than the population size cannot be produced.

logical unit:
ordinary accounting subsidiary unit that contains the dollar unit selected in a dollar-unit sample.

planned control risk assessment:
emphasis on planned; the auditors' selection of a control risk level for which they want to justify a control risk assessment after completing the test of controls audit work.

projected likely misstatement (PLM):
auditors' best estimate of misstatement based on the errors found in a sample.

risk model:
AR = IR x CR x DR (chapter 12); AR = IR x CR x AP x RIA
simple extension:
calculation of projected likely misstatement based on sample evidence using the difference and ratio methods.

smoke/fire concept:
means there can be more exposure to error (smoke) that actual error (fire), in analogy to test of controls sampling determination of a tolerable deviation rate.

tainting percentage:
ratio of misstatement in a sampling unit to the recorded amount of the sampling unit.

unrestricted random sample:
items in a population are associated with numbers in a random number table or computer program for selection of a sample; no population stratification.

upper error limit (UEL):
largest amount of monetary misstatement that can be calculated, using the coefficient for the decision criterion risk of incorrect acceptance.