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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.

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.

The auditor will determine why that type of misstatement occurred and then determine the implications on other auditor areas.

The auditor’s preliminary judgment about materiality should be the amount used as tolerable misstatement in all applications of MUS.

The problem with PPS selection is that population items with a zero recorded balance have no chance of being selected with a PPS sample.

Thus, the dollar value of the misstatement is not likely to exceed $36,000.

The change from 100% to 10% significantly affects the misstatement bounds.

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.

When there were no misstatements in the sample, an assumption was required as to the average percent of misstatement for the population items misstated.

A point estimate of misstatements is made for both overstatement and understatement amounts.

Each bound is reduced by the opposite point estimate.

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.

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.

The use of variable methods shares many similarities with non-statistical sampling. All 14 steps must be performed for variable methods.

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.

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.

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.

ARIR is the risk of rejecting accounts receivable as incorrect if it is not actually misstated by a material amount.

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.

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 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.

- 1. Audit Sampling for Tests of Details of Balances Chapter 17 ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 5-5
- 2. Learning Objective 1 Differentiate audit sampling for tests of details of balances and for tests of controls and substantive tests of transactions. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 2
- 3. Tests of Details of Balances and Controls, and Substantive Tests of Transactions Differences among tests Type of Test Type of Test What It Measures What It Measures Controls Effectiveness of controls Transactions Monetary correctness of transactions Existence of material misstatements Balances ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 3
- 4. Learning Objective 2 Apply nonstatistical sampling to tests of details of balances. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 4
- 5. Nonstatistical Sampling 14 steps required in audit sampling for tests of details of balances. Steps parallel the sampling approach used to test controls and/or test transactions. There are a few differences because of the different objectives of the tests. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 5
- 6. Comparison of the 14 Steps Audit sampling for tests of details of balances 1. State the objectives of the audit test. 2. Decide whether audit sampling applies. 3. Define a misstatement . 4. Define the population. 5. Define the sampling unit. Audit sampling for tests of controls and substantive tests of transactions 1. State the objectives of the audit test. 2. Decide whether audit sampling applies. 3. Define attributes and exception conditions. 4. Define the population. 5. Define the sampling unit. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 6
- 7. Comparison of the 14 Steps Audit sampling for tests of details of balances 6. Specify tolerable misstatement . 7. Specify acceptable risk of incorrect acceptance . 8. Estimate misstatements in the population. 9. Determine the initial sample size. Audit sampling for tests of controls and substantive tests of transactions 6. Specify the tolerable exception rate. 7. Specify acceptable risk of assessing control risk too low. 8. Estimate the population exception rate. 9. Determine the initial sample size. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 7
- 8. Comparison of the 14 Steps Audit sampling for tests of Audit sampling for tests controls and substantive of details of balances tests of transactions 10. Select the sample. 10. Select the sample. 11. Perform the audit 11. Perform the audit procedures. procedures. 12. Generalize from the 12. Generalize from the sample to the population. sample to the population. 13. Analyze the misstatements. 13. Analyze the exceptions. 14. Decide the acceptability 14. Decide the acceptability of the population. of the population. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 8
- 9. Action When a Population Is Rejected Take no action until tests of other audit areas are completed Perform expanded audit tests in specific areas Increase the sample size Adjust the account balance Request the client to correct the population Refuse to give an unqualified opinion ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 9
- 10. Learning Objective 3 Apply monetary unit sampling. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 10
- 11. Monetary Unit Sampling MUS is an innovation in statistical sampling methodology that was developed specifically for use by auditors. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 11
- 12. Differences between MUS and Nonstatistical Sampling • The definition of the sampling unit is an individual dollar. • The population size is the recorded dollar population. • Preliminary judgment of materiality is used for each account instead of tolerable misstatement. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 12
- 13. Differences between MUS and Nonstatistical Sampling •Sample size is determined using a statistical formula. •A formal decision rule is used for deciding the acceptability of the population. •Sample selection is done using probability proportional to size sample selection (PPS). ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 13
- 14. Differences between MUS and Nonstatistical Sampling The auditor generalizes from the sample to the population using MUS techniques. •Attribute sampling tables are used to calculate results •Attribute results must be converted to dollars •Make an assumption about the % of misstatement for each item misstated •Determine misstatement bounds. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 14
- 15. Generalizing from the Sample to the Population Assumption 1: Population is $1,200,000 Sample size is 100 customer accounts Overstatement amounts equal 100%. Understatement amounts equal 100%. Misstatement bounds at a 5% ARIA are: Upper misstatement bound = $1,200,000 × 3% × 100% = $36,000 Lower misstatement bound = $1,200,000 × 3% × 100% = $36,000 ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 15
- 16. Generalizing from the Sample to the Population The following two conditions both have to exist before the $36,000 correctly reflects the true overstatement amount: 1. All amounts have to be overstatements. 2. All population items misstated have to be 100% misstated. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 16
- 17. Generalizing from the Sample to the Population Assumption 2: Overstatement amounts equal 10%. Understatement amounts equal 10%. Misstatement bounds at a 5% ARIA are: Upper misstatement bound = $1,200,000 × 3% × 10% = $3,600 Lower misstatement bound = $1,200,000 × 3% × 10% = $3,600 ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 17
- 18. Generalizing from the Sample to the Population Assumption 3: Overstatement amounts equal 20%. Understatement amounts equal 200%. Misstatement bounds at a 5% ARIA are: Upper misstatement bound = $1,200,000 × 3% × 20% = $7,200 Lower misstatement bound = $1,200,000 × 3% × 200% = $72,000 ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 18
- 19. Appropriate Percent of Misstatement Assumption The appropriate assumption for the overall percent of misstatement in those population items containing a misstatement is an auditor’s decision. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 19
- 20. Generalizing When Misstatements Are Found 1. Overstatement and understatement amounts are dealt with separately and then combined. 2. A different misstatement assumption is made for each misstatement, including the zero misstatements. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 20
- 21. Generalizing When Misstatements Are Found 3. The auditor must deal with layers of the computed upper exception rate (CUER) from the attributes sampling table. 4. Misstatement assumptions must be associated with each layer. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 21
- 22. Illustration of the Auditor’s Decision Rule for MUS ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 22
- 23. Determining Sample Size Using MUS Materiality Assumption of the average percent of misstatement for population items that contain a misstatement Acceptable risk of incorrect acceptance Recorded population value ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 23
- 24. Determining Sample Size Using MUS Estimate of the population exception rate Relationship of the audit risk model to sample size for MUS PDR = AAR ÷ (IR × CR) ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 24
- 25. Advantages of Using MUS MUS increases the likelihood of selecting high-dollar items MUS often reduces the cost of audit testing Easy to apply MUS provides a statistical conclusion ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 25
- 26. Learning Objective 4 Describe variables sampling. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 26
- 27. Frequency of values in percent Frequency Distribution of Sample Means Value of x in dollars ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 27
- 28. Sampling Distributions Three things shape the results of the experiment of taking a large number of samples from a known population: 1. The mean value of all the sample means is equal to the population mean ( ). X ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 28
- 29. Sampling Distributions 2. The shape of the frequency distribution of the sample means is that of a normal distribution (curve), as long as the sample size is sufficiently large, regardless of the distribution of the population . 3. The percentage of sample means between any two values of the sampling distribution is measurable. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 29
- 30. Mean Sampling distribution – Normal Population distribution – Skewed Value of x Frequency of values in percent Sampling Distribution for a Population Distribution in dollars ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 30
- 31. Variables Methods Difference estimation Ratio estimation Mean-per-unit estimation ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 31
- 32. Stratified Statistical Methods All of the elements of the population are divided into two or more subpopulations Each subpopulation is independently tested The calculations are then made for each stratum and then combined into one overall population estimate ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 32
- 33. Sampling Risks (ARIA and ARIR) Actual state of the population Materially Not materially Actual audit decision misstated misstated Conclude that the population is materially misstated Correct conclusion – no risk Incorrect conclusion – risk is ARIR Conclude that the population is not materially misstated Incorrect conclusion – risk is ARIA Correct conclusion – no risk ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 33
- 34. Learning Objective 5 Use difference estimation in tests of details of balances. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 34
- 35. Plan the Sample and Calculate the Sample Size State the objectives of the audit test Decide whether audit sampling applies Define misstatement conditions Define the population Define the sampling unit Specify tolerable misstatement ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 35
- 36. Specify Acceptable Risk ARIA ARIR ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 36
- 37. Estimate Misstatement in the Population 1. Estimate an expected point estimate 2.Make an advance population standard deviation estimate – variability of the population. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 37
- 38. Calculate the Initial Sample Size n= SD*(ZA + ZR)N (TM – E *) 2 where: n SD* ZA ZR N TM E* = = = = = = = initial sample size advance estimate of the standard deviation confidence coefficient for ARIA confidence coefficient for ARIR population size tolerable misstatement for the population (materially) estimated point estimate of the population misstatement ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 38
- 39. Select the Sample and Perform the Procedures The auditor must use one of the probabilistic sample selection methods to select the items for confirmation. The auditor must use care in confirming and performing alternative procedures. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 39
- 40. Evaluate the Results Generalize from the sample to the population 1. Compute the point estimate of the total misstatement 2. Compute an estimate of the population standard deviation 3. Compute the precision interval 4. Compute the confidence limits ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 40
- 41. Effect of Changing Each Factor Type of change Effect on the computed precision interval Increase ARIA Increase the point estimate of the misstatements Increase the standard dev. Increase the sample size ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 41
- 42. Analyze the Misstatements The auditor must evaluate misstatements to determine the cause of each misstatement and decide whether modification of the audit risk model is needed. ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 42
- 43. Auditor’s Decision Rule for Difference Estimation ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 43
- 44. End of Chapter 17 ©2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 5-5

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