# Audit Sampling For Tests Of Details Of Balances

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Audit Sampling for Tests ofDetails of BalancesChapter 17 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley5-5

Learning Objective 1Differentiate audit sampling for tests ofdetails of balances and for tests ofcontrols and substantive tests oftransactions. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 2

Tests of Details of Balancesand Controls, and SubstantiveTests of TransactionsDifferences among testsType of TestWhat It MeasuresControlsEffectiveness ofcontrolsTransactionsMonetary correctnessof transactionsBalancesExistence of materialmisstatements 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 3

Learning Objective 2Apply nonstatistical sampling to tests ofdetails of balances. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 4

Nonstatistical Sampling14 steps required in audit sampling fortests of details of balances.Steps parallel the sampling approachused to test controls and/or testtransactions.There are a few differences becauseof the different objectives of the tests. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 5

Comparison of the 14 StepsAudit sampling for testsof details of balances1. State the objectivesof the audit test.2. Decide whether auditsampling applies.3. Define a misstatement.4. Define the population.5. Define the sampling unit.Audit sampling for tests ofcontrols and substantivetests of transactions1. State the objectivesof the audit test.2. Decide whether auditsampling applies.3. Define attributes andexception conditions.4. Define the population.5. Define the sampling unit. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 6

Comparison of the 14 StepsAudit sampling for testsof details of balances6. Specify tolerablemisstatement.7. Specify acceptable riskof incorrect acceptance.8. Estimate misstatementsin the population.9. Determine the initialsample size.Audit sampling for tests ofcontrols and substantivetests of transactions6. Specify the tolerableexception rate.7. Specify acceptable riskof assessing controlrisk too low.8. Estimate the populationexception rate.9. Determine the initialsample size. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 7

Comparison of the 14 StepsAudit sampling for testsof details of balances10. Select the sample.Audit sampling for tests ofcontrols and substantivetests of transactions10. Select the sample.11. Perform the audit11. Perform the auditprocedures.procedures.12. Generalize from the12. Generalize from thesample to the population.sample to the population.13. Analyze the misstatements. 13. Analyze the exceptions.14. Decide the acceptability14. Decide the acceptabilityof the population.of the population. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 8

Action When a PopulationIs Rejected Take no action until tests of other audit areasare completedPerform expanded audit tests in specific areasIncrease the sample sizeAdjust the account balanceRequest the client to correct the populationRefuse to give an unqualified opinion 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 9

Learning Objective 3Apply monetary unit sampling. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 10

Monetary Unit SamplingMUS is an innovation in statisticalsampling methodology that wasdeveloped specifically for useby auditors. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 11

Differences between MUSand Nonstatistical Sampling The definition of the sampling unitis an individual dollar. The population size is the recordeddollar population. Preliminary judgment of materialityis used for each account instead oftolerable misstatement. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 12

Differences between MUSand Nonstatistical Sampling Sample size is determined using astatistical formula. A formal decision rule is used fordeciding the acceptabilityof the population. Sample selection is done usingprobability proportional to sizesample selection (PPS). 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 13

Differences between MUSand Nonstatistical SamplingThe auditor generalizes from thesample to the population using MUStechniques. Attribute sampling tables are used tocalculate results Attribute results must be converted todollars Make an assumption about the % ofmisstatement for each item misstated Determine misstatement bounds. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 14

Generalizing from the Sampleto the PopulationAssumption 1:Population is 1,200,000Sample size is 100 customer accountsOverstatement amounts equal 100%.Understatement amounts equal 100%.Misstatement bounds at a 5% ARIA are:Upper misstatement bound 1,200,000 3% 100% 36,000Lower misstatement bound 1,200,000 3% 100% 36,000 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 15

Generalizing from the Sampleto the PopulationThe following two conditions both have toexist before the 36,000 correctly reflectsthe true overstatement amount:1. All amounts have to be overstatements.2. All population items misstated have tobe 100% misstated. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 16

Generalizing from the Sampleto the PopulationAssumption 2:Overstatement amounts equal 10%.Understatement amounts equal 10%.Misstatement bounds at a 5% ARIA are:Upper misstatement bound 1,200,000 3% 10% 3,600Lower misstatement bound 1,200,000 3% 10% 3,600 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 17

Generalizing from the Sampleto the PopulationAssumption 3:Overstatement amounts equal 20%.Understatement amounts equal 200%.Misstatement bounds at a 5% ARIA are:Upper misstatement bound 1,200,000 3% 20% 7,200Lower misstatement bound 1,200,000 3% 200% 72,000 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 18

Appropriate Percent ofMisstatement AssumptionThe appropriate assumption for the overallpercent of misstatement in those populationitems containing a misstatement is anauditor’s decision. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 19

Generalizing WhenMisstatements Are Found1. Overstatement and understatementamounts are dealt with separatelyand then combined.2. A different misstatement assumptionis made for each misstatement,including the zero misstatements. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 20

Generalizing WhenMisstatements Are Found3. The auditor must deal with layers of thecomputed upper exception rate (CUER)from the attributes sampling table.4. Misstatement assumptions must beassociated with each layer. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 21

Illustration of the Auditor’sDecision Rule for MUS 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 22

Determining Sample Size UsingMUS Materiality Assumption of the average percentof misstatement for population itemsthat contain a misstatement Acceptable risk of incorrect acceptance Recorded population value 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 23

Determining Sample Size UsingMUS Estimate of the population exception rate Relationship of the audit risk modelto sample size for MUSPDR AAR (IR CR) 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 24

Advantages of Using MUS MUS increases the likelihood of selectinghigh-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/Beasley17- 25

Learning Objective 4Describe variables sampling. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 26

Frequency of values in percentFrequency Distribution ofSample MeansValue of x in dollars 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 27

Sampling DistributionsThree things shape the results of theexperiment of taking a large number of samplesfrom a known population:1. The mean value of all the sample meansis equal to the population mean ( ).X 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 28

Sampling Distributions2. The shape of the frequency distributionof the sample means is that of a normaldistribution (curve), as long as the samplesize is sufficiently large, regardless of thedistribution of the population.3. The percentage of sample means betweenany two values of the samplingdistribution is measurable. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 29

MeanSamplingdistribution –NormalPopulationdistribution –SkewedValue ofxFrequency of values in percentSampling Distribution fora Population Distributionin dollars 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 30

Variables Methods Difference estimation Ratio estimation Mean-per-unit estimation 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 31

Stratified Statistical Methods All of the elements of the population aredivided into two or more subpopulations Each subpopulation is independently tested The calculations are then made for eachstratum and then combined into one overallpopulation estimate 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 32

Sampling Risks (ARIA and ARIR)Actual audit decisionActual state of the populationMateriallyNot materiallymisstatedmisstatedConclude that thepopulation ismaterially misstatedCorrectconclusion –no riskIncorrectconclusion –risk is ARIRConclude that thepopulation is notmaterially misstatedIncorrectconclusion –risk is ARIACorrectconclusion –no risk 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 33

Learning Objective 5Use difference estimation in tests of detailsof balances. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 34

Plan the Sample and Calculatethe 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/Beasley17- 35

Specify Acceptable RiskARIAARIR 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 36

Estimate Misstatementin the Population1. Estimate an expected point estimate2.Make an advance population standard deviationestimate – variability of the population. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 37

Calculate the InitialSample Sizen SD*(ZA ZR)N(TM – E *)2where:n initial sample sizeSD* advance estimate of the standard deviationZA confidence coefficient for ARIAZR confidence coefficient for ARIRN population sizeTM tolerable misstatement for the population (materially)E* estimated point estimate of the population misstatemen 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 38

Select the Sample and Performthe ProceduresThe auditor must use one of theprobabilistic sample selection methodsto select the items for confirmation.The auditor must use care in confirmingand performing alternative procedures. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 39

Evaluate the ResultsGeneralize from the sample to the population1. Compute the point estimate of thetotal misstatement2. Compute an estimate of the populationstandard deviation3. Compute the precision interval4. Compute the confidence limits 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 40

Effect of Changing Each FactorType of changeEffect on the computedprecision intervalIncrease ARIAIncrease the point estimateof the misstatementsIncrease the standard dev.Increase the sample size 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 41

Analyze the MisstatementsThe auditor must evaluate misstatements todetermine the cause of each misstatementand decide whether modification of theaudit risk model is needed. 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 42

Auditor’s Decision Rule forDifference Estimation 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley17- 43

End of Chapter 17 2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley5-5

2012 Prentice Hall Business Publishing, Auditing 14/e, Arens/Elder/Beasley 17- 6 Comparison of the 14 Steps 2. Decide whether audit sampling applies. 2. Decide whether audit sampling applies. 3. Define a misstatement. 3. Define attributes and exception conditions. 4. Define the population.

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