15 - 1 ©2006 prentice hall business publishing, auditing 11/e, arens/beasley/elder audit sampling...
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15 - 1©2006 Prentice Hall Business Publishing, ©2006 Prentice Hall Business Publishing, Auditing 11/e,Auditing 11/e, Arens/Beasley/Elder Arens/Beasley/Elder
Audit Sampling for Audit Sampling for Tests of Controls and Tests of Controls and Substantive Tests of Substantive Tests of TransactionsTransactions
Chapter 15Chapter 15
15 - 2©2006 Prentice Hall Business Publishing, ©2006 Prentice Hall Business Publishing, Auditing 11/e,Auditing 11/e, Arens/Beasley/Elder Arens/Beasley/Elder
Learning Objective 1Learning Objective 1
Explain the concept ofExplain the concept of
representative sampling.representative sampling.
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Representative SamplesRepresentative Samples
A A representative samplerepresentative sample is one in which is one in whichthe characteristics in the sample ofthe characteristics in the sample ofaudit interest are approximately theaudit interest are approximately thesame as those of the population.same as those of the population.
Nonsampling riskNonsampling risk is the risk that audit is the risk that audittests do not uncover existingtests do not uncover existingexceptions in the sample.exceptions in the sample.
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Representative SamplesRepresentative Samples
Sampling riskSampling risk is the risk that an auditor is the risk that an auditorreaches an incorrect conclusionreaches an incorrect conclusionbecause the sample is notbecause the sample is notrepresentative of the population.representative of the population.
Sampling risk is an inherent part ofSampling risk is an inherent part ofsampling that results from testingsampling that results from testingless than the entire population.less than the entire population.
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Learning Objective 2Learning Objective 2
Distinguish between statisticalDistinguish between statistical
and nonstatistical sampling andand nonstatistical sampling and
between probabilistic and non-between probabilistic and non-
probabilistic sample selection.probabilistic sample selection.
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Statistical Versus Nonstatistical Statistical Versus Nonstatistical SamplingSampling
Step 1Step 1 Plan the sample.Plan the sample.
Step 2Step 2 Select the sampleSelect the sampleand perform the tests.and perform the tests.
Step 3Step 3 Evaluate the results.Evaluate the results.
Similarities:Similarities:
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Statistical Versus Nonstatistical Statistical Versus Nonstatistical SamplingSampling
Statistical samplingStatistical sampling allows the quantification of allows the quantification ofsampling risk in planning the sample (Step 1)sampling risk in planning the sample (Step 1)and evaluating the results (Step 3).and evaluating the results (Step 3).
In In nonstatistical samplingnonstatistical sampling those items that the those items that theauditor believes will provide the mostauditor believes will provide the mostuseful information are selected.useful information are selected.
Differences:Differences:
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Probabilistic Versus Probabilistic Versus Nonprobabilistic Sample Selection Nonprobabilistic Sample Selection
Probabilistic sample selectionProbabilistic sample selection is a method is a methodof selecting a sample such that eachof selecting a sample such that eachpopulation item has a known probabilitypopulation item has a known probabilityof being included in the sample.of being included in the sample.
Nonprobabilistic sample selectionNonprobabilistic sample selection is a is amethod in which the auditor uses professionalmethod in which the auditor uses professionaljudgment rather than probabilistic methods.judgment rather than probabilistic methods.
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Probabilistic Versus Probabilistic Versus Nonprobabilistic Sample Selection Nonprobabilistic Sample Selection
1. Directed sample selection1. Directed sample selection2. Block sample selection2. Block sample selection3. Haphazard sample selection3. Haphazard sample selection
Nonprobabilistic:Nonprobabilistic:
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Probabilistic Versus Probabilistic Versus Nonprobabilistic Sample SelectionNonprobabilistic Sample Selection
1. Simple random sample selection1. Simple random sample selection2. Systematic sample selection2. Systematic sample selection3. Probability proportional to size3. Probability proportional to size sample selectionsample selection4. Stratified sample selection4. Stratified sample selection
Probabilistic:Probabilistic:
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Nonprobabilistic SampleNonprobabilistic SampleSelection MethodsSelection Methods
Directed sample selectionDirected sample selection is the selection of eachis the selection of eachitem based on auditor judgmental criteria.item based on auditor judgmental criteria.
Items most likely to contain misstatementsItems most likely to contain misstatements
Items containing selected population characteristicsItems containing selected population characteristics
Large dollar coverageLarge dollar coverage
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Nonprobabilistic SampleNonprobabilistic SampleSelection MethodsSelection Methods
Block sample selectionBlock sample selection is the selection is the selectionof several items in sequence.of several items in sequence.
Haphazard sample selectionHaphazard sample selection is the selection is the selectionof items without any conscious biasof items without any conscious biason the part of the auditor.on the part of the auditor.
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Learning Objective 3Learning Objective 3
Select representative samples.Select representative samples.
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Probabilistic Sample Selection Probabilistic Sample Selection MethodsMethods
A simpleA simple random sample random sample is one in whichis one in whichevery possible combination of elementsevery possible combination of elementsin the population has an equal chancein the population has an equal chanceof constituting the sample.of constituting the sample.
Computer generation of random numbersComputer generation of random numbers
Random number tablesRandom number tables
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Probabilistic Sample Selection Probabilistic Sample Selection MethodsMethods
Systematic sample selection:Systematic sample selection:
The auditor calculates an interval andThe auditor calculates an interval andthen selects the items for the samplethen selects the items for the samplebased on the size of the interval.based on the size of the interval.
The interval is determined by dividingThe interval is determined by dividingthe population size by the number ofthe population size by the number ofsample items desired.sample items desired.
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Probabilistic Sample Selection Probabilistic Sample Selection MethodsMethods
Probability proportional to size and stratifiedProbability proportional to size and stratifiedsample selection:sample selection:
A sample is taken where the probabilityA sample is taken where the probabilityof selecting any individual population itemof selecting any individual population itemis proportional to its recorded amount (PPS).is proportional to its recorded amount (PPS).
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Probabilistic Sample Selection Probabilistic Sample Selection MethodsMethods
Stratified sample selection:Stratified sample selection:
The population is divided into subpopulationsThe population is divided into subpopulationsby size and larger samplesby size and larger samples are takenare takenof the larger subpopulations.of the larger subpopulations.
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Learning Objective 4Learning Objective 4
Define and describe auditDefine and describe audit
sampling for exception rates.sampling for exception rates.
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Sampling for Exception RatesSampling for Exception Rates
The The occurrence rateoccurrence rate, or , or exception rateexception rate,,is the ratio of the items containing theis the ratio of the items containing thespecific attribute to the total numberspecific attribute to the total numberof population items.of population items.
15 - 20©2006 Prentice Hall Business Publishing, ©2006 Prentice Hall Business Publishing, Auditing 11/e,Auditing 11/e, Arens/Beasley/Elder Arens/Beasley/Elder
Sampling for Exception RatesSampling for Exception Rates
Following are types of exceptions inFollowing are types of exceptions inpopulations of accounting data:populations of accounting data:
deviations from client’s established controlsdeviations from client’s established controls monetary misstatements in populationsmonetary misstatements in populations
of transaction dataof transaction data monetary misstatements in populationsmonetary misstatements in populations
of account balance detailsof account balance details
15 - 21©2006 Prentice Hall Business Publishing, ©2006 Prentice Hall Business Publishing, Auditing 11/e,Auditing 11/e, Arens/Beasley/Elder Arens/Beasley/Elder
Learning Objective 5Learning Objective 5
Use nonstatistical sampling inUse nonstatistical sampling in
tests of controls and substantivetests of controls and substantive
tests of transactions.tests of transactions.
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Terms Used in Audit SamplingTerms Used in Audit Sampling
Characteristic or attributeCharacteristic or attribute Acceptable risk of assessing control risk tooAcceptable risk of assessing control risk too low (ARACR)low (ARACR) Tolerable exception rate (TER)Tolerable exception rate (TER) Estimated population exceptionEstimated population exception rate (EPER)rate (EPER) Initial sample sizeInitial sample size
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Terms Used in Audit SamplingTerms Used in Audit Sampling
ExceptionException
Sample exception rate (SER)Sample exception rate (SER)
Computed upper exception rate (CUER)Computed upper exception rate (CUER)
15 - 24©2006 Prentice Hall Business Publishing, ©2006 Prentice Hall Business Publishing, Auditing 11/e,Auditing 11/e, Arens/Beasley/Elder Arens/Beasley/Elder
I: Plan the SampleI: Plan the Sample
Step 1: State the objectives of the audit test.Step 1: State the objectives of the audit test.
Step 2: Decide whether audit sampling applies.Step 2: Decide whether audit sampling applies.
Step 3: Define attributes and exception conditions.Step 3: Define attributes and exception conditions.
Step 4: Define the population.Step 4: Define the population.
Step 5: Define the sampling unit.Step 5: Define the sampling unit.
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I: Plan the SampleI: Plan the Sample
Step 7: Specify acceptable risk of assessingStep 7: Specify acceptable risk of assessing control risk too low.control risk too low.
Step 8: Estimate the population exception rate.Step 8: Estimate the population exception rate.
Step 9: Determine the initial sample size.Step 9: Determine the initial sample size.
Step 6: Specify the tolerable exception rate.Step 6: Specify the tolerable exception rate.
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II: Select the Sample and Perform II: Select the Sample and Perform the Audit Proceduresthe Audit ProceduresStep 10: Select the sample.Step 10: Select the sample.
Step 11: Perform the audit procedures.Step 11: Perform the audit procedures.
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III: Evaluate the ResultsIII: Evaluate the Results
Step 12: Generalize from the sample to theStep 12: Generalize from the sample to the population.population.
Step 13: Analyze exceptions.Step 13: Analyze exceptions.
Step 14: Decide the acceptability of the population.Step 14: Decide the acceptability of the population.
15 - 28©2006 Prentice Hall Business Publishing, ©2006 Prentice Hall Business Publishing, Auditing 11/e,Auditing 11/e, Arens/Beasley/Elder Arens/Beasley/Elder
Guidelines for ARACR and TER Guidelines for ARACR and TER Tests of ControlTests of Control
Assessed control risk – Consider:Assessed control risk – Consider:• Need to issue a separate report on internal control overNeed to issue a separate report on internal control over financial reporting for public companiesfinancial reporting for public companies• Nature, extent, and timing of substantive testsNature, extent, and timing of substantive tests• Quality of evidence available for tests of controlsQuality of evidence available for tests of controls
FactorFactor
• Lowest assessed control riskLowest assessed control risk• Moderate assessed control riskModerate assessed control risk• Higher assessed control riskHigher assessed control risk• 100% assessed control risk100% assessed control risk
JudgmentJudgment• ARACR of lowARACR of low• ARACR of mediumARACR of medium• ARACR of highARACR of high• ARACR is not applicableARACR is not applicable
GuidelineGuideline
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Guidelines for ARACR and TER Guidelines for ARACR and TER Tests of ControlTests of Control
Significance of the transactions and related accountSignificance of the transactions and related accountbalances that the internal controls are intended to affect.balances that the internal controls are intended to affect.
FactorFactor
• Highly significant balancesHighly significant balances• Significant balancesSignificant balances• Less significant balancesLess significant balances
JudgmentJudgment
• TER of 4%TER of 4%• TER of 5%TER of 5%• TER of 6%TER of 6%
GuidelineGuideline
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Guidelines for ARACR and TER Guidelines for ARACR and TER Tests of TransactionsTests of Transactions
ModerateModerate ExcellentExcellentGoodGoodNot goodNot good
SmallSmall ExcellentExcellentGoodGoodNot goodNot good
LargeLarge ExcellentExcellentGoodGoodNot goodNot good
Planned reduction inPlanned reduction insubstantive tests ofsubstantive tests ofdetails of balancesdetails of balances
Results of understandingResults of understandinginternal control andinternal control andtests of controlstests of controls
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Guidelines for ARACR and TER Guidelines for ARACR and TER Tests of TransactionsTests of Transactions
LargeLarge High High Percent or amountPercent or amount MediumMedium based on materialitybased on materiality LowLow considerationsconsiderations
ModerateModerate High High Percent or amountPercent or amount MediumMedium based on materialitybased on materiality Medium-lowMedium-low considerationsconsiderations
SmallSmall High High Percent or amount Percent or amount Medium-highMedium-high based on materialitybased on materiality MediumMedium considerations considerations
Planned reduction inPlanned reduction insubstantive tests ofsubstantive tests ofdetails of balancesdetails of balances
ARACR forARACR forsubstantive testssubstantive testsof transactionsof transactions
TER for substantiveTER for substantivetests of transactionstests of transactions
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Effect on Sample Size of Changing Effect on Sample Size of Changing FactorsFactors
Effect on initialEffect on initialType of changeType of change sample sizesample size
Increase acceptable risk ofIncrease acceptable risk ofassessing control risk too lowassessing control risk too low DecreaseDecrease
Increase tolerable risk rateIncrease tolerable risk rate DecreaseDecrease
Increase estimated populationIncrease estimated populationexception rateexception rate IncreaseIncrease
Increase population sizeIncrease population size Increase (minor)Increase (minor)
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Decide the Acceptability of the Decide the Acceptability of the PopulationPopulation
Revise TER or ARACR.Revise TER or ARACR.
Expand the sample size.Expand the sample size.
Revise assessed control risk.Revise assessed control risk.
Communicate with the auditCommunicate with the auditcommittee or management.committee or management.
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Summary of Audit Sample StepsSummary of Audit Sample Steps
Plan the samplePlan the sample(Steps 1-9)(Steps 1-9)
Select the sampleSelect the sample(Step 10)(Step 10)
Perform the testsPerform the tests(Step 11)(Step 11)
Evaluate the resultsEvaluate the results(Steps 12-14)(Steps 12-14)
Number ofNumber ofexceptionsexceptionsin samplein sampleand actualand actual
sample sizesample size
To Step 12To Step 12To Step 14To Step 14
Fro
mF
rom
Ste
p 1
2S
tep
12
Co
mp
are
Co
mp
are
To/FromTo/From Step 6Step 6
ComputedComputedupperupper
exceptionexceptionraterate
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Learning Objective 6Learning Objective 6
Define and describe attributesDefine and describe attributes
sampling and a samplingsampling and a sampling
distribution.distribution.
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Statistical Audit SamplingStatistical Audit Sampling
The statistical sampling method mostThe statistical sampling method mostcommonly used for tests of controlscommonly used for tests of controlsand substantive tests of transactionsand substantive tests of transactionsis is attributes samplingattributes sampling..
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Sampling DistributionSampling Distribution
It is a frequency distribution of the resultsIt is a frequency distribution of the resultsof all possible samples of a specified sizeof all possible samples of a specified sizethat could be obtained from a populationthat could be obtained from a populationcontaining some specific parameters.containing some specific parameters.
Attributes samplingAttributes sampling is based on the is based on thebinomial distribution.binomial distribution.
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Learning Objective 7Learning Objective 7
Use attributes sampling in testsUse attributes sampling in tests
of controls and substantiveof controls and substantive
tests of transactions.tests of transactions.
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Application of Attributes SamplingApplication of Attributes Sampling
2. Locate the TER on the top of the table.2. Locate the TER on the top of the table.
3. Locate the EPER in the far left column.3. Locate the EPER in the far left column.
1. Select the table corresponding to the ARACR.1. Select the table corresponding to the ARACR.
4. Read down the appropriate TER column until4. Read down the appropriate TER column until it intersects with the appropriate EPER rowit intersects with the appropriate EPER row in order to get the initial sample size.in order to get the initial sample size.
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Application of Attributes SamplingApplication of Attributes Sampling
Population size is a minor consideration inPopulation size is a minor consideration indetermining sample size.determining sample size.
Representativeness is ensured by the sampleRepresentativeness is ensured by the sampleselection process more than by sample size.selection process more than by sample size.
15 - 41©2006 Prentice Hall Business Publishing, ©2006 Prentice Hall Business Publishing, Auditing 11/e,Auditing 11/e, Arens/Beasley/Elder Arens/Beasley/Elder
End of Chapter 15End of Chapter 15