15 - 1 ©2006 Prentice Hall Business Publishing, Auditing 11/e, Arens/Beasley/Elder Audit Sampling for Tests of Controls and Substantive Tests of Transactions.

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


Learning Objective 1Learning Objective 1

Explain the concept ofExplain the concept of

representative sampling.representative sampling.


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.


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.



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.


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:


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:


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.


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:


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:


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


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.



Select representative samples.Select representative samples.


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



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.



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).



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.



Define and describe auditDefine and describe audit

sampling for exception rates.sampling for exception rates.


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.


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



Use nonstatistical sampling inUse nonstatistical sampling in

tests of controls and substantivetests of controls and substantive

tests of transactions.tests of transactions.


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


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)


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.


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.


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.


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.


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


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


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


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


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)


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.


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



Define and describe attributesDefine and describe attributes

sampling and a samplingsampling and a sampling

distribution.distribution.


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..


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.



Use attributes sampling in testsUse attributes sampling in tests

of controls and substantiveof controls and substantive

tests of transactions.tests of transactions.


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.


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.


End of Chapter 15End of Chapter 15

15 - 1 ©2006 Prentice Hall Business Publishing, Auditing 11/e, Arens/Beasley/Elder Audit Sampling for Tests of Controls and Substantive Tests of Transactions.

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