Audit Sampling for Tests of Controls and Substantive Tests of Transactions

©2010 Prentice Hall Business Publishing, ©2010 Prentice Hall Business Publishing, Auditing 13/e,Auditing 13/e, Arens//Elder/Beasley Arens//Elder/Beasley 15 - 1

Audit Sampling for Tests of Audit Sampling for Tests of Controls and Substantive Tests of Controls and Substantive Tests of

TransactionsTransactions

Chapter 15Chapter 15

©2010 Prentice Hall Business Publishing, ©2010 Prentice Hall Business Publishing, Auditing 13/e,Auditing 13/e, Arens//Elder/Beasley Arens//Elder/Beasley 15 - 15 - 22

Learning Objective 1Learning Objective 1

Explain the concept ofExplain the concept ofrepresentative sampling.representative sampling.


Representative SamplesRepresentative Samples

A representative sample is one in whichthe characteristics in the sample of auditinterest are approximately the same asthose of the population.

Nonsampling risk is the risk that audittests do not uncover existing exceptionsin the sample.


Representative SamplesRepresentative Samples

Sampling risk is the risk that an auditorreaches an incorrect conclusionbecause the sample is notrepresentative of the population.

Sampling risk is an inherent part ofsampling that results from testingless than the entire population.


Minimizing Sampling RiskMinimizing Sampling Risk

1. Adjust sample size

2. Use an appropriate method of selectingsample items from the population



Distinguish between statisticalDistinguish between statisticaland nonstatistical sampling andand nonstatistical sampling andbetween probabilistic and non-between probabilistic and non-probabilistic sample selection.probabilistic sample selection.


Statistical Versus Nonstatistical Statistical Versus Nonstatistical SamplingSampling

Step 1: Plan the sample

Step 2: Select the sample and perform the tests

Step 3: Evaluate the results

Similarities:


Statistical Versus Nonstatistical Statistical Versus Nonstatistical SamplingSampling

Statistical sampling allows the quantificationof sampling risk in planning the sample (Step 1)and evaluating the results (Step 3)

In nonstatistical sampling those items thatthe auditor believes will provide the mostuseful information are selected

Differences:


Probabilistic Versus Nonprobabilistic Probabilistic Versus Nonprobabilistic Sample Selection Sample Selection

Probabilistic sample selection is a methodof selecting a sample such that eachpopulation item has a known probabilityof being included in the sample.

Nonprobabilistic sample selection is amethod in which the auditor uses professionaljudgment rather than probabilistic methods.


Probabilistic Versus Nonprobabilistic Probabilistic Versus Nonprobabilistic Sample Selection Sample Selection

1. Directed sample selection2. Block sample selection3. Haphazard sample selection

Nonprobabilistic:


Probabilistic Versus Nonprobabilistic Probabilistic Versus Nonprobabilistic Sample SelectionSample Selection

1. Simple random sample selection2. Systematic sample selection3. Probability proportional to size sample selection4. Stratified sample selection

Probabilistic:


Nonprobabilistic SampleNonprobabilistic SampleSelection MethodsSelection Methods

Directed sample selection is the selection ofeach item based on auditor judgmental criteria.

Items most likely to contain misstatements

Items containing selected population characteristics

Large dollar coverage


Nonprobabilistic SampleNonprobabilistic SampleSelection MethodsSelection Methods

Block sample selection is the selectionof several items in sequence.

Haphazard sample selection is the selectionof items without any conscious bias on the part of the auditor.



Select representative samples.Select representative samples.


Probabilistic Sample Selection Probabilistic Sample Selection MethodsMethods

A simple random sample is one in whichevery possible combination of elementsin the population has an equal chanceof constituting the sample.

Computer generation of random numbers

Random number tables



Systematic sample selection:

The auditor calculates an interval andthen selects the items for the samplebased on the size of the interval.

The interval is determined by dividingthe population size by the number ofsample items desired.



Probability proportional to size:

A sample is taken where the probabilityof selecting any individual population itemis proportional to its recorded amount (PPS).



Stratified sample selection:

The population is divided into subpopulationsby size and larger samples are taken of thelarger subpopulations.



Define and describe auditDefine and describe auditsampling for exception rates.sampling for exception rates.


Sampling for Exception RatesSampling for Exception Rates

The occurrence rate, or exception rate,is the ratio of the items containing thespecific attribute to the total numberof population items.


Sampling for Exception RatesSampling for Exception Rates

Following are types of exceptions inpopulations of accounting data:

1. Deviations from client’s established controls2. Monetary misstatements in populations

of transaction data3. Monetary misstatements in populations of

account balance details



Use nonstatistical sampling inUse nonstatistical sampling intests of controls and substantivetests of controls and substantivetests of transactions.tests of transactions.


Terms Used in Audit SamplingTerms Used in Audit Sampling

Characteristic or attribute Acceptable risk of assessing control risk too

low (ARACR) Tolerable exception rate (TER) Estimated population exception rate (EPER) Initial sample size

Terms related to planning:


Terms Used in Audit SamplingTerms Used in Audit Sampling

Exception Sample exception rate (SER) Computed upper exception rate (CUER)

Terms related to evaluating results:


I: Plan the SampleI: Plan the Sample

Step 1: State the objectives of the audit test.

Step 2: Decide whether audit sampling applies.

Step 3: Define attributes and exception conditions.

Step 4: Define the population.

Step 5: Define the sampling unit.


I: Plan the SampleI: Plan the Sample

Step 7: Specify acceptable risk of assessing control risk too low.

Step 8: Estimate the population exception rate.

Step 9: Determine the initial sample size.

Step 6: Specify the tolerable exception rate.


II: Select the Sample and Perform II: Select the Sample and Perform the Audit Proceduresthe Audit Procedures

Step 10: Select the sample.

Step 11: Perform the audit procedures.


III: Evaluate the ResultsIII: Evaluate the Results

Step 12: Generalize from the sample to the population.

Step 13: Analyze exceptions.

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:Need to issue a separate report on internal control

over financial reporting for public companiesNature, extent, and timing of substantive testsQuality of evidence available for tests of controls

Factor

Lowest assessed control risk Moderate assessed control risk Higher assessed control risk 100% assessed control risk

Judgment ARACR of low ARACR of medium ARACR of high ARACR not applicable

Guideline


Guidelines for ARACR and TER Guidelines for ARACR and TER Tests of ControlTests of Control

Significance of the transactions and relatedaccount balances that the internalcontrols are intended to affect

Factor

Highly significant balances Significant balances Less significant balances

Judgment TER of 4% TER of 5% TER of 6%

Guideline


Guidelines for ARACR and TER Guidelines for ARACR and TER Tests of TransactionsTests of Transactions

Results of understandinginternal control andtests of controls

Planned reduction insubstantive tests ofdetails of balances

Large

Moderate

Small

ExcellentGoodNot good



ARACR forsubstantive tests of transactionsHighMediumLow

HighMediumMedium-low

HighMedium-highMedium


Guidelines for ARACR and TER Guidelines for ARACR and TER Tests of Transactions Tests of Transactions (cont’d)(cont’d)

Planned reduction insubstantive tests ofdetails of balances

TER for substantivetests of transactions

Percent or amountbased on materialityconsiderations



Large

Moderate

Small


Effect on Sample Size of Effect on Sample Size of Changing FactorsChanging Factors

Effect on initialType of change sample size

Increase acceptable risk ofassessing control risk too low Decrease

Increase tolerable risk rate Decrease

Increase estimated populationexception rate Increase

Increase population size Increase (minor)


Actions When Population isActions When Population isNot AcceptableNot Acceptable

Revise TER or ARACR

Expand the sample size

Revise assessed control risk

Communicate with the auditcommittee or management


Summary of Audit Sampling StepsSummary of Audit Sampling Steps

Plan the sample(Steps 1-9)

Select the sample(Step 10)

Perform the tests(Step 11)

Evaluate the results(Steps 12-14)

Number ofexceptionsin sampleand actual

sample size

To Step 12To Step 14

From

Step

12

Com

pare

To/From Step 6

Computedupper

exceptionrate



Define and describe attributesDefine and describe attributessampling and a samplingsampling and a samplingdistribution.distribution.


Statistical Audit SamplingStatistical Audit Sampling

The statistical sampling method mostcommonly used for tests of controlsand substantive tests of transactionsis attributes sampling.


Sampling DistributionSampling Distribution

It is a frequency distribution of the resultsof all possible samples of a specified sizethat could be obtained from a populationcontaining some specific parameters.

Attributes sampling is based on thebinomial distribution.



Use attributes sampling in testsUse attributes sampling in testsof controls and substantiveof controls and substantivetests of transactions.tests of transactions.


Application of Attributes Application of Attributes SamplingSampling

ii. Locate the TER on the top of the table

iii. Locate the EPER in the far left column

i. Select the table corresponding to the ARACR

iv. Read down the appropriate TER column untilit intersects with the appropriate EPER rowin order to get the initial sample size

Use of the tables:



Population size is a minor considerationin determining sample size

Representativeness is ensured by the sampleselection process more than by sample size

Effect of population size:



Select the sample

Perform the audit procedures

Evaluate the results

©2010 Prentice Hall Business Publishing, ©2010 Prentice Hall Business Publishing, Auditing 13/e,Auditing 13/e, Arens//Elder/Beasley Arens//Elder/Beasley 15 - 43

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Audit Sampling for Tests of Controls and Substantive Tests of Transactions

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