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Audit Sampling for Tests ofControls and Substantive

Tests of Transactions

Chapter 14

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Learning Objective 1

Explain the concept of

representative sampling.

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Representative Samples

A representative sample is one in whichthe characteristics in the sample of auditinterest are approximately the same as

those of the population.

Nonsampling risk is the risk thataudit tests do not uncover existing

exceptions in the sample.

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Representative Samples

Sampling risk is the risk that an auditor reachesan incorrect conclusion because the sample is

not representative of the population.

Sampling risk is an inherent part of sampling thatresults from testing less than the entire population.

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Learning Objective 2

Distinguish between statistical

and nonstatistical sampling

and between probabilistic and

nonprobabilistic sample selection.

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Statistical VersusNonstatistical Sampling

Step 1 Plan the sample.

Step 2Select the sample

and perform the tests.

Step 3 Evaluate the results.

SimilaritiesSimilarities

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Statistical VersusNonstatistical Sampling

Statistical sampling allows the quantification ofsampling risk in planning the sample (Step 1)

and evaluating the results (Step 3).

In nonstatistical sampling those items that theauditor believes will provide the most useful

information are selected.

DifferencesDifferences

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Sample Selection Methods

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

NonprobabilisticNonprobabilistic

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Sample Selection Methods

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

ProbabilisticProbabilistic

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Nonprobabilistic SampleSelection Methods

Item selection based on auditor judgmental criteria

Items most likely to contain misstatements

Items containing selected population characteristics

Large dollar coverage

Directed Sample SelectionDirected Sample Selection

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Nonprobabilistic SampleSelection Methods

Selection of several items in sequence

Items most likely to contain misstatements

Block Sample SelectionBlock Sample Selection

Haphazard Sample SelectionHaphazard Sample Selection

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Learning Objective 3

Select representative samples.

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Probabilistic SampleSelection Methods

Simple Random Sample SelectionSimple Random Sample Selection

Every possible combination of elementsin the population has an equal chance

of constituting the sample.

Computer generation of random numbers

Random number tables

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Probabilistic SampleSelection Methods

Systematic Sample SelectionSystematic Sample Selection

The auditor calculates an interval andthen selects the items for the sample

based on the size of the interval.

The interval is determined by dividingthe population size by the number of

sample items desired.

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Probabilistic SampleSelection Methods

Probability Proportional to SizeSample Selection

Probability Proportional to SizeSample Selection

A sample is taken where the probabilityof selecting any individual population item

is proportional to its recorded amount (PPS).

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Probabilistic SampleSelection Methods

Stratified Sample SelectionStratified Sample Selection

The population is divided into subpopulationsby size and larger samples are taken of the

larger subpopulations.

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Learning Objective 4

Define and describe audit

sampling for exception rates.

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Sampling forException Rates

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

of population items.

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Sampling forException Rates

Following are types of exceptions inpopulations of accounting data:

– deviations from client’s established controls

– monetary misstatements in populationsof transaction data

– monetary misstatements in populationsof account balance details

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Learning Objective 5

Use nonstatistical sampling in

tests of controls and substantive

tests of transactions.

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Terms Used inAudit Sampling

Terms Related to PlanningTerms Related to Planning

Characteristic or attributeAcceptable risk of assessing control risk

too low (ARACR)Tolerable exception rate (TER)

Estimated population exception rate (EPER)Initial sample size

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Terms Used inAudit Sampling

Terms Related to Evaluating ResultsTerms Related to Evaluating Results

Exception

Sample exception rate (SER)

Computed upper exception rate (CUER)

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I: 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.

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I: Plan the Sample

Specify acceptable risk of assessingcontrol risk too low.

Estimate the population exception rate.

Determine the initial sample size.

Step 7

Step 8

Step 9

Specify the tolerable exception rate.Step 6

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II: Select the Sample and Perform the Tests

Select the sample.

Perform the audit procedures.

Step 10

Step 11

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III: Evaluate the Results

Generalize from the sampleto the population.

Analyze exceptions.

Decide the acceptability of the population.

Step 12

Step 13

Step 14

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Guidelines for ARACR and TER Tests of Control

Factor

Assessed control risk – Consider:Nature, extent, and timing of substantive testsQuality of evidence available for tests of controls

Significance of the transactions and related accountbalances that the internal controls are intended toaffect

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Guidelines for ARACR and TER Tests of Control

Judgment

• Lowest assessed control risk• Moderate assessed control risk• Higher assessed control risk• 100% assessed control risk• Highly significant balances• Significant balances• Less significant balances

Guideline

• ARACR of low• ARACR of med.• ARACR of high• ARACR is N/A• TER of 4%• TER of 5%• TER of 6%

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Guidelines for ARACR and TER Tests of Transaction

Planned Reduction in Results of UnderstandingSubstantive Tests of Internal Control andDetails of Balances Tests of Controls

Large ExcellentGoodNot good

Moderate ExcellentGoodNot good

Small ExcellentGoodNot good

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Guidelines for ARACR and TER Tests of Transaction

Planned Reduction in ARACR for TER forSubstantive Tests of Substantive Tests Substantive TestsDetails of Balances of Transactions of Transactions

Large High Percent or amount Medium based on materiality Low considerations

Moderate High Percent or amount Medium based on materiality Medium-low considerations

Small High Percent or amount Medium-high based on materiality Medium considerations

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Effect on Sample Sizeof Changing Factors

Type of Change Effect on InitialSample 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)

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Decide the Acceptabilityof the Population

Revise TER or ARACR

Expand the sample size

Revise assessment control risk

Communicate with the auditcommittee or management

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Summary of AuditSample StepsPLAN THE SAMPLE

(Steps 1-9)

SELECT THE SAMPLE(Step 10)

PERFORM THE TESTS(Step 11)

EVALUATE THE RESULTS(Steps 12-14)

Number ofexceptionsin sampleand actualsample size

To Step 12

Computerupper

exceptionrate

To Step 14

Fro

mS

tep

12

Com

par

e

To/From Step 6

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Learning Objective 6

Define and describe

attributes sampling and

a sampling distribution.

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Statistical Audit Sampling

The statistical sampling method mostcommonly used for tests of controlsand substantive tests of transactions

is attributes sampling.

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Sampling Distribution

It is a frequency distribution of the resultsof all possible samples of a specified sizethat could be obtained from a population

containing some specific parameters.

Attributes sampling is based on thebinomial distribution.

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Learning Objective 7

Use attributes sampling

in tests of controls and

substantive tests

of transactions.

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Application ofAttributes Sampling

Select the table corresponding to the ARACR.

2 Locate the TER on the top of the table.

3 Locate the EPER on the far left column.

4

1

Read down the appropriate TER column untilit intersects with the appropriate EPER row

in order to get the initial sample size.

Use of the TablesUse of the Tables

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Application ofAttributes Sampling

Population size is a minor considerationin determining sample size.

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

Effect of Population SizeEffect of Population Size

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End of Chapter 14