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©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 1
Audit Sampling for Tests ofControls and Substantive
Tests of Transactions
Chapter 14
©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 2
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,resulting in nonsampling errors.
©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 3
Representative Samples
Sampling risk is the risk that an auditor reachesan incorrect conclusion because the sample is
not representative of the population,resulting in sampling error.
Sampling risk is an inherent part of sampling thatresults from testing less than the entire population.
Note: A 95% confidence level = 5% sampling risk.
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Representative Samples
Reducing Nonsampling Risk –Careful design of audit procedures,
Proper instruction, supervision, and review.
Reducing Sampling Risk – Adjust sample size,
Use appropriate method for selecting sample items.
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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. Conclusions are judgmental = judgmental sampling
DifferencesDifferences
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Probabilistic Versus Nonprobabilistic Sample Selection
Probabilistic Sample Selection – Selecting a sample such that each population item has a known probability of being included in the
sample and the sample is selected by a random process.
Nonprobabilistic Sample Selection – Selecting a sample in which the auditor uses professional judgment rather than probabilistic
methods to select sample items.
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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
©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 10
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 sequenceforming “blocks” of items
Selection without regard to size, source, or Distinguishing characteristics
Block Sample SelectionBlock Sample Selection
Haphazard Sample SelectionHaphazard Sample Selection
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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
Systematic Sample Selection ExampleSystematic Sample Selection Example
Population of sales invoices 652 – 3151Desired sample size = 125
Interval = (3151 – 651) / 125 = 20
Select a random start between 1 & 19 (ex. 9)First item in sample is invoice # 661 (652 + 9)
Remaining 124 items = 681 (661+20), 701 (681+20),721 (701+20) etc.
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Probabilistic SampleSelection Methods
Probability Proportional to SizeSample Selection – for emphasis on
large dollar items
Probability Proportional to SizeSample Selection – for emphasis on
large dollar items
A sample is taken where the probabilityof selecting any individual population item
is proportional to its recorded amount (PPS).
Evaluated using monetary unit samplingDiscussed in Chapter 16
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Probabilistic SampleSelection Methods
Stratified Sample SelectionFor emphasis on large dollar items
Stratified Sample SelectionFor emphasis on large dollar items
The population is divided into subpopulationsby size and larger samples are taken of the
larger subpopulations.
Evaluated using variables samplingDiscussed in Chapter 16
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Sampling for Tests of Controlsand Substantive Tests of Transactions
The occurrence rate, or exception rate,is the ratio of the items containing thespecific attribute to the total number
of population items.Ex. invoices are not properly verified 3 percent of the time
Estimate the proportion (ratio) of itemsin a population containing a
characteristic or attribute of interest.
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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 (requires a dollar estimate)
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Sampling forException Rates
Exceptions versus Deviations
Difference between sample exception rate andpopulation exception rate is Sampling Error
Reliability of sampling error estimate isSampling Risk
Ex. Find a 3% sample exception rate and sampling error of 1%With a sampling risk of 10%. We conclude that the populationException rate is between 2 – 4% at a 10% risk of being wrong
(or 90% chance of being right)
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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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Plan the Sample: TER, ARACR, EPER
TER = Tolerable Exception Rate The exception rate that the auditor will permit in the
population and still be willing to use the assessed control risk (CR) and/or amount of monetary misstatements in the transactions (tolerable materiality).
Result of auditor judgment; affected by materiality. What amount of exceptions is material to reject a control? More controls operating for an audit objective results in
higher TER. High TER => low sample size; low TER => high sample size
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Plan the Sample:TER, ARACR, EPER
ARACR = Acceptable Risk of Assessing Control Risk too low The risk the auditor is willing to take of accepting a control
as effective (or monetary amount as tolerable) when the true population exception rate is greater than TER.
ARACR = measure of sampling risk The lower the assessed control risk => the lower the
ARACR => the fewer tests of detailed balances.
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Plan the Sample:TER, ARACR, EPER
EPER = Expected Population Error Rate A judgmental estimate based on knowledge of client. Used to determine appropriate sample size. Low EPER => low sample size As EPER approaches TER, more precision is needed and
larger sample size is needed.
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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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Effect on Sample Sizeof Changing Factors
Type of Change Effect on InitialSample Size
Increase acceptable risk ofassessing control risk too low Decrease
Increase tolerable exception rate Decrease
Increase estimated populationexception rate Increase
Increase population size Increase (minor)
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Generalize Sample to Population
SER = Sample exception rate = exceptions/sample size
Subtract SER from TER = sampling error If sampling error is sufficiently large, then true
population exception rate is acceptable.
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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
(good for all 3 options)
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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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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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Application ofAttributes Sampling
Select the table corresponding to the ARACR.
2 Locate the actual number of exceptions on the top of the table.
3 Locate the sample size on the far left column.
4
1
Read down the appropriate exceptions column untilit intersects with the appropriate sample size row
in order to get the CUER (calculated upper exception rate).
Use of the TablesUse of the Tables
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End of Chapter 14