1. Audit Sampling for Tests of
Controls and Substantive
Tests of Transactions
Chapter 14
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2. Representative Samples
A representative sample is one in which
the characteristics in the sample of audit
interest are approximately the same as
those of the population.
Nonsampling risk is the risk that
audit tests do not uncover existing
exceptions in the sample,
resulting in nonsampling errors.
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3. Representative Samples
Sampling risk is the risk that an auditor reaches
an incorrect conclusion because the sample is
not representative of the population,
resulting in sampling error.
Sampling risk is an inherent part of sampling that
results from testing less than the entire population.
Note: A 95% confidence level = 5% sampling risk.
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4. 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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5. Statistical Versus
Nonstatistical Sampling
Similarities
Similarities
Step 1 Plan the sample.
Select the sample
Step 2
and perform the tests.
Step 3 Evaluate the results.
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6. Statistical Versus
Nonstatistical Sampling
Differences
Differences
Statistical sampling allows the quantification of
sampling risk in planning the sample (Step 1)
and evaluating the results (Step 3).
In nonstatistical sampling those items that the
auditor believes will provide the most useful
information are selected.
Conclusions are judgmental = judgmental sampling
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7. 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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8. Sample Selection Methods
Nonprobabilistic
Nonprobabilistic
1. Directed sample selection
2. Block sample selection
3. Haphazard sample selection
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9. Sample Selection Methods
Probabilistic
Probabilistic
1. Simple random sample selection
2. Systematic sample selection
3. Probability proportional to size sample selection
4. Stratified sample selection
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10. Nonprobabilistic Sample
Selection Methods
Directed Sample Selection
Directed Sample Selection
Item selection based on auditor judgmental criteria
Items most likely to contain misstatements
Items containing selected population characteristics
Large dollar coverage
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11. Nonprobabilistic Sample
Selection Methods
Block Sample Selection
Block Sample Selection
Selection of several items in sequence
forming “blocks” of items
Haphazard Sample Selection
Haphazard Sample Selection
Selection without regard to size, source, or
Distinguishing characteristics
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12. Probabilistic Sample
Selection Methods
Simple Random Sample Selection
Simple Random Sample Selection
Every possible combination of elements
in the population has an equal chance
of constituting the sample.
Random number tables
Computer generation of random numbers
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13. Probabilistic Sample
Selection Methods
Systematic Sample Selection
Systematic Sample Selection
The auditor calculates an interval and
then selects the items for the sample
based on the size of the interval.
The interval is determined by dividing
the population size by the number of
sample items desired.
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14. Probabilistic Sample
Selection Methods
Systematic Sample Selection Example
Systematic Sample Selection Example
Population of sales invoices 652 – 3151
Desired 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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15. Probabilistic Sample
Selection Methods
Probability Proportional to Size
Probability Proportional to Size
Sample Selection – for emphasis on
Sample Selection – for emphasis on
large dollar items
large dollar items
A sample is taken where the probability
of selecting any individual population item
is proportional to its recorded amount (PPS).
Evaluated using monetary unit sampling
Discussed in Chapter 16
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16. Probabilistic Sample
Selection Methods
Stratified Sample Selection
Stratified Sample Selection
For emphasis on large dollar items
For emphasis on large dollar items
The population is divided into subpopulations
by size and larger samples are taken of the
larger subpopulations.
Evaluated using variables sampling
Discussed in Chapter 16
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17. Sampling for Tests of Controls
and Substantive Tests of Transactions
Estimate the proportion (ratio) of items
in a population containing a
characteristic or attribute of interest.
The occurrence rate, or exception rate,
is the ratio of the items containing the
specific attribute to the total number
of population items.
Ex. invoices are not properly verified 3 percent of the time
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18. Sampling for
Exception Rates
Following are types of exceptions in
populations of accounting data:
– deviations from client’s established controls
– monetary misstatements in populations
of transaction data
– monetary misstatements in populations
of account balance details (requires a dollar estimate)
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19. Sampling for
Exception Rates
Exceptions versus Deviations
Difference between sample exception rate and
population exception rate is Sampling Error
Reliability of sampling error estimate is
Sampling Risk
Ex. Find a 3% sample exception rate and sampling error of 1%
With a sampling risk of 10%. We conclude that the population
Exception rate is between 2 – 4% at a 10% risk of being wrong
(or 90% chance of being right)
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20. 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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21. I: Plan the Sample
Step 6 Specify the tolerable exception rate.
Specify acceptable risk of assessing
Step 7
control risk too low.
Step 8 Estimate the population exception rate.
Step 9 Determine the initial sample size.
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22. II: Select the Sample and
Perform the Tests
Step 10 Select the sample.
Step 11 Perform the audit procedures.
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23. III: Evaluate the Results
Generalize from the sample
Step 12
to the population.
Step 13 Analyze exceptions.
Step 14 Decide the acceptability of the population.
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24. 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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25. 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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26. 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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27. Guidelines for ARACR and
TER Tests of Control
Judgment Guideline
• Lowest assessed control risk • ARACR of low
• Moderate assessed control risk • ARACR of med.
• Higher assessed control risk • ARACR of high
• 100% assessed control risk • ARACR is N/A
• Highly significant balances • TER of 4%
• Significant balances • TER of 5%
• Less significant balances • TER of 6%
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28. Effect on Sample Size
of Changing Factors
Type of Change Effect on Initial
Sample Size
Increase acceptable risk of
assessing control risk too low Decrease
Increase tolerable exception rate Decrease
Increase estimated population
exception rate Increase
Increase population size Increase (minor)
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29. 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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30. Decide the Acceptability
of the Population
Revise TER or ARACR
Expand the sample size
Revise assessment control risk
Communicate with the audit
committee or management
(good for all 3 options)
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31. Statistical Audit Sampling
The statistical sampling method most
commonly used for tests of controls
and substantive tests of transactions
is attributes sampling.
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32. Sampling Distribution
It is a frequency distribution of the results
of all possible samples of a specified size
that could be obtained from a population
containing some specific parameters.
Attributes sampling is based on the
binomial distribution.
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33. Application of
Attributes Sampling
Use of the Tables
Use of the Tables
1 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 Read down the appropriate TER column until
it intersects with the appropriate EPER row
in order to get the initial sample size.
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34. Application of
Attributes Sampling
Effect of Population Size
Effect of Population Size
Population size is a minor consideration
in determining sample size.
Representativeness is ensured by the sample
selection process more than by sample size.
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35. Application of
Attributes Sampling
Use of the Tables
Use of the Tables
1 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 Read down the appropriate exceptions column until
it intersects with the appropriate sample size row
in order to get the CUER (calculated upper exception rate).
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36. End of Chapter 14
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