Audit Sampling for Tests of
Controls and Substantive
Tests of Transactions
Chapter 15
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Learning Objective 1
Explain the concept of
representative (probabilistic)
sampling.
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What does this have to do with
representative sampling and sampling risk?
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Representative Samples
A representative sample (probabilistic)
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. Competence,
Budget, Boredom, Power-ticking.
Matching task to worker, realistic budgets, review.
Modesto,
CA, students, and a media hungry Professor
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Representative Samples
Sampling risk is the risk that an auditor reaches
an incorrect conclusion for population because the
sample is not representative of the population.
Sampling risk is an inherent part of sampling that
results from testing less than the entire population.
How to reduce/measure? Increase sample size /
appropriate (statistical) sampling methods
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Learning Objective 2
Distinguish between statistical
and nonstatistical sampling (n?)
and between probabilistic and
nonprobabilistic sample selection
(which n?).
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Statistical Versus
Nonstatistical Sampling
Similarities
Plan the sample: obj., attributes,
exception, population, sampling
Step 1
unit, stat or non-stat to get n.
Select the sample: (prob or non-prob?)
Step 2
and perform the tests.
Step 3
Evaluate the results: SER
generalize to pop., more
sampling?
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Statistical Versus
Nonstatistical Sampling
Differences
Statistical sampling allows the quantification of
sampling risk (ARACR) in planning the sample
(Step 1) and evaluating the results (Step 3). Plus
must use Probabilistic sampling methods
In nonstatistical sampling
Sampling risk is not quantified. More discretion
with sampling, more judgmental. Can use either
Prob. or non. Prob. Why use??
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Sample Selection Methods
Nonprobabilistic/nonrepresentative
1. Directed sample selection
2. Haphazard sample selection
Only use w/ nonstat. sampling
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Sample Selection Methods
Probabilistic/representative
1. Simple random sample selection
2. Systematic sample selection
3. Probability proportional to size sample selection
Use with either stat. or nonstat. sampling.
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Nonprobabilistic Sample
Selection Methods
Directed Sample Selection
Item selection based on auditor judgmental criteria
Items most likely to contain misstatements: risk-based
Items containing selected population characteristics:
5 shipping docs from each month or
30% of sample from one division
Large dollar coverage
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Nonprobabilistic Sample
Selection Methods
Haphazard Sample Selection
Auditor randomly selects sample items.
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Learning Objective 3
Select representative samples.
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Probabilistic Sample
Selection Methods – see handout
Simple Random Sample Selection
Every possible combination of elements
in the population has an equal chance
of constituting the sample.
Computer generation of random numbers
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Probabilistic Sample
Selection Methods
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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Probabilistic Sample
Selection Methods
Probability Proportional to Size
Sample Selection
A sample is taken where the probability
of selecting any individual population item
is proportional to its recorded amount.
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Learning Objective 4
Define and describe audit
sampling for exception rates.
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Sampling for
Exception Rates
The exception rate is the ratio of
the items NOT containing the
specific attribute to the total number
of population items (e.g. invoice data not
traced to shipping doc. (ToT-occurrence)),
daily batch total of qty shipped
NOT compared with qty
billed (I/C-occurrence)).
SER: 3 exceptions / 100 sample = 3%
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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 – no shipping doc for
invoice
– monetary misstatements in populations
of
account
balance
details
–
A/R
not
confirmed
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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 in
Audit Sampling
Terms Related to Planning: Table 15-1 p. 485
Characteristic or attribute (test)
Acceptable risk of assessing control risk too low
or accept ToT results (ARACR) = sampling risk!
Tolerable exception rate (TER)
Estimated population exception rate (EPER)
Initial sample size: determined by all 3 above
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Terms Used in
Audit Sampling
Terms Related to Evaluating Results
Exception
Sample exception rate (SER)
Computed upper exception rate (CUER)
Mathematically incorporates (adds) sampling
risk or ARACR to SER (only related to stat. sampling)
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I: Plan the Sample - Fig 15-2 p.
490
State the objectives of the audit test –
Step 1 Ex. ToT accuracy – Attribute 5.
Step 2 Decide whether audit sampling applies.
Step 3 Define attributes and exception conditions.
Ex. Table 15-3 p. 492, attribute 5.
Step 4 Define the population– all sales invoices in year
Step 5 Define the sampling unit – sales invoice
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I: Plan the Sample - Fig 15-2 p.
490
Step 6 Specify the tolerable exception rate. How?
Specify acceptable risk of assessing
Step 7
control risk too low or accepting ToT.
Key – qual. w/ non-stat. quant. w/ stat.
Step 8 Estimate the population exception rate. How?
Step 9 Determine the initial sample size – use
professional judgment, w/ statistical sampling
use tables/computers. TER-EPER =
precision

smaller
=
bigger
sample
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II: Select the Sample and
Perform the Tests
Step 10 Select the sample = prob. or non prob.
Step 11 Perform the audit procedures.
Fig 15-3 p. 498. Attribute 5:
4 ex. / 100 sample- SER = 4%
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III: Evaluate the Results-Fig 15-4
p. 496
Generalize from the sample to the population.
SER sig. < TER: CR OK, ToT provides no
Step 12 adjustment: reduce AP and detail testing.
SER≥TER: inc. CR, ToT – adj proposed
(project to pop. or isolate w/ more sampling):
do more AP/detailed tests. Too close to
call? → Conservative (not an issue w/ stat)
Step 13 Analyze exceptions – isolated or distributed?
Step 14 Decide the acceptability of the population.
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Guidelines for ARACR and
TER for Tests of Control
Factors:
Preliminary assessed control risk (lower)
– ARACR/Sampling Risk (lower)
Significance of the transactions and related account
balances that the internal controls are intended to
affect (higher) – TER (lower)
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Guidelines for ARACR and
TER for Tests of Control
Judgment
Guideline
• Lowest assessed control risk
• Moderate assessed control risk
• Higher assessed control risk
• 100% assessed control risk
• Highly significant balances
• Significant balances
• Less significant balances
• 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 of Tests of Transactions
Planned Reduction in ARACR for
TER for
Substantive Tests of Substantive Tests Substantive Tests
Details of Balances
of Transactions
of Transactions
Large
Moderate
Small
Low
Medium
High
Low
Medium
High
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Effect on Sample Size
of Changing Factors Table 15-6 p. 493
Type of Change
Effect on Initial
Sample Size
Increase ARACR
Decrease
or sampling risk (usually constant)
Increase tolerable exception rate Decrease
Increase estimated population
exception rate
Increase population size
Increase
Increase (minor)
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Decide the Acceptability
of the Population
Is SER > TER???
Revise TER or ARACR – no-no
Expand the sample size–isolate exceptions (known mist)
Revise assessment control risk, SOX 404?
ToT – book adj. and inc. AP
and detail testing
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Learning Objective 6
Define and describe
attributes (statistical) sampling and
a sampling distribution.
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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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Sampling Distribution
Attributes (statistical) sampling is based on the
binomial distribution (think 2 columns). And since
we quantify sampling risk and use
only representative samples, we can use
tables (like the normal distribution table you have
used for z or t-tests in stat classes)!
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Learning Objective 7
Use attributes sampling
in tests of controls and
substantive tests
of transactions.
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Application of
Attributes Sampling
See Fig 15-8 p. 506 – Attribute 5 where
did all this come from?
1 EPER and TER the same as non-statistical
testing – see p. 496. Still judgments!
2 We quantify sampling risk (ARACR) = 5%,
We want to be 95% confident in our conclusion.
3 How did we get initial sample size of 93? We judgmentally selected a sample size of 100 on p. 496
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Application of
Attributes Sampling
Use of the Tables – Table 15-8 (Sample Size) p . 504
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 = 93!
Get Hall
93Business
invoices
a and
REPRESENTATIVE
sample.
14 - 37
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Publishing,via
Auditing
Assurance Services 9/e, Arens/Elder/Beasley
Application of
Attributes Sampling
Back to Figure 15-8 p. 506
1 Samples rounded up to even number–not necessary!
2 # exceptions same as p. 500, SER = 4%
3 Do not compare SER to TER like p. 496, go to
Table 15-9 p. 505 to get Computed Upper
Exception Rate (CUER) – compare CUER to TER.
CUER > TER: I/C - increase CR, ToT – book
adjustment
and/or
increase
AP
and
detail
testing
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Application of
Attributes Sampling
Use of the CUER tables – Generalize
To Population – Table 15-9 p. 505
1 Use table that corresponds to your ARACR
2 Locate the SER on the top of the table.
3 Locate the Sample Size 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 CUER – we are 95% confident
PER
for no.
5andisAssurance
≤ 9.0,Services
but9/e,9.0
> TER =145!
- 39
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Hall Business
Publishing,
Auditing
Arens/Elder/Beasley
End of Chapter 15
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