Chapter 8
Audit Sampling:
An Overview and
Application to
Tests of Controls
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
LO# 1
Introduction
Auditing standards recognize and permit both statistical
and nonstatistical methods of audit sampling.
Two technological advances have reduced the number
of times auditors need to apply sampling techniques to
gather audit evidence:
1
Development of
well-controlled,
automated
accounting
systems.
2
Advent of powerful
PC audit software to
download and
examine client
data.
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LO# 1
Introduction
However, technology will never eliminate the need for
auditors to rely on sampling to some degree because:
1. Many control processes require human involvement.
2. Many testing procedures require the auditor to
physically examine an asset.
3. In many cases auditors are required to obtain and
evaluate evidence from third parties.
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LO# 1
and 2
Definitions and Key Concepts
On the following slides we will define:
1. Audit Sampling.
2. Sampling Risk.
3. Confidence Level.
4. Tolerable and Expected Error.
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LO# 1
Audit Sampling
The selection and evaluation of less than 100
percent of the items in a population of audit
relevance selected in such a way that the
auditor expects the sample to be
representative of the population and thus
likely to provide a reasonable basis for
conclusions about the population.
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LO# 2
Sampling Risk
Sampling risk is the element of uncertainty that enters
into the auditor’s conclusions anytime sampling is
used. There are two types of sampling risk.
Risk of incorrect rejection (Type I) – in a test of internal
controls, it is the risk that the sample supports a conclusion that the
control is not operating effectively when, in fact, it is operating effectively.
In substantive testing, it is the risk that the sample indicates that the
recorded balance is materially misstated when, in fact, it is not.
Risk of incorrect acceptance (Type II) – in a test of internal
controls, it is the risk that the sample supports a conclusion that the
control is operating effectively when, in fact, it is not operating effectively.
In substantive testing, it is the risk that the sample supports the recorded
balance when it is, in fact, materially misstated.
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LO# 2
Sampling Risk
Three Important Factors in Determining Sample Size
1.The desired level of assurance in the results
(or confidence level),
2.Acceptable defect rate (or tolerable error), and
3.The historical defect rate (or expected error).
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LO# 2
Confidence Level
Confidence level is the
complement of sampling risk.
The auditor may set
sampling risk for a
particular sampling
application at
5 percent, which
results in a
confidence level of
95 percent.
8-8
LO# 2
Tolerable and Expected Error
Once the desired confidence level is established, the
sample size is determined largely by how much the
tolerable error exceeds expected error.
Precision, at the
planning stage of
audit sampling, is
the difference
between the
expected and
tolerable deviation
rates.
Auditing Standards
refer to Precision
as the “Allowance for
sampling risk.”
8-9
LO# 3
Audit Evidence – To Sample or
Not?
Relationship between Evidence Types and Audit Sampling
Audit Sampling
Commonly Used
Type of Evidence
Yes
Inspection of tangible assets
Yes
Inspection of records or documents
Yes
Reperformance
Yes
Recalculation
Yes
Confirmation
No
Analytical procedures
No
Scanning
No
Inquiry
No
Observation
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LO# 3
Audit Evidence – To Sample or
Not?
• Inspection of tangible assets. Auditors typically attend
the client’s year-end inventory count. When there are a
large number of items in inventory, the auditor will select a
sample to physically inspect and count.
• Inspection of records or documents. Certain controls
may require the matching of documents. The procedure
may take place many times a day. The auditor may gather
evidence on the effectiveness of the control by testing a
sample of the document packages.
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LO# 3
Audit Evidence – To Sample or
Not?
 Reperformance. To comply with PCAOB standards,
publicly traded clients must document and test controls
over important assertions for significant accounts. The
auditor may reperform a sample of the tests performed by
the client.
 Confirmation. Rather than confirm all customer account
receivable balances, the auditor may select a sample of
customers.
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LO# 3
Testing All Items with a Particular
Characteristic
When an account or class of transactions is made up
of a few large items, the auditor may examine all the
items in the account or class of transaction.
When a small number of large transactions make up
a relatively large percent of an account or class of
transactions, auditors will typically test all the
transactions greater than a particular dollar amount.
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LO# 3
Testing Only One or a Few
Items
Highly automated information systems
process transactions consistently unless the
system or programs are changed.
The auditor may test the
general controls over the
system and any program
changes, but test only a few
transactions processed by
the IT system.
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LO# 4
Types of Audit Sampling
Auditing standards recognize and permit both statistical
and nonstatistical methods of audit sampling.
In nonstatistical (or
judgmental) sampling, the
auditor does not use
statistical techniques to
determine sample size,
select the sample items,
or measure sampling risk.
Statistical sampling uses
the laws of probability to
compute sample size and
evaluate results. The
auditor is able to use the
most efficient sample size
and quantify sampling risk.
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LO# 4
Types of Audit Sampling
Advantages of statistical sampling:
1. Design an efficient sample.
2. Measure the sufficiency of
evidence obtained.
3. Quantify sampling risk.
Disadvantages of statistical sampling:
1. Training auditors in proper use.
2. Time to design and conduct
sampling application.
3. Lack of consistent application
across audit teams.
8-16
LO# 4
Statistical Sampling Techniques
1. Attribute Sampling.
2. Monetary-Unit Sampling.
3. Classical Variables Sampling.
8-17
LO# 4
Attribute Sampling
Used to estimate the proportion of a
population that possess a specified
characteristic. The most common use of
attribute sampling is for tests of controls.
Yes, I know. We are
planning a test of that
control using
attribute sampling.
Our client’s controls
require that all checks
have two independent
signatures.
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LO# 4
Monetary-Unit Sampling
Monetary-unit sampling uses attribute sampling theory
to estimate the dollar amount of misstatement for a
class of transactions or an account balance.
This technique is used
extensively because it has
a number of advantages
over classical variables
sampling.
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LO# 4
Classical Variables Sampling
Auditors sometimes use variables sampling to
estimate the dollar value of a class of transactions or
account balance. It is more frequently used to
determine whether an account is materially
misstated.
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LO#
Attribute Sampling Applied to
Tests of Controls
5, 6, & 7
In conducting a statistical sample for a
test of controls, auditing standards
require the auditor to properly plan,
perform, and evaluate the sampling
application and to adequately document
each phase of the sampling application.
Plan
Perform
Evaluate
Document
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LO#
5, 6, & 7
Planning
Planning
1. Determine the test objectives.
2. Define the population characteristics:
• Define the sampling population.
• Define the sampling unit.
• Define the control deviation conditions.
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable deviation rate.
• The expected population deviation rate.
The objective of attribute sampling when used for
tests of controls is to evaluate the operating
effectiveness of the internal control.
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LO#
5, 6, & 7
Planning
Planning
2. Define the population characteristics:
• Define the sampling population.
• Define the sampling unit.
• Define the control deviation conditions.
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable deviation rate.
• The expected population deviation rate.
All of the items that constitute the class of
transactions make up the sampling population.
8-23
LO#
5, 6, & 7
Planning
Planning
2. Define the population characteristics:
• Define the sampling population.
• Define the sampling unit.
• Define the control deviation conditions.
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable deviation rate.
• The expected population deviation rate.
Each sampling unit makes up one item in the
population. The sampling unit should be defined in
relation to the specific control being tested.
8-24
LO#
5, 6, & 7
Planning
Planning
2. Define the population characteristics:
• Define the sampling population.
• Define the sampling unit.
• Define the control deviation conditions.
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable deviation rate.
• The expected population deviation rate.
A deviation is a departure from adequate
performance of the internal control.
8-25
LO#
5, 6, & 7
Planning
Planning
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable deviation rate.
• The expected population deviation rate.
The confidence level is the desired level of
assurance that the sample results will support a
conclusion that the control is functioning
effectively. Generally, when the auditor has
decided to rely on controls, the confidence level
is set at 90% or 95%. This means the auditor is
willing to accept a 10% or 5% risk of accepting
the control as effective when it is not.
8-26
LO#
5, 6, & 7
Planning
Planning
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable deviation rate.
• The expected population deviation rate.
The tolerable deviation rate is the maximum deviation
rate from a prescribed control that the auditor is willing to
accept and still consider the control effective.
Example Suggested Tolerable Deviation Rates:
Assessed Improtance of a
Control
Highly important
Moderately important
Tolerable
Deviation
Rate
3–5%
6–10%
8-27
LO#
5, 6, & 7
Planning
Planning
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable deviation rate.
• The expected population deviation rate.
The expected population deviation rate is
the rate the auditor expects to exist in the
population. The larger the expected
population deviation rate, the larger the
sample size must be, all else equal.
EXAMPLE: Assume a
desired confidence level of
95%, and a large
population, the effect of the
expected population
deviation rate on sample
size is shown right:
Expected Population
Deviation Rate
Sample
Size
1.0%
93
1.5%
124
2.0%
181
3.0%
‡
‡ Sam ple size too large to be cost-effective.
8-28
LO#
Population Size: Attributes
Sampling
5, 6, & 7
Population size is not an important factor in determining
sample size for attributes sampling. The population size
has little or no effect on the sample size, unless the
population is relatively small, say less than 500 items.
Factor
Desired confidence level
Tolerable deviation rate
Expected population deviation rate
Population size
Examples
Relationship to
Change in
Effect on
Sample Size
Factor
Sample Size
Lower
Decrease
Direct
Higher
Increase
Lower
Increase
Inverse
Higher
Decrease
Lower
Decrease
Direct
Higher
Increase
Decreases sample size only when population
is small (fewer than 500 items)
8-29
LO#
5, 6, & 7
Performance
Performance and Evaluation
4. Select sample items:
• Random-Number Selection.
• Systematic Selection.
5. Perform the Audit Procedures:
• Voided documents.
• Unused or inapplicable documents.
• Inability to examine a sample item.
• Stopping the test before completion.
6. Calculate the Sample Deviation and Upper Deviation Rates.
7. Draw Final Conclusions.
Every item in the population has the same
probability of being selected as every other
sampling unit in the population.
8-30
LO#
5, 6, & 7
Performance
Performance and Evaluation
4. Select sample items:
• Random-Number Selection.
• Systematic Selection.
5. Perform the Audit Procedures:
• Voided documents.
• Unused or inapplicable documents.
• Inability to examine a sample item.
• Stopping the test before completion.
6. Calculate the Sample Deviation and Upper Deviation Rates.
7. Draw Final Conclusions.
The auditor determines the sampling interval by dividing
the population by the sample size. A starting number is
randomly selected in the first interval and every nth item is
8-31
selected thereafter.
LO#
5, 6, & 7
Performance
Performance and Evaluation
5. Perform the Audit Procedures:
• Voided documents.
• Unused or inapplicable documents.
• Inability to examine a sample item.
• Stopping the test before completion.
6. Calculate the Sample Deviation and Upper Deviation Rates.
7. Draw Final Conclusions.
For example, assume a sales invoice should not be
prepared unless there is a related shipping document. If
the shipping document is present, there is evidence the
control is working properly. If the shipping document is not
present, a control deviation exists.
8-32
LO#
5, 6, & 7
Performance
Performance and Evaluation
5. Perform the Audit Procedures:
• Voided documents.
• Unused or inapplicable documents.
• Inability to examine a sample item.
• Stopping the test before completion.
6. Calculate the Sample Deviation and Upper Deviation Rates.
7. Draw Final Conclusions.
Unless the auditor finds something unusual about
either of these items, they should be replaced with a
new sample item.
8-33
LO#
5, 6, & 7
Performance
Performance and Evaluation
5. Perform the Audit Procedures:
• Voided documents.
• Unused or inapplicable documents.
• Inability to examine a sample item.
• Stopping the test before completion.
6. Calculate the Sample Deviation and Upper Deviation Rates.
7. Draw Final Conclusions.
If the auditor is unable to examine a document or to
use an alternative procedure to test the control, the
sample item is a deviation for purposes of evaluating
the sample results.
8-34
LO#
5, 6, & 7
Performance
Performance and Evaluation
5. Perform the Audit Procedures:
• Voided documents.
• Unused or inapplicable documents.
• Inability to examine a sample item.
• Stopping the test before completion.
6. Calculate the Sample Deviation and Upper Deviation Rates.
7. Draw Final Conclusions.
If a large number of deviations are detected
early in the tests of controls, the auditor should
consider stopping the test, as soon as it is clear
that the results of the test will not support the
planned assessed level of control risk.
8-35
LO#
5, 6, & 7
Evaluation
Evaluation
6. Calculate the Sample Deviation and Upper Deviation Rates.
7. Draw Final Conclusions.
After completing the audit procedures, the
auditor summarizes the deviations for each
control tested and evaluates the results. For
example, if the auditor discovered two
deviations in a sample of 50, the deviation rate
in the sample would be 4% (2 ÷ 50).
The upper deviation rate is the sum of the
sample deviation rate and an appropriate
allowance for sampling risk.
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LO#
5, 6, & 7
Evaluation
Evaluation
6. Calculate the Sample Deviation and Upper Deviation Rates.
7. Draw Final Conclusions.
The auditor compares the tolerable deviation rate
to the computed upper deviation rate.
True State of Internal Control
Auditor's Decision Based on
Sample Evidence
Supports the planned level
of control risk
Does not support the
planned level of control risk
Reliable
Correct decision
Risk of incorrect
rejection (Type I)
Not Reliable
Risk of incorrect
acceptance (Type II)
Correct decision
8-37
LO#
5, 6, & 7
Attribute Sampling Example
The auditor has decided to test a control at Calabro
Wireless Services. The test is to determine that the sales
and service contracts are properly authorized for credit
approval. A deviation in this test is defined as the failure of
the credit department personnel to follow proper credit
approval procedures for new and existing customers. Here
is information relating to the test:
Desired confidence level
Tolerable deviation rate
Expected population deviation rate
Sample size
95%
6%
1%
78
8-38
LO#
5, 6, & 7
Attribute Sampling Example
Part of the table used to determine sample size when
the auditor specifies a 95% desired confidence level.
If there are 125,000 items in the population numbered
from 1 to 125,000, the auditor can use Excel to generate
random selections from the population for testing.
8-39
LO#
5, 6, & 7
Attribute Sampling Example
The auditor examines each selected contract for credit
approval and determines the following:
Number of deviations
Sample size
Sample deviation rate
Computed upper deviation rate
Tolerable deviation rate
2
78
2.6%
8.2%
6.0%
Let’s see how we get the computed
upper deviation rate.
8-40
LO#
5, 6, & 7
Attribute Sampling Example
Part of the table used to determine the computed upper
deviation rate at 95% desired confidence level:
Sample
Size
25
30
35
40
45
50
55
60
65
70
75
80
Actual Number of Deviations Found
0
1
2
3
11.3
17.6
9.5
14.9
19.6
8.3
12.9
17.0
7.3
11.4
15.0
18.3
6.5
10.2
13.4
16.4
5.9
9.2
12.1
14.8
5.4
8.4
11.1
13.5
4.9
7.7
10.2
12.5
4.6
7.1
9.4
11.5
4.2
6.6
8.8
10.8
4.0
6.2
8.2
10.1
3.7
5.8
7.7
9.5
8-41
LO#
5, 6, & 7
Attribute Sampling Example
Tolerable
Deviation
Rate (6%)
<
Computed
Upper Deviation
Rate (8.2%)
Auditor’s Decision:
Does not support reliance on the control.
8-42
LO# 8
Nonstatistical Sampling for Tests of
Controls
Determining the Sample Size
An auditing firm may establish a nonstatistical sampling
policy like the one below:
Desired
Level of
Controls
Reliance
Low
Moderate
High
Sample
Size
15–20
25–35
40–60
Such a policy will promote consistency in sampling
applications.
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LO# 8
Nonstatistical Sampling for
Tests of Controls
Selecting the Sample Items
Nonstatistical sampling allows the use of
random or systematic selection, but also
permits the use of other methods such as
haphazard sampling.
When haphazard sample
selection is used, sampling
units are selected without any
bias, that is to say, without a
special reason for including
or omitting the item in the
sample.
8-44
LO# 8
Nonstatistical Sampling for
Tests of Controls
Calculating the Upper Deviation Rate
With a nonstatistical sample, the auditor can
calculate the sample deviation rate, but cannot
mathematically quantify the computed upper
deviation rate and sampling risk associated
with the test.
8-45
LO# 8
Control Tests for Low Control
Frequency
The sample size tables in the chapter assume a large
population. Sample size can be adjusted using the
“finite correction factor” in the Advanced Module or by
using the table below for very small populations
(control performed less frequently):
Control Frequency
and Population Size
Sample Size
Quarterly (4)
2
Monthly (12)
2-4
Semimonthly (24)
3-8
Weekly (52)
5-9
8-46
LO# 8
Terminology Comparison for
Attribute Sampling
ACL versus Sampling Tables
8-47