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Chapter 9
Audit Sampling:
An Application to
Substantive Tests
of Account
Balances
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
LO# 1
Substantive Tests of Details of
Account Balances
The statistical concepts we discussed in the last
chapter apply to this chapter as well. Three important
determinants of sample size are
1. Desired confidence level.
2. Tolerable misstatement.
3. Estimated misstatement.
Population plays a bigger role in some of the sampling
techniques used for substantive testing.
Misstatements discovered in the audit sample must be
projected to the population, and there must be an
allowance for sampling risk.
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LO# 2
Monetary-Unit Sampling (MUS)
MUS uses attribute-sampling theory to express a
conclusion in dollar amounts rather than as a rate of
occurrence. It is commonly used by auditors to test
accounts such as accounts receivable, loans receivable,
investment securities, and inventory.
MUS uses attribute-sampling theory (used primarily to
test controls) to estimate the percentage of monetary
units in a population that might be misstated and then
multiplies this percentage by an estimate of how much
the dollars are misstated.
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LO# 2
Monetary-Unit Sampling (MUS)
Advantages
1. When the auditor expects no
misstatement, MUS usually
results in a smaller sample
size than classical variables
sampling.
2. When applied using the
probability-proportional-to-size
procedure, MUS automatically
results in a stratified sample.
3. MUS does not require the
user to make assumptions
about the distribution of
misstatements.
Disadvantages
1. The selection of zero or
negative balances generally
requires special design
consideration.
2. The general approach to MUS
assumes that the audited
amount of the sample item is
not in error by more than
100%.
3. When more than one or two
misstatements are detected,
the sample results calculations
may overstate the allowance
for sampling risk.
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LO# 2
Steps in MUS
Steps in MUS Application
Planning
1. Determine the test objectives.
2. Define the population characteristics:
• Define the population.
• Define the sampling unit.
• Define a misstatement.
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable misstatement.
• The expected population misstatement.
• Population size.
Performance
4. Select sample items.
5. Perform the auditing procedures.
• Understand and analyze any misstatements observed.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
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LO# 3
Steps in MUS
If the upper misstatement limit is greater than the
tolerable misstatement, the auditor concludes that the
account balance is materially misstated.
When faced with this situation, the auditor may:
1. Increase the sample size.
2. Perform other substantive procedures.
3. Request the client adjust the accounts receivable balance.
4. If the client refuses to adjust the account balance, the
auditor would consider issuing a qualified or an adverse
opinion.
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LO# 3
Risk When Evaluating Account
Balances
True State of Financial Statement Account
Auditor's Decision Based
on Sample Evidence
Supports the fairness of
the account balance
Does not support the
fairness of the account
balance
Not Materially Misstated
Correct decision
Risk of incorrect
rejection (Type I)
Materially Misstated
Risk of incorrect
acceptance (Type II)
Correct Decision
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LO# 4
Nonstatistical Sampling for Tests
of Account Balances
The sampling unit for nonstatistical sampling is normally a
customer account, an individual transaction, or a line item
on a transaction. When using nonstatistical sampling, the
following items must be considered:
o Identifying individually significant items.
o Determining the sample size.
o Selecting sample items.
o Calculating the sample results.
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LO# 4
Why Did Statistical Sampling
Fall Out Of Favor?
1.Firms found that some auditors were
over relying on statistical sampling
techniques to the exclusion of good
judgment.
2.There appears to be poor
linkage between the applied audit
setting and traditional statistical
sampling applications.
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LO# 5
Classical Variable Sampling
Classical variables sampling uses normal distribution
theory to evaluate the characteristics of a population
based on sample data. Auditors most commonly use
classical variables sampling to estimate the size of
misstatement.
Sampling distributions are formed by plotting the
projected misstatements yielded by an infinite
number of audit samples of the same size taken
from the same underlying population.
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LO# 5
Classical Variables Sampling
A sampling
distribution is useful
because it allows us
to estimate the
probability of
observing any single
sample result.
In classical variables
sampling, the sample
mean is the best
estimate of the
population mean.
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LO# 5
Classical Variables Sampling
Advantages
1. When the auditor expects a
relatively large number of
differences between book and
audited values, this method will
normally result in smaller
sample size than MUS.
2. The techniques are effective for
both overstatements and
understatements.
3. The selection of zero balances
generally does not require
special sample design
considerations.
Disadvantages
1. Does not work well when little or no
misstatement is expected in the
population.
2. To determine sample size, the
auditor must estimate the standard
deviation of the audit differences.
3. If few misstatements are detected
in the sample data, the true
variance tends to be
underestimated, and the resulting
projection of the misstatements and
the related confidence limits are not
likely to be reliable.
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LO# 6
Applying Classical Variables
Sampling
Defining the Sampling Unit
The sampling unit can be a customer account,
an individual transaction, or a line item. In
auditing accounts receivable, the auditor can
define the sampling unit to be a customer’s
account balance or an individual sales invoice
included in the account balance.
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LO# 6
Applying Classical Variables
Sampling
Determining the Sample Size
Population size (in sampling units) × CC × SD
Sample
=
Tolerable misstatement – Estimated misstatement
Size
where
CC = Confidence coefficient
SD = Estimated standard deviation
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2
LO# 6
Applying Classical Variables
Sampling
Project the error
and the SD:
Mean
Total audit difference
misstatement
=
Sample size
per sampling
item
Projected
population = Population size × Mean misstatement
(in sampling units)
per sampling item
misstatement
SD =
Total audit
–
differences squared
Sample
Mean difference
×
Size
per sampling item2
Sample size – 1
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LO# 6
Applying Classical Variables
Sampling
SD
Confidence
Population
=
× CC ×
bound
size
Confidence
=
interval
Projected
misstatement
Sample size
±
Confidence
bound
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LO# 6
Applying Classical Variables
Sampling
Lower
limit
($1,653)
($50,000)
Projected
misstatement
$14,575
$0
Upper
limit
$30,803
$50,000
Tolerable Misstatement
If both limits are within the bounds of tolerable
misstatement, the evidence supports the conclusion
that the account is not materially misstated.
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End of Chapter 9
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