17-Audit-Sampling-for-Tests-of-Details-of-Balances.pdf

Auditing and Assurance Services
Seventeenth Edition
Chapter 17
Audit Sampling for Tests of
Details of Balances
Copyright © 2020, 2017, 2014 by Pearson Education, Inc. All Rights Reserved

Learning Objectives
17.1 Differentiate audit sampling for tests of details of
balances and for tests of controls and substantive
tests of transactions
17.2 Apply nonstatistical sampling to tests of details of
balances
17.3 Apply monetary unit sampling
17.4 Describe variables sampling
17.5 Use difference estimation in tests of details of
balances

Learning Objective 17.1
Differentiate audit sampling for tests of details of balances
and for tests of controls and substantive tests of
transactions

Comparisons of Audit Sampling for Tests of
Details of Balances and for Tests of Controls
and Substantive Tests of Transactions (1 of 3)
• Auditor wants to make inferences about the entire
population based on a sample
• Both sampling and nonsampling risks are therefore
important for tests of controls, substantive tests of
transactions, and tests of details of balances
• To address sampling risk, auditors can use either
nonstatistical or statistical methods for all three types of
tests

• The main differences among tests of controls, substantive
tests of transactions, and tests of details of balances are
in what the auditor wants to measure
Type of Test What It Measures
Tests of controls • The operating effectiveness of internal controls
Substantive tests of
transactions
• The operating effectiveness of internal controls
• The monetary correctness of transactions in the
accounting system
Tests of details of
balances
• Whether the dollar amounts of account balances are
materially misstated

• Auditors perform tests of controls and substantive
tests of transactions to:
– Determine whether the exception rate in the population
is sufficiently low
– Reduce assessed control risk and thereby reduce
tests of details of balances
– Conclude that the control is operating effectively for
purposes of auditing internal control over financial
reporting for larger public companies

Apply nonstatistical sampling to tests of details of
balances

Nonstatistical Sampling (1 of 4)
• The 14 audit sampling steps for tests of details of
balances (1 of 4):
– (1) State the objectives of the audit test
– (2) Decide whether audit sampling applies
– (3) Define a misstatement/Define attributes and
exception conditions—for tests of controls (TOC) and
substantive tests of transactions (TOT)

balances (2 of 4):
– (4) Define the population
– (5) Define the sampling unit
– (6) Specify tolerable misstatement/Specify the
tolerable exception rate—for TOC and TOT
– (7) Specify acceptable risk of incorrect
acceptance/Specify acceptable risk of overreliance—
for TOC and TOT

balances (3 of 4):
– (8) Estimate misstatements in the population/Estimate
the population exception rate—for TOC and TOT
– (9) Determine the initial sample size
– (10) Select the sample
– (11) Perform the audit procedures

balances (4 of 4):
– (12) Generalize from the sample to the population
– (13) Analyze the misstatements/Analyze the
exceptions for TOC and TOT
– (14) Decide the acceptability of the population

Figure 17.1 Effect of ARO and ARIA
on Substantive Testing

Table 17.2 Relationship Among Factors Affecting ARIA,
Effect on ARIA, and Required Sample Size for Audit
Sampling for Tests of Details of Balances (1 of 2)
Factor Affecting
ARIA
Example
Effect on
ARIA
Effect on Sample Size for
Tests of Details of
Balances
Effectiveness of
internal controls
(control risk)
Internal controls are
effective (reduced
control risk).
Increase Decrease
Likelihood of
misstatements
(inherent risk)
Misstatements are
considered unlikely
(lower inherent risk).
Increase Decrease
Substantive tests
of transactions
No exceptions were
found in substantive
tests of transactions.
Increase Decrease

Table 17.2 Relationship Among Factors Affecting ARIA,
Effect on ARIA, and Required Sample Size for Audit
Sampling for Tests of Details of Balances (2 of 2)
Factor Affecting
ARIA
Example
Effect on
ARIA
Effect on Sample Size for
Tests of Details of
Balances
Acceptable audit
risk
Likelihood of
bankruptcy is low
(increased
acceptable audit
risk).
Increase Decrease
Substantive
analytical
procedures
Substantive analytical
procedures are
performed with no
indications of likely
misstatements.
Increase Decrease

Table 17.3 Factors Influencing Sample Sizes for
Tests of Details of Balances (1 of 2)
Factor
Conditions Leading to
Smaller Sample Size
Larger Sample Size
Inherent risk—Affects acceptable
risk of incorrect acceptance
Low inherent risk High inherent risk
Control risk (ARO)—Affects
acceptable risk of incorrect
acceptance
Low control risk High control risk
Results of other substantive
procedures related to the same
assertion (including substantive
analytical procedures and other
relevant substantive tests)—
Affect acceptable risk of
incorrect acceptance
Satisfactory results in
other related
substantive
procedures
Unsatisfactory results in
other related
substantive
procedures

Table 17.3 Factors Influencing Sample Sizes for
Tests of Details of Balances (2 of 2)
Factor
Smaller Sample Size
Larger Sample Size
Tolerable misstatement for a
specific account
Larger tolerable
misstatement
Smaller tolerable
misstatement
Expected size and frequency of
misstatements—Affect estimated
misstatements in the population
Smaller misstatements
or lower frequency
Larger misstatements or
higher frequency
Dollar amount of population Smaller account
balance
Larger account balance
Number of items in the population Almost no effect on
sample size unless
population is very
small
Almost no effect on
sample size unless
population is very
small

Figure 17.2 Formula for Computing
Nonstatistical Tests of Details of Balances
Sample Size Based on AICPA Audit Sampling
Formula

Let’s Discuss (1 of 8)
• What are the major differences in the 14 steps used in
nonstatistical sampling for tests of details of balances
versus the steps for tests of controls and substantive tests
of transactions?
• What alternative courses of action are appropriate when a
population is rejected using nonstatistical sampling for
tests of details of balances?
– When should each option be followed?

• What are the major differences between (a) audit sampling
for tests of controls and substantive tests of transactions
and (b) audit sampling for tests of details of balances?
• Define stratified sampling and explain its importance in
auditing.
– How can an auditor obtain a stratified sample of 30
items from each of three strata in the confirmation of
accounts receivable?

Apply monetary unit sampling

Monetary Unit Sampling (1 of 4)
• Monetary unit sampling (MUS) is the most commonly
used statistical method of sampling for tests of details of
balances
• Differences between MUS and nonstatistical
sampling:
– The definition of the sampling unit is an individual
dollar
– The population size is the recorded dollar population
– Sample size is determined using a formula
– Sample selection is done using probability proportional
to size sample selection (PPS)

• Sampling steps for MUS:
– Decide the acceptability of the population using MUS
– Determining sample sizes using MUS
– Generalizing from the sample to the population when
no misstatements are found using MUS
– Generalizing from the sample to the population when
misstatements are found using MUS

• MUS appeals to auditors by:
– Automatically increases the likelihood of selecting high
dollar items from the population being audited
– Reducing the cost of doing the audit testing because
several sample items are tested at once
– Its ease of use as monetary unit samples can be
evaluated by the application of simple tables
– Providing auditors with better and more defensible
conclusions based on statistical conclusion

• There are two main disadvantages of MUS:
– The total misstatement bounds resulting when
misstatements are found may be too high to be useful
– It may be cumbersome to select PPS samples from
large populations without computer assistance
• Auditors commonly use MUS when:
– Zero or few misstatements are expected, a dollar result
is desired, and the population data are accessible in
electronic format

Table 17-6 Summary of Steps to Calculate
Sample Size in MUS

• Define the sampling interval when using MUS sampling.
How is it calculated?
• Assume that the auditor tested an account receivable with
a balance of $3,000 and determined that the audited value
was $2,700. That is, the auditor determined the receivable
was overstated by $300.
– What is the projected misstatement (excluding the
incremental allowance for sampling risk) if the
sampling interval is $15,000?

• Define monetary unit sampling and explain its importance
in auditing.
– How does it combine the features of attributes and
variables sampling?
• Describe why the use of MUS sampling provides little, if
any, evidence related to the completeness balance-related
audit objective.

• An auditor is determining the appropriate sample size for
testing inventory valuation using MUS. The population has
3,140 inventory items valued at $19,325,000. The
tolerable misstatement is $575,000 at a 10% ARIA. No
misstatements are expected in the population.
– Calculate the preliminary sample size.

Describe variables sampling

Variables Sampling (1 of 4)
• Variables sampling is a statistical method that auditors use
• The use of variables methods shares many similarities
with nonstatistical sampling
• It is useful to understand sampling distributions and how
they affect auditor’s statistical conclusions

• The knowledge of sampling distributions enables auditors
to draw statistical conclusions, or statistical inferences,
about the population
• Auditors can state the conclusions drawn from a
confidence interval using statistical inferences in different
ways, taking care to avoid incorrect conclusions because
the true population value is always unknown

• Auditors use the statistical inference process for all of the
variable sampling methods
• The three variables methods include:
– Difference estimation
– Ratio estimation
– Mean-per-unit estimation

• Stratified sampling is a sampling method that is applicable
to difference, ratio, and mean-per-unit estimation, but is
most commonly used with mean-per-unit estimation
• For variables sampling, auditors use acceptable risk of
incorrect acceptance (ARIA) and acceptable risk of
incorrect rejection (ARIR) for variables sampling

Table 17.13 ARIA and ARIR

• Distinguish among difference estimation, ratio estimation,
mean-per-unit estimation, and stratified mean-per-unit
estimation.
– Give one example in which each can be used.
• An essential step in difference estimation is the
comparison of each computed confidence limit with
tolerable misstatement.
– Why is this step so important, and what should the
auditor do if one of the confidence limits is larger than
the tolerable misstatement?

• Evaluate the following statement made by an auditor: “I
took a random sample and derived a 90 percent
confidence interval of $800,000 to $900,000. That means
that the true population value will be between $800,000
and $900,000, 90 percent of the time.”
• Explain why difference estimation is commonly used by
auditors.

Use difference estimation in tests of details of balances

Illustration Using Difference
Estimation (1 of 2)
• Plan the sample and calculate the sample size using
difference estimation:
– Accounts receivable consists of 4,000 accounts with a
recorded value of $600,000
– Tolerable misstatement is $21,000
• Specify acceptable risk—the auditor specifies two
risks:
– Acceptable risk of incorrect acceptance (ARIA)—10%
– Acceptable risk of incorrect rejection (ARIR)—25%

Illustration Using Difference
Estimation (2 of 2)
• Estimate misstatements in the population:
– Estimate an expected point estimate
– Make an advance population standard deviation
estimate—variability of the population
• Calculate the initial sample size
• Evaluate the results
• Generalize from the sample to the population

• In using difference estimation, an auditor took a random
sample of 100 inventory items from a large population to
test for proper pricing. Several of the inventory items were
misstated, but the combined net amount of the sample
misstatement was not material. In addition, a review of the
individual misstatements indicated that no misstatement
was by itself material. As a result, the auditor did not
investigate the misstatements or make a statistical
evaluation.
– Explain why this practice is improper.

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