AUDITING
CHAPTER 9
Audit Sampling
By
David N. Ricchiute
TOPICS
Use of sampling in audit engagements
Role of sampling, nonsampling risk


Risk of assessing control risk too high, too low
Risks of incorrect rejection, acceptance
Distinction between statistical, nonstatistical
sampling
Audit sampling for tests of controls and
substantive tests of details
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Attribute estimation, sequential sampling
Probability-proportional-to-size (PPS)
GBW 8th ed., Ch. 9
SAMPLING:
Definitions
Sampling: examining less than 100% of items
in a population
Population: all items within a class of
transactions
Sampling plan: procedures to test a sample
Attributes sampling: tests rate of deviation
from a prescribed control procedure
Variables sampling: tests whether recorded
account balances are fairly stated
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GBW 8th ed., Ch. 9
AUDIT RISK
Risk that auditor may unknowingly fail to
modify opinion on materially misstated
financial statements
2 parts

Risk that errors will occur: uncontrollable
 Inherent risk & control risk

Risk that material errors will not be
detected: controllable
 Detection risk
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UNCERTAINTIES
Sampling risk

Risk that sample may contain
disproportionately more/less error than
exists in population
Nonsampling risk
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5
Aspects of audit risk not attributable to
sampling such as human error
GBW 8th ed., Ch. 9
CONTROL RISK
ASSESSMENT: Too High
Inefficient
Assessing control risk at maximum
when it should be lower
Concluding control not effective when it
is
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GBW 8th ed., Ch. 9
CONTROL RISK
ASSESSMENT: Too Low
Ineffective
Lowering control risk when should be
set at maximum
Concluding control is effective when it
isn’t
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GBW 8th ed., Ch. 9
STATISTICAL SAMPLING
Apply the laws of probability to


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Design efficient sample
Measure sufficiency of sample
Evaluate sample results
Measures sampling risk quantitatively
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GBW 8th ed., Ch. 9
NONSTATISTICAL
SAMPLING
Relies exclusively on judgment to


Determine sample size
Evaluate sample results
Cannot measure sampling risk
quantitatively
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(NON)STATISTICAL
SAMPLING CHOICE
Choice based on relative costs &
benefits
Independent of audit procedures
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ATTRIBUTES &
DEVIATIONS
Attribute

A characteristic of control
Deviation
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Absence of the attribute
GBW 8th ed., Ch. 9
ATTRIBUTE ESTIMATION
SAMPLING
Used to test controls that leave an audit
trail
1 Determine objectives, attributes,
deviation conditions
2 Define population
3 Define sample size
4 Perform sampling plan
5 Evaluate sample results
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GBW 8th ed., Ch. 9
ATTRIBUTE ESTIMATION
SAMPLING: Objectives
Whether controls for class of transactions
sufficiently effective to lower control
risk below maximum

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Trail of observable & documented evidence
Does not rely primarily on segregation of
duties
GBW 8th ed., Ch. 9
ATTRIBUTE ESTIMATION
SAMPLING: Sample Size
Sample size components

Acceptable risk of assessing control risk too
low
 Inverse relationship with sample size

Tolerable rate of deviation
 Maximum population rate of deviation from
control

Expected population deviation rate
 Estimated from prior year or pilot sample
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GBW 8th ed., Ch. 9
SAMPLE SELECTION
METHODS
A Random-number sampling
B Systematic sampling
C Block sampling
D Haphazard sampling
E Stratified
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GBW 8th ed., Ch. 9
SAMPLE SELECTION
METHODS: Random Number
Uses computer-generated numbers to
select sampling units
Match number to prenumbered
documents
Appropriate for both statistical &
nonstatistical sampling
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SAMPLE SELECTION
METHODS: Systematic Sampling
Selecting every nth item from
population of sequentially ordered items
Useful when identification numbers
lacking
Appropriate for both statistical &
nonstatistical sampling
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SAMPLE SELECTION
METHODS: Block Sampling
A group of items arranged contiguously
within a larger grouping
Inefficient & not generalizable
Should not be used for statistical or
nonstatistical sampling without care in
controlling sampling risk
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GBW 8th ed., Ch. 9
SAMPLE SELECTION
METHODS: Haphazard Sampling
Sampling units selected without special
reason or conscious bias
Inappropriate for statistical sampling
Useful for nonstatistical sampling
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GBW 8th ed., Ch. 9
SAMPLE SELECTION
METHODS: Stratified Sampling
Subdivide population into homogeneous
strata
Select separate sample for each strata
by one of prior methods
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GBW 8th ed., Ch. 9
OTHER TECHNIQUES:
Sequential Sampling
Stop-or-go
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Performed in stages
Auditor decides to stop or continue
sampling after each stage
GBW 8th ed., Ch. 9
OTHER TECHNIQUES:
Nonstatistical Sampling
Used when costs outweigh benefits of
statistical sampling
Auditor judgment guided by
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Experience
Prior knowledge
Current information
GBW 8th ed., Ch. 9
SUBSTANTIVE SAMPLING
RISK: 2 Sources
Risk of incorrect rejection

Risk that audit sample suggests account
balance is materially misstated when it is
fairly stated
Risk of incorrect acceptance
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Risk that sample suggests account balance
is fairly stated when it is materially
misstated
GBW 8th ed., Ch. 9
VARIABLES SAMPLING
PLAN
Determine objectives of test
Define population
Choose sampling technique
Determine sample size
Determine method of sample selection
Perform sampling plan
Evaluate sample results
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OBJECTIVES OF TEST
To estimate account balance that is not
recorded
To test reasonableness of recorded
account balance
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GBW 8th ed., Ch. 9
DEFINING POPULATION
Audit population

All items constituting an account balance
or class of transactions defined by auditor’s
characteristic of interest
Sampling unit
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Any individual elements of a population
GBW 8th ed., Ch. 9
AUDIT SAMPLING
Sampling used only for those
accounts where it is appropriate

When large number transactions
within one account
Techniques
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Probability proportional to size
(PPS)
Nonstatistical sampling
Classical variables sampling
(appendix)
GBW 8th ed., Ch. 9
SAMPLING DECISIONS
Choice between statistical &
nonstatistical sampling based on
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Costs
Effectiveness
Need for quantitative estimate of sampling
risk
GBW 8th ed., Ch. 9
PROBABILITY-PROPORTIONALTO-SIZE (PPS)
Derived from attributes sampling theory
Appropriate when 1 or a few errors
expected
Characteristics


Automatically stratifies an audit population
Appropriate for testing for overstatement
 Useful for testing assets & revenues
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PPS
An Example
Define population for accounts
receivable


All customer debit balances testing
overstatement or
All customer balances, including 0 &
negative
 Requires special consideration
Dollar is sample unit
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GBW 8th ed., Ch. 9
PPS SAMPLE SIZE
ELEMENTS
Determine

Reliability factor for overstatement errors
based on
 Expected number overstatement errors
 Risk of incorrect acceptance
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Tolerable (acceptable) error
Anticipated error & expansion factor
GBW 8th ed., Ch. 9
PPS SAMPLE SIZE MODEL
n=
RF x B
TE – (AE x EF)
where
RF – reliability factor (from table)
B – book value (from client)
TE – tolerable error (auditor judgment)
AE – anticipated error (auditor judgment)
EF – expansion factor (from table)
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PPS SAMPLE SELECTION
Used for statistical sampling methods
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Random number
Systematic sampling
GBW 8th ed., Ch. 9
EVALUATING RESULTS:
PPS Decision Rule
If the upper error limit is less than or
equal to the tolerable error, the account
is fairly presented
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GBW 8th ed., Ch. 9
NONSTATISTICAL
SAMPLING
Used when
No apparent need to quantify sampling
risk
Cost of statistical sampling exceeds
benefits
Cost to select sampling units exceeds
benefits
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GBW 8th ed., Ch. 9
SAMPLE SIZE IN
NONSTATISTICAL SAMPLING
Requires

Degree audit assurance
 Substantial, moderate, little
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Assurance factor
Estimated tolerable error
GBW 8th ed., Ch. 9
EVALUATING SAMPLE
RESULTS
When likely error is estimated,
auditor has 4 choices
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Accept client’s book value
Propose audit adjustment
Perform additional substantives tests
Request client to revalue entire
population
GBW 8th ed., Ch. 9