Audit Sampling
Slide 9-1
© The McGraw-Hill Companies, Inc., 2006
Audit Detection Risk (DR)

Detection Risk - Auditors’ planning and
tests cause them to reach incorrect
conclusion about management assertions.

Sampling & Nonsampling Portions
Nonsampling - Auditor Deficiencies or Mistakes
Sampling - Probability that sample will NOT
yield same result as 100% test; causing auditor
to draw incorrect conclusion.
Slide 9-2
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Population Variability

Increases Sampling Error since it
increases risk that sample may not be
representative of the entire population of
balances or transactions.

Called “Standard Deviation”

Most common way to minimize impact:
Population Stratification
Slide 9-3
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Population Variability
Item
Population A
1
2
3
4
5
Mean
Standard Deviation
Slide 9-4
Population B
2,100
2,100
2,100
2,100
2,100
8,000
25
2,000
400
75
2,100
2,100
-0-
3,395
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Advantages of
Statistical Sampling
 Design
efficient samples
 Measure
sufficiency of evidence
 Objectively
evaluate sample results
Can project sample results so that you
can draw a conclusion about the entire
universe or population from which
sample was taken.
Slide 9-5
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Selection of Statistical Samples
 Random
number (tables, generators)
 Systematic
selection
 Probability
Proportional to Size(PPS)
A form of automatic stratification
(all items > sampling interval are sampled)
Slide 9-6
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Types of
Statistical Sampling
 Attributes
 Variables
Sampling
Sampling
 Discovery
Slide 9-7
Sampling
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Requirements of Audit
Sampling Plans
• Consider specific audit objective being tested.
• Establish Materiality: Maximum Tolerable:
 Deviation rate (testing internal controls) or
 Misstatement (substantive tests)
• Set Allowable sampling risk (what auditor will accept)
• Consider population characteristics (variability, etc.)
• Select items in such a manner (statistical) so that they
can be expected to be representative of the population.
• Project sample results to the entire population.
• Treat items that cannot be audited as misstatements or
deviations in evaluating the sample results. Unless...
• Evaluate nature and cause of deviations/misstatements.
Slide 9-8
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Determining Tolerable Deviation

How Important is the Control Activity?

Are There Other Compensating Controls?

Rules of Thumb per AICPA Study:
Planned CR
Tolerable Deviation
Low
2% - 7%
Moderate
6% - 12%
Slightly < Maximum
11% - 20%
Maximum
No Testing
Slide 9-9
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Projecting Deviations
Number of exceptions or deviations from
compliance with internal controls found
divided by
Number of opportunities sampled
=
Deviation %
Notes:
 If
sample deviation % less than tolerable, then CR is
lower than planned & vice versa.
 Reliability is based on sampling +precision & CL.
Slide 9-10
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Sampling Risks
Tests of Controls
Auditors’ Conclusion
From the Sample Is:
Deviation Rate
Is Less than
Tolerable Rate
Deviation Rate
Exceeds
Tolerable Rate
Slide 9-11
True State of Population
Deviation Rate
Deviation Rate
Is Less Than
Exceeds
Tolerable Rate
Tolerable Rate
Correct
Decision
Incorrect
Decision
(Risk of Assessing
Control Risk
Too High)
Incorrect
Decision
(Risk of Assessing
Control Risk
Too Low)
Correct
Decision
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Substantive Tests of Details
Tolerable Misstatement
Based
on overall F.S. materiality threshold
and that for the particular account.
For
the particular test (with sampling or not)
the tolerable misstatement would be lower
than either of the overall because of:
 Misstatements which could occur in other accounts.
 Misstatements in same account from other tests/
assertions.

At account level, normally no more than 75%
of overall materiality threshold.
Slide 9-12
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Sampling Risks
Substantive Tests of Details
Auditors’ Conclusion
From the Sample Is:
True State of Population
Misstatement in
Misstatement in
A/C is Less Than
A/C Exceeds
Tolerable Amount
Tolerable Amount
Misstatement in
A/C is Less Than
Tolerable Amount
(not materially misstated)
Correct
Decision
Misstatement in
A/C is Exceeds
Tolerable Amount
(materially misstated)
Incorrect
Decision
Slide 9-13
(Risk of Incorrect
rejection)
Incorrect
Decision
(Risk of Incorrect
acceptance)
Correct
Decision
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What Effects Sample Size?
Population Size
Little impact, except very
small populations
Expected Error Rate
Direct Relationship
Actual Error Rate
Direct Relationship
Standard Deviation
Direct Relationship
Auditor’s Tolerable:
Deviation/Misstatement
Opposite Relationship
Risk of Incorrect
Acceptance/Rejection
Opposite Relationship
Slide 9-14
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Projecting Misstatements

Classical variables sampling
» Mean-per-unit estimation
» Ratio estimation
» Difference estimation

Probability-Proportional-to-Size (PPS)
sampling
Slide 9-15
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Projecting Misstatements-Classical
Population: 1,000, $200,000 (average/mean = $200)
Sample: 50, $9,000 (mean = $180)
Audited sample value: $8,500 (mean = $170)
Mean-per-unit estimation (used in universe $ unknown)
Audited value = Audited mean ($170) X items in population (1,000) =
$170,000 . Misstatement = $30,000 ($200,000 - $170,000)
Ratio estimation
Sampled misstatement of $500 ($9,000-8,500)/ Sample $ (9,000) =
5.56% X Population ($200,000) = $11,200 misstatement
Difference estimation
Sample book mean ($180) – Audited mean ($170) = $10
difference. Misstatement = $10,000 (1,000 X $10)
Note: These are point estimates within + precision at CL.
Slide 9-16
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Projecting Misstatements-PPS
 Computation
is by sampled item and then is
totaled for all items sampled to get total
misstatement per audit.
 For
items > sampling interval (generally = or <
materiality threshold), misstatement is NOT
projected to the entire population (just like
stratified classical sampling).
 For
items < sampling interval, misstatement is
projected to the entire population (just like unstratified classical sampling).
Note: These are point estimates within + precision at CL.
Slide 9-17
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Projecting Misstatements-PPS
Sampling Interval = $3,000 (number of $/sample size)
Sampled item (trans or subaccount) book value = $100
Sampled Item Audit-determined value = $95
Item misstatement = Tainted % ($100-95=$5/$100 = 5%) X
sampling interval ($3,000) = $150
__________________________________________________
Sampling Interval = $3,000 (number of $/sample size)
Sampled item (trans or subaccount) book value = $4,000
Sampled Item Audit-determined value = $40
Item misstatement = $4,000 - $40 = $3,960
Slide 9-18
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