Download Audit Sampling: Concepts and Techniques

Chapter 9
Audit Sampling
9-2
What is Audit Sampling?
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Applying a procedure to less than
100% of a population
To estimate some characteristic of the
population
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Qualitative
Quantitative
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9-3
Advantages of Statistical Sampling
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Design efficient samples
Measure sufficiency of evidence
Objectively evaluate sample results
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9-4
Selection of Random Sample
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Random number tables
Random number generators
Systematic selection
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9-5
Random Number Table
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9-6
Types of Statistical Sampling Plans
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Attributes sampling
Discovery sampling
Classical variables sampling
Probability-proportional-to-size sampling
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Requirements of Audit
Sampling Plans

When planning the sample consider:
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9-7
The relationship of the sample to the relevant audit
objective
Materiality or the maximum tolerable misstatement or
deviation rate
Allowable sampling risk
Characteristics of the population
Select sample items in such a manner that they can be
expected to be representative of the population
Sample results should be projected to the population
Items that cannot be audited should be treated as
misstatements or deviations in evaluating the sample
results
Nature and cause of misstatements or deviations should
be evaluated
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9-8
Sampling Risks--Tests of Controls
Actual Extent of Operating Effectiveness
of the Control Procedure is
Adequate Inadequate
The Test of Controls
Sample Indicates:
Extent of Operating
Effectiveness is
Adequate
Correct
Decision
Extent of Operating
Effectiveness
Inadequate
Incorrect
Decision
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(Risk of Assessing
Control Risk
Too Low)
Incorrect
Decision
(Risk of Assessing
Control Risk
Too High)
Correct
Decision
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9-9
Audit Sampling for Tests of Controls
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Determine the objective of the test
Define the attributes and deviation conditions
Define the population to be sampled
Specify:
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The risk of assessing control risk too low
The tolerable deviation rate
Estimate the population deviation rate
Determine the sample size
Select the sample
Test the sample items
Evaluate the sample results
Document the sampling procedure
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9-10
Sampling Risks--Substantive Tests
The Substantive
Procedure Sample
Indicates
Misstatement in
Account Exceeds
Tolerable Amount
Misstatement in
Account Is Less
Than Tolerable
Amount
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The Population Actually is
Not Materially
Materially
Misstated
Misstated
Correct
Decision
Incorrect
Decision
(Risk of Incorrect
Acceptance)
Incorrect
Decision
(Risk of Incorrect
Rejection)
Correct
Decision
© 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Audit Sampling for Substantive
Tests
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9-11
Determine the objective of the test
Define the population and sampling unit
Choose an audit sampling technique
Determine the sample size
Select the sample
Test the sample items
Evaluate the sample results
Document the sampling procedure
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9-12
Population Variability—Why it Matters
Item
1
2
3
4
5
Population A
Population B
2,100
2,100
2,100
2,100
2,100
8,000
25
2,000
400
75
Mean
2,100
2,100
Standard
deviation
-0-
3,395

The variability determines how much information each of
the items in the population tells you about the other items in
the population.
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9-13
Factors Affecting Sample Size
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9-14
Determining Sample Size--MPU
Sample size =
 Pop. size x Incorrect rej. coef . x Est. SD  2


 Planned allowance for sampling risk 
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Determining Sample Size--MPU
Sampling
Planned allowance
=
for sampling risk
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9-15
Tolerable misstatement
______________________
1 + Incorrect acceptance coef.
Incorrect rejection coef.
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9-16
Variables Sampling Illustration--MPU
Adjusted allowance
for sampling risk
=
Tolerable
_ (Population size * Incorrect acceptance coef. * Sample stan. dev.)
misstatement
Sample size

This formula “adjusts” the allowance for sampling risk to consider the standard
deviation of the audited values in the sample. It holds the risk of incorrect
acceptance at its planned level.
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9-17
Variables Sampling Illustration--MPU
Using the text example with a standard deviation of audited values of $16
Adjusted allowance
for sampling risk
=
Tolerable
_ (Population size * Incorrect acceptance coef. * Sample stan. dev.)
misstatement
Sample size
= $364,000
_
($100,000 * 1.64 * $16)
225
= $189,067

We would still “accept” the book balance because the $6,250,000 (book
value) falls within this interval
Estimate of total
audited value
$6,100,000
[$5,910,933
McGraw-Hill/Irwin
+
+
to
Adjusted allowance
for sampling risk
$189,067
$6,289,067]
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9-18
Acceptance Interval
Figure 9-12
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9-19
Nonstatistical Variables Sampling
Illustration
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Plan Sample:
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Population:
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Tolerable misstatement = $10,000
Risk assessments:
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Size = 363 items
Book value = $200,000
Inherent and control risk = Slightly below maximum
Other substantive tests = Moderate
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9-20
Nonstatistical Sampling-Determination of Sample Size
Sample size = Population book value X Reliability factor
Tolerable misstatement
= $200,000 X 2.0
$10,000
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= 40 items
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Nonstatistical Sampling--Evaluation
of Sample Results
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9-21
Sample results:
40 accounts in sample
$350 net overstatement
$60,000 book value of sample items
Projected misstatement:
= [Sample net misstatement]
[ Book value of sample ]
X Book value of population
= [ $350 ] X $200,000
[$60,000]
= $1,167
Since the projected misstatement is only 11.7 percent ($1,167/$10,000)
of tolerable misstatement, it is likely that the auditors would conclude that
the account balance is materially correct.
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9-22
PPS Sampling Illustration
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Population book value = $6,250,000
Other Information:
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Tolerable misstatement = $364,000
Sampling risk--Incorrect acceptance = 5%
Expected misstatement = $50,000
Use Figures 9-14 and 9-15 to obtain a
“reliability factor” and an “expansion
factor.”
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9-23
PPS Sample Size Computation
Sample
size =
Recorded amount of population * Reliability factor
Tolerable misstatement - (Expected misstatement * Expansion factor)
=
$6,250,000 * 3.0
$364,000 - ($50,000 * 1.6)
=
66
Sampling interval = Book value of the population
Sample size
= $6,250,000
66
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= $95,000 (approximately)
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9-24
PPS Evaluation of Results
Upper Limit on misstatement =
Projected misstatement
+ Basic precision (Rel. factor x interval)
+ Incremental allowance
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9-25
Calculation of Upper Limit on Misstatement
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