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2000 by Prentice Hall,Inc.
16
AUDIT SAMPLING FOR TEST
OF DETAILS OF BALANCES
BOTH STATISTICAL ANDNONSTATISTICAL SAMPLING ARE
ACCEPTABLE UNDER GAAS,BUT
WHICHEVER IS USED,IT MUST
BE DONE RIGHT
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2000 by Prentice Hall,Inc.
Comparisons of Audit Sampling for Tests of
Details of Balances and for Tests of Controls
and Substantive Tests of Transactions
Nonstatistical Sampling
There are 14 steps required in audit sampling for tests of
details of balance.
These steps parallel the 14 steps used for sampling for tests of
controls and substantive tests of transactions,There are a few
differences because of the different objectives of the tests.
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2000 by Prentice Hall,Inc.
1,State the objectives of the audit tests.
2,Decide whether audit sampling applies.
3,Define misstatement conditions.
4,Define the population.
5,Define the sampling unit.
6,Specify tolerable misstatement.
7,Specify acceptable risk of incorrect
acceptance.
8,Estimate misstatements in the
population.
9,Determine the initial sample size.
Steps
Plan the Sample
1,State the objectives of the audit tests.
2,Decide whether audit sampling applies.
3,Define attributes and exception
conditions.
4,Define the population.
5,Define the sampling unit.
6,Specify the tolerable exception rate.
7,Specify acceptable risk of assessing
control risk too low.
8,Estimate the population exception rate.
9,Determine the initial sample size.
Plan the Sample
Audit Sampling
for Tests of Details
of Balances
Audit Sampling
for Tests of Controls and
Substantive Tests
of Transactions (see p,445)
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2000 by Prentice Hall,Inc.
Select the Sample and
Perform the Audit Procedures
10,Select the sample.
11,Perform the audit procedures.
12,Generalize from the sample to the
population.
13,Analyze the misstatements.
14,Decide the acceptability of the
population.
Evaluate the Results
10,Select the sample.
11,Perform the audit procedures.
12,Generalize from the sample to the
population.
13,Analyze the exceptions.
14,Decide the acceptability of the
population.
Evaluate the Results
Select the Sample and
Perform the Audit Procedures
Steps
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2000 by Prentice Hall,Inc.
Action When a Population Is Rejected
Take No Action Until Tests of Other Audit Areas Are Completed
Perform Expanded Audit Tests in Specific Areas
Increase the Sample Size
Adjust the Account Balance
Request the Client to Correct the Population
Refuse to Give an Unqualified Opinion
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2000 by Prentice Hall,Inc.
MONETARY UNIT SAMPLING
Difference between Monetary Unit
Sampling and Nonstatistical Sampling
The Definition of the Sampling Unit Is an Individual Dollar
The Population Size Is the Recorded Dollar Population
Preliminary Judgment of Materiality Is Used for Each
Account Instead of Tolerable Misstatement
Sample Size Is Determined Using a Statistical Formula
A Formal Decision Rule Is Used for Deciding the Acceptability
of the Population
Sample Selection Is Done Using Probability Proportional to Size
Sample Selection (PPS)
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2000 by Prentice Hall,Inc.
The Auditor Generalizes from the Sample
to the Population Using
Monetary Unit Sampling Techniques
1,Attributes sampling tables are used to calculate the results.
2,The attributes results must be converted to dollars.
3,The auditor must make an assumption about the percentage
of misstatement for each population item that is misstated.
4,The statistical results when Monetary Units Sampling is used
are called misstatement bounds.
Arens,Loebbecke; Auditing,8/E
2000 by Prentice Hall,Inc.
Overstatement amounts equal 100 percent; understatement
amounts equal 100 percent; misstatement bounds at a 5 percent
ARIA are
Upper misstatement bound = $1,200,000 X 3% X 100% = $36,000
Lower misstatement bound = $1,200,000 X 3% X 100% = $36,000
1,All amounts have to be overstatements,
2,All population items misstated have to be 100 percent misstated.
Arens,Loebbecke; Auditing,8/E
2000 by Prentice Hall,Inc.
Overstatement amounts equal 10 percent; understatement
amounts equal 10 percent; misstatement bounds at a 5 percent
ARIA are
Upper misstatement bound = $1,200,000 X 3% X 10% = $3,600
Lower misstatement bound = $1,200,000 X 3% X 10% = $3,600
The assumption is that,on average,those items that are misstated are
misstated by no more than 10 percent.
Arens,Loebbecke; Auditing,8/E
2000 by Prentice Hall,Inc.
Overstatement amounts equal 20 percent; understatement
amounts equal 200 percent; misstatement bounds at a 5 percent
ARIA are
Upper misstatement bound = $1,200,000 X 3% X 20% = $7,200
Lower misstatement bound = $1,200,000 X 3% X 200% = $72,000
The justification for a larger percent for understatements is the potential for a
larger misstatement in percentage terms.
Arens,Loebbecke; Auditing,8/E
2000 by Prentice Hall,Inc.
Appropriate Percent of Misstatement Assumption
The appropriate assumption for the overall percent of
misstatement is those population items containing a
misstatement is an auditor’s decision.
Generalizing When Misstatements Are Found
1,Overstatement and understatement amounts are dealt with separately
and then combined.
2,A different misstatement assumption is made for each misstatement,
including the zero misstatements.
3,The auditor must deal with layers of the computed upper exception
rate (CUER) from the attributes sampling table.
4,Misstatement assumptions must be associated with each layer.
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2000 by Prentice Hall,Inc.
Table 16 - 1
Illustrative Accounts Receivable Population
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2000 by Prentice Hall,Inc.
Differences between Variables and Nonstatistical Sampling
Sampling Distributions
1,The mean value of all the sample means is equal to the population mean (X),A
corollary is that the sample mean value (x) with the highest frequency of occurrence
is also equal to the population mean.
2,The shape of the frequency distribution of the sample means is that of a normal
distribution (curve),as long as the sample size is sufficiently large,regardless of the
distribution of the population.
3,The percentage of sample means between any two values of the sampling
distribution is measurable
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2000 by Prentice Hall,Inc.
An examination of the formula in step 5 of Table 16 - 13
indicates the effect of changing each factor while the other
factors remain constant is as follows:
Effect on the Computed
Type of Change Precision Interval
Increase ARIA Decrease
Increase the point estimate of
the misstatements Increase
Increase the standard deviation Increase
Increase the sample size Decrease
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2000 by Prentice Hall,Inc.
FIGURE 16 - 1
Effect of ARACR and ARIA
on Substantive Testing
*Assumes tests of controls results were
satisfactory,which permits control risk
to remain low.
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2000 by Prentice Hall,Inc.
TABLE 16 - 2
Relationship among Factors Affecting ARIA,Effect on ARIA,and
Required Sample Size for Audit Sampling
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2000 by Prentice Hall,Inc.
TABLE 16 -3
Factors Influencing Sample Sizes for Tests of Details of Balances
Arens,Loebbecke; Auditing,8/E
2000 by Prentice Hall,Inc.
Acceptable risk of incorrect acceptance (ARIA) Monetary unit sampling (MUS)
Acceptable risk of incorrect rejection (ARIR) Point estimate
Difference estimation Probability proportion to
size sample selection (PPS)
Mean-per-unit estimation Ratio estimation
Misstatement bounds Statistical inferences
Stratified sampling Variables sampling