There are 14 steps required for audit sampling for tests of details of balances. The steps are similar for sampling tests of controls and transactions, with the main differences being that sampling for balances tests for monetary errors rather than exceptions. Stratified sampling is most commonly used to divide the population into subgroups and select independent samples from each. Sample size is determined based on tolerable misstatement, and statistical or nonstatistical methods can be used to analyze results and determine if the population should be rejected. Monetary unit sampling is an innovative statistical method developed for auditors that samples at the individual dollar level.

1. Audit Sampling for Tests
of Details of Balances
Chapter 16
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2. 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.
The few differences result from
testing for misstatements (dollar errors)
instead of exceptions.
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3. Testing Balances
 Population is defined as “recorded dollar
population”
 Errors are dollar misstatements
 Stratified sampling is most common. Divide
the population into subpopulations. Select
independent samples from each subpopulation.
 Tolerable misstatement is used to determine
sample size.
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4. Testing Balances
 Acceptable risk of incorrect acceptance
(ARIA) = risk that the auditor is willing to take
of accepting a balance as correct when the true
misstatement is greater than the tolerable
misstatement.
 ARIA is equivalent to ARACR
 ARIA is inversely related to sample size.
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5. Refer to Charts in Text
 See Figure 16-1
 See Table 16-2
 See Table 16-3
 See Figure 16-2
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6. Analyzing Results of Tests
 Calculate total misstatement for each stratum:
misstatement = recorded value – audited value
 Calculate the total point estimate of
misstatement (i.e. extrapolate to population):
Point estimate = misstatement/stratum
recorded value X total stratum population
value
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7. Analyzing Results of Tests
 Nonstatistical = compare point estimate to
tolerable misstatement. Big difference =
acceptable population
 Statistical = calculate sampling error; add to
point estimate; compare to tolerable error,
accept/reject population.
 Analyze each misstatements for nature and
cause before rejecting total population.
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8. 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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9. Monetary Unit Sampling
MUS is an innovation in statistical
sampling methodology that was
developed specifically for
use by auditors.
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10. Differences between MUS 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.
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11. Differences between MUS and
Nonstatistical Sampling
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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12. Probability Proportional to Size
Sample Selection Method
 Can’t audit individual “dollar” although the
“dollar” is the selection tool in MUS.
 Find the account balance in which the selected
“dollar” resides and audit the whole account
balance.
 Probability proportional to size means that
large balances are more likely to be selected as
the sampling unit since the balances have more
“dollars” that might be selected.
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13. The Auditor Generalizes from the
Sample to the Population Using MUS
Attributes sampling tables are used to
calculate the results.
The attributes percentages of exception
must be converted to dollar misstatement.
The auditor must make an assumption about
the percentage of misstatement for each
population item that is misstated.
The statistical results when MUS is used
are called misstatement bounds.
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14. Calculating Sample Size under
MUS
 Use the attributes sampling tables where:
 ARIA = ARACR
 EPER usually = 0 for MUS, but can be equal to
estimated misstatement / total population dollars
 TER = Tol. Miss. / Avg % of Miss. Assump. / total
population dollars
 Calculate 2 sample sizes – one for
understatements; one for overstatements
 Choose the largest sample size
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15. Why Use MUS?
 Automatically increases likelihood of selecting high
dollar items
 Reduces cost of doing test because several sample
items fall within one account balance, thus several
sample items are tested at once
 Easy to apply; uses tables
 Provides a statistical conclusion rather than a
judgmental one.
 Disadvantages: 1. misstatement bounds may be too
high to be useful; 2. best when zero or few
misstatements are expected.
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16. Variables Sampling Methods
Difference estimation – standard statistical method
Most commonly used
Ratio estimation – population point estimate
= sample misstatement x total population dollars
Total sample dollars
Mean-per-unit estimation – uses the audited value
To create a precision interval (like difference est.)
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17. Effect of Changing Factors
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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18. End of Chapter 16
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