Audit Sampling for Tests of Details of Balances

Testing the balances and Testing of Control and Substantive Tests. This where Auditing meets Statistics

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Audit Sampling for Tests of Audit Sampling for Tests of
Details of BalancesDetails of Balances
Chapter 17Chapter 17

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Learning Objective 1Learning Objective 1
Differentiate audit sampling for tests of Differentiate audit sampling for tests of
details of balances and for tests of details of balances and for tests of
controls and substantive tests of controls and substantive tests of
transactions.transactions.

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Tests of Details of BalancesTests of Details of Balances
and Controls, and Substantiveand Controls, and Substantive
Tests of TransactionsTests of Transactions
Differences among tests
Transactions
Controls
Balances
Effectiveness of
controls
Monetary
correctness of
transactions
Existence of material
misstatements$4nnt
Type of Test& tn'tn# u What It Measures

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Learning Objective 2Learning Objective 2
Apply nonstatistical sampling to tests of Apply nonstatistical sampling to tests of
details of balances.details of balances.

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Nonstatistical SamplingNonstatistical Sampling
14 steps required in audit sampling for
tests of details of balances.
Steps parallel the sampling approach
used to test controls and/or test
transactions.
There are a few differences because
of the different objectives of the tests.

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Comparison of the 14 StepsComparison of the 14 Steps
2. Decide whether audit
sampling applies.
2. Decide whether audit
sampling applies.
3. Define a misstatement. 3. Define attributes and
exception conditions.
4. Define the population. 4. Define the population.
5. Define the sampling unit. 5. Define the sampling unit.
Audit sampling for tests
of details of balances
Audit sampling for tests of
controls and substantive
tests of transactions
1. State the objectives
of the audit test.
1. State the objectives
of the audit test.

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Comparison of the 14 StepsComparison of the 14 Steps
7. Specify acceptable risk
of incorrect acceptance.
7. Specify acceptable risk
of assessing control
risk too low.
8. Estimate misstatements
in the population.
8. Estimate the population
exception rate.
9. Determine the initial
sample size.
9. Determine the initial
sample size.
6. Specify tolerable
misstatement.
6. Specify the tolerable
exception rate.
Audit sampling for tests
of details of balances
Audit sampling for tests of
controls and substantive
tests of transactions

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Comparison of the 14 StepsComparison of the 14 Steps
10. Select the sample. 10. Select the sample.
11. Perform the audit
procedures.
11. Perform the audit
procedures.
12. Generalize from the
sample to the population.
12. Generalize from the
sample to the population.
13. Analyze the misstatements.13. Analyze the exceptions.
14. Decide the acceptability
of the population.
14. Decide the acceptability
of the population.
Audit sampling for tests
of details of balances
Audit sampling for tests of
controls and substantive
tests of transactions

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Action When a PopulationAction When a Population
Is RejectedIs 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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Learning Objective 3Learning Objective 3
Apply monetary unit sampling.Apply monetary unit sampling.

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Monetary Unit SamplingMonetary Unit Sampling
MUS is an innovation in statistical
sampling methodology that was
developed specifically for use
by auditors.

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Differences between MUSDifferences between MUS
and Nonstatistical Samplingand 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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Differences between MUSDifferences between MUS
and Nonstatistical Samplingand 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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Differences between MUSDifferences between MUS
and Nonstatistical Samplingand Nonstatistical Sampling
The auditor generalizes from the
sample to the population using MUS
techniques.
•Attribute sampling tables are used to
calculate results
•Attribute results must be converted to
dollars
•Make an assumption about the % of
misstatement for each item misstated
•Determine misstatement bounds.

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Generalizing from the SampleGeneralizing from the Sample
to the Populationto the Population
Population is $1,200,000
Sample size is 100 customer accounts
Overstatement amounts equal 100%.
Understatement amounts equal 100%.
Misstatement bounds at a 5% ARIA are:
Upper misstatement bound
= $1,200,000 × 3% × 100% = $36,000
Assumption 1:
Lower misstatement bound
= $1,200,000 × 3% × 100% = $36,000

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Generalizing from the SampleGeneralizing from the Sample
to the Populationto the Population
1.All amounts have to be overstatements.
2.All population items misstated have to
be 100% misstated.
The following two conditions both have to
exist before the $36,000 correctly reflects
the true overstatement amount:

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Generalizing from the SampleGeneralizing from the Sample
to the Populationto the Population
Overstatement amounts equal 10%.
Understatement amounts equal 10%.
Misstatement bounds at a 5% ARIA are:
Upper misstatement bound
= $1,200,000 × 3% × 10% = $3,600
Assumption 2:
Lower misstatement bound
= $1,200,000 × 3% × 10% = $3,600

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Generalizing from the SampleGeneralizing from the Sample
to the Populationto the Population
Overstatement amounts equal 20%.
Understatement amounts equal 200%.
Misstatement bounds at a 5% ARIA are:
Upper misstatement bound
= $1,200,000 × 3% × 20% = $7,200
Assumption 3:
Lower misstatement bound
= $1,200,000 × 3% × 200% = $72,000

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Appropriate Percent of Appropriate Percent of
Misstatement AssumptionMisstatement Assumption
The appropriate assumption for the overall
percent of misstatement in those population
items containing a misstatement is an
auditor’s decision.

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Generalizing When Generalizing When
Misstatements Are FoundMisstatements 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.

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Generalizing When Generalizing When
Misstatements Are FoundMisstatements Are Found
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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Illustration of the Auditor’s Illustration of the Auditor’s
Decision Rule for MUSDecision Rule for MUS

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Determining Sample Size Using Determining Sample Size Using
MUSMUS
Materiality
Assumption of the average percent
of misstatement for population items
that contain a misstatement
Acceptable risk of incorrect acceptance
Recorded population value

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Determining Sample Size Using Determining Sample Size Using
MUSMUS
Estimate of the population exception rate
Relationship of the audit risk model
to sample size for MUS
PDR = AAR ÷ (IR × CR)

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Advantages of Using MUSAdvantages of Using MUS
MUS increases the likelihood of selecting
high-dollar items
MUS often reduces the cost of audit testing
Easy to apply
MUS provides a statistical conclusion

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Learning Objective 4Learning Objective 4
Describe variables sampling.Describe variables sampling.

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Frequency Distribution of Frequency Distribution of
Sample MeansSample Means
F
r
e
q
u
e
n
c
y

o
f

v
a
l
u
e
s

i
n

p
e
r
c
e
n
t
Value of x in dollars

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Sampling DistributionsSampling Distributions
1.The mean value of all the sample means
is equal to the population mean ( ).
Three things shape the results of the
experiment of taking a large number of samples
from a known population:
X

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Sampling DistributionsSampling Distributions
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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Sampling Distribution forSampling Distribution for
a Population Distributiona Population Distribution
Sampling
distribution –
Normal
Population
distribution –
Skewed
Mean
Value of in dollars
xF
r
e
q
u
e
n
c
y

o
f

v
a
l
u
e
s

i
n

p
e
r
c
e
n
t

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Variables MethodsVariables Methods
 Difference estimation
Ratio estimation
Mean-per-unit estimation

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Stratified Statistical MethodsStratified Statistical Methods
 All of the elements of the population are
divided into two or more subpopulations
 Each subpopulation is independently tested
The calculations are then made for each
stratum and then combined into one overall
population estimate

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Sampling Risks (ARIA and ARIR)Sampling Risks (ARIA and ARIR)
Conclude that the
population is
materially misstated
Conclude that the
population is not
materially misstated
Correct
conclusion –
no risk
Incorrect
conclusion –
risk is ARIA
Incorrect
conclusion –
risk is ARIR
Correct
conclusion –
no risk
Actual audit decision
Materially
misstated
Not materially
misstated
Actual state of the population

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Learning Objective 5Learning Objective 5
Use difference estimation in tests of details Use difference estimation in tests of details
of balances.of balances.

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Plan the Sample and CalculatePlan the Sample and Calculate
the Sample Sizethe Sample Size
 State the objectives of the audit test
Decide whether audit sampling applies
Define misstatement conditions
Define the population
Define the sampling unit
Specify tolerable misstatement

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Specify Acceptable RiskSpecify Acceptable Risk
ARIA
ARIR

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Estimate MisstatementEstimate Misstatement
in the Populationin the Population
1.Estimate an expected point estimate
2.Make an advance population standard deviation
estimate – variability of the population.

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22
Calculate the InitialCalculate the Initial
Sample SizeSample Size
n= initial sample size
SD*= advance estimate of the standard deviation
Z
A
= confidence coefficient for ARIA
Z
R
= confidence coefficient for ARIR
N= population size
TM= tolerable misstatement for the population (materially)
E*= estimated point estimate of the population misstatement
SD*(SD*(ZZ
AA + + ZZ
RR))NN
((TMTM – – E E *)*)
nn = =
where:

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Select the Sample and Perform Select the Sample and Perform
the Proceduresthe Procedures
The auditor must use one of the
probabilistic sample selection methods
to select the items for confirmation.
The auditor must use care in confirming
and performing alternative procedures.

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Evaluate the ResultsEvaluate the Results
1. Compute the point estimate of the
total misstatement
2. Compute an estimate of the population
standard deviation
3. Compute the precision interval
4. Compute the confidence limits
Generalize from the sample to the population

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Effect of Changing Each FactorEffect of Changing Each Factor
Increase ARIA
Increase the point estimate
of the misstatements
Increase the standard dev.
Increase the sample size
Type of change
Effect on the computed
precision interval

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Analyze the MisstatementsAnalyze the Misstatements
The auditor must evaluate misstatements to
determine the cause of each misstatement
and decide whether modification of the
audit risk model is needed.

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Auditor’s Decision Rule for Auditor’s Decision Rule for
Difference EstimationDifference Estimation

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End of Chapter 17End of Chapter 17