1. Audit Sampling for Tests of Details of Balances
Chapter 16

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

3. Tests of Details of Balances, Controls, and Substantive Transactions
Tests of Controls
Substantive tests of transactions
Sampling for tests of details of balances

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

5. 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.

6. Tests of Controls and Substantive Tests of Transactions
Step 1
State the objectives of the audit test.
Step 2
Decide whether audit sampling applies.
Step 3
Define attributes and exception conditions.
Step 4
Define the population.
Step 5
Define the sampling unit.

7. Audit Sampling for Tests of Details of Balances
Step 1
State the objectives of the audit test.
Step 2
Decide whether audit sampling applies.
Step 3
Define misstatement conditions.
Step 4
Define the population.
Step 5
Define the sampling unit.
Difference

8. Tests of Controls and Substantive Tests of Transactions
Step 6
Specify the tolerable exception rate.
Step 7
Specify acceptable risk of assessing
control risk too low.
Step 8
Estimate the population exception rate.
Step 9
Determine the initial sample size.

9. Audit Sampling for Tests of Details of Balances
Step 6
Specify tolerable misstatement.
Step 7
Specify acceptable risk of incorrect
acceptance.
Step 8
Estimate misstatements in the
population.
Step 9
Determine the initial sample size.
Difference

10. Tests of Controls and Substantive Tests of Transactions
Step 10
Select the sample.
Step 11
Perform the audit procedures.
This is the same as in
“Audit Sampling for Tests of Details of Balances.”

11. Tests of Controls and Substantive Tests of Transactions
Step 12
Generalize from the sample
to the population.
Step 13
Analyze the exceptions.
Step 14
Decide the acceptability of the population.

12. Audit Sampling for Tests of Details of Balances
Step 12
Generalize from the sample
to the population.
Step 13
Analyze the misstatements.
Step 14
Decide the acceptability of the population.
Difference

13. 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

14. Apply monetary unit sampling.
Learning Objective 3
Apply monetary unit sampling.

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

16. 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.

17. 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).

18. The Auditor Generalizes from the Sample to the Population Using MUS
Attributes sampling tables are used to
calculate the results.
The attributes results must be converted to dollars.
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.

19. Generalizing from the Sample to the Population
Assumption 1
Overstatement amounts equal 100 percent;
understatement amounts equal 100 percent;
misstatement bounds at a 5 percent ARIA are:
Upper misstatement bound
= $1,200,000 × 3% × 100% = $36,000
Lower misstatement bound

20. Generalizing from the Sample to the Population
All amounts have to be overstatements.
All population items misstated have to
be 100 percent misstated.

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

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

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

24. 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.

25. Generalizing When Misstatements 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.

26. Illustration of the Auditor’s Decision Rule for MUS
– Tolerable
Misstatement
$0 Misstatement
+ Tolerable
Misstatement
LMB
UMB #1
LMB
UMB #2 #2
LMB
UMB #3
LMB
UMB #4
LMB
UMB #5

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

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

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

30. Frequency Distribution of Sample Means
Frequency of values
in percent
Value of in dollars x

31. Sampling Distribution
The mean value of all the sample means
is equal to the population mean
(X)
A corollary is that the sample mean value
with the highest frequency of occurrence
is also equal to the population mean.
(x)

32. Sampling Distribution
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.

33. Sampling Distribution
The percentage of sample means between
any two values of the sampling
distribution is measurable.

34. Sampling Distribution for a Population Distribution
Mean
Sampling distribution –
Normal
Population distribution –
Skewed
Frequency of values
in percent
Value of in dollars x

35. Variables Methods Difference estimation Ratio estimation
Mean-per-unit estimation

36. Stratified Statistical Methods
All of the elements of the population are
divided into two or more subpopulations.
Each subpopulation is independently tested.

37. Sampling Risks (ARIA and ARIR)
Actual State of the Population
Actual Audit Materially Not Materially
Decision Misstated Misstated
Conclude that the Correct conclusion Incorrect conclusion
population is – no risk – risk is ARIR
materially
misstated
Conclude that the Incorrect conclusion Correct conclusion
population is – risk is ARIA – no risk
not materially
misstated

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

39. Plan the Sample and Calculate the 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.

40. Plan the Sample and Calculate the Sample Size
Specify acceptable risk.
ARIA
ARIR

41. Estimate Misstatement in the Population
Estimate an expected point estimate.
Make an advance population standard deviation
estimate – variability of the population.

42. Calculate the Initial Sample Size
n = {[SD*(ZA + ZB)N] ÷ (TM – E*)}2
where:
n = initial sample size
SD* = advance estimate of the standard deviation
ZA = confidence coefficient for ARIA
ZB = confidence coefficient for ARIR
N = population size
TM = tolerable misstatement for the population (materially)
E* = estimated point estimate of the population misstatement

43. Select the Sample and Perform the Procedures
Perform the audit procedures.

44. Evaluate the Results Compute the point estimate
of the total misstatement.
Compute an estimate of the
population standard deviation.
Compute the precision interval.
Compute the confidence limits.

45. 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

46. Analyze 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.

47. Auditor’s Decision Rule for Difference Estimation
– Tolerable
Misstatement
$0 Misstatement
+ Tolerable
Misstatement
LCL
UCL #1
LCL
UCL #2 #2
LCL
UCL #3
LCL
UCL #4
LCL
UCL #5

48. End of Chapter 16