2. Slide 9- 2
Audit Sampling Defined
SAS No. 39 defines audit sampling as
the application of an audit procedure to
less than 100 percent of the items within
an account balance or class of
transactions for the purpose of
evaluating some characteristic of the
balance or class (AU 350.01).
3. Slide 9- 3
Advantages of
Statistical Sampling
Design efficient samples
Measure sufficiency of evidence
Objectively evaluate sample results
4. Slide 9- 4
Requirements of
Audit Sampling Plans
When planning the sample consider:
» 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
5. Slide 9- 5
Selection of Random Sample
Random number tables
Random number generators
Systematic selection
Haphazard Selection
Note that these methods are often used in conjunction
with a stratification process.
6. Slide 9- 6
Terminology
Sampling risk
» Risk of assessing CR too high / Risk of
incorrect rejection
» Risk of assessing CR too low / Risk of
incorrect acceptance
Precision (allowance for sampling risk)
8. Slide 9- 8
Attribute Sampling Applied To
Tests Of Controls
Attribute sampling is a statistical method
used to estimate the proportion of a
characteristic in a population.
The auditor is normally attempting to
determine the operating effectiveness of
a control procedure in terms of
deviations from the prescribed internal
control.
9. Slide 9- 9
Sampling Risk for
Tests of Controls
Correct
Decision
Incorrect
Decision
(Risk of Assessing
Control Risk
Too High)
Incorrect
Decision
(Risk of Assessing
Control Risk
Too Low)
Correct
Decision
True State of Population
Deviation Rate Deviation Rate
Exceeds Is Less Than
Auditors’ Conclusion Tolerable Rate Tolerable Rate
From the Sample Is:
Deviation Rate
Exceeds
Tolerable Rate
Deviation Rate
Is Less Than
Tolerable Rate
10. Slide 9- 10
Attribute Sampling for
Tests of Controls
Determine the objective of the test
Define the attributes and deviation conditions
Define the population to be sampled
Specify:
» The risk of assessing control risk too low
» The tolerable deviation rate
» The estimated population deviation rate
Determine the sample size
Select the sample
Test the sample items
Evaluate the sample results
Document the sampling procedure
Planning
Performance
Evaluation
Documentation
11. Slide 9- 11
Discovery Sampling
A modified case of attributes sampling
Purpose is to detect at least one deviation (i.e.
critical deviations)
Useful in fraud detection
Auditor risk and deviation assessments:
» Risk of assessing control risk too low (i.e. 5%)
» Tolerable rate (normally set very low, i.e. < 2%)
» Expected deviation rate is generally set at 0
12. Slide 9- 12
Nonstatistical
Attributes Sampling
Determination of required sample size
» Must consider risk of assessing control risk too low
and tolerable deviation rate
» Need not quantify the risks
Evaluation of results
» Compare tolerable deviation rate to sample
deviation rate. Assuming appropriate n:
– If SDR somewhat less than TDR, then conclude that risk
of assessing control risk too low is set appropriately.
– If SDR approaches TDR it becomes less likely that PDR
< TDR
– Must use professional judgment
13. Slide 9- 13
Audit Sampling for Substantive Tests
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
Planning
Performance
Evaluation
Documentation
14. Slide 9- 14
Audit Sampling for Substantive Tests
Sampling Risk
True State of Population
Misstatement in Misstatement in
Account Exceeds Account Is Less
Auditors’ Conclusion Tolerable Amount Than Tolerable
From the Sample Is: Amount
Misstatement in
Account Exceeds
Tolerable Amount
Misstatement in
Account Is Less
Than Tolerable
Amount
Correct
Decision
Incorrect
Decision
(Risk of Incorrect
Rejection)
Incorrect
Decision
(Risk of Incorrect
Acceptance)
Correct
Decision
15. Slide 9- 15
Risk of Incorrect Acceptance (RIA)
Modification of audit risk model:
AR = IR x CR x DR
DR comprised of two types of substantive procedures,
each with an associated type of risk:
Risk associated with AP and other procedures that do not
involve audit sampling (AP)
Risk associated with procedures involving audit sampling (RIA)
AR = IR x CR x AP x RIA
RIA = AR /(IR x CR x AP)
16. Slide 9- 16
Classic Variables Sampling
Mean per-unit estimation
Difference and Ratio Estimation
» Appropriate when differences between audited and
book values are frequent
» Difference estimation is most appropriate when the
size of the misstatements does not vary
significantly in comparison to book value
» Ratio estimation is most appropriate when the size
of misstatements is nearly proportional to the book
values of the items.
17. Slide 9- 17
Mean Per-unit (MPU) Estimation
Determining the Sample Size
N = population size
Ur = incorrect rejection coefficient (Table 9-8)
SDE = estimated population standard deviation
A = planned allowance for sampling risk
2
××
=
A
SDUN
n Er
18. Slide 9- 18
Mean Per-unit (MPU) Estimation
Determining the Sample Size
N
)Xx( 2
∑ −
=σ
Standard deviation
1
)( 2
−
−
=
∑
n
Xx
s
Population SD
Sample SD
19. Slide 9- 19
MPU Estimation
Determining the Sample Size
Calculation of planned allowance for sampling
risk (A):
r
a
U
U
TM
A
+
=
1
TM = tolerable misstatement
Ua = Incorrect acceptance coefficient (Table 9-8)
Ur = incorrect rejection coefficient (Table 9-8)
20. Slide 9- 20
MPU Estimation
Adjusted Allowance for Sampling Risk
Calculation of adjusted allowance for sampling
risk (A´):
TM = Tolerable misstatement
Ua = Incorrect acceptance coefficient (Table 9-8)
SDC = Sample (calculated) standard deviation
n = sample size
n
SDUN
TMA Ca ××
−=′
21. Slide 9- 21
MPU Estimation
Estimated total audited value
= Mean audited value x Number of accounts
Acceptance interval
= Estimated total audited value +/- Adjusted allowance
for sampling risk
Projected misstatement
= Estimated total audited value – Book value of
population
22. Slide 9- 22
Nonstatistical Variables Sampling
Determination of required sample size
» Must consider IR, CR and AP risk
Evaluation of results
» Compare projected misstatement to tolerable
misstatement.
» As PM approaches TM then likelihood of material
misstatement increasing.
» Rule-of-thumb: if PM exceeds 1/3 of TM, PM
“becoming too high”
23. Slide 9- 23
Probability-proportional-to-size (PPS)
Sampling
Applies the theory of attributes sampling to estimate
the total dollar amount of misstatement in a population.
Population is defined by the individual dollars
comprising the population’s book value ($1 = 1 item).
Relatively easy to use and often results in smaller
sample sizes than classical variables approaches.
Assumptions underlying PPS sampling:
» Expected misstatement rate in the population is small.
» Amount of misstatement in physical unit should not exceed
recorded BV of the item.
» PPS focuses on overstatements.
24. Slide 9- 24
PPS Sampling
Determination of Sample Size
)(
0
EFEMTM
RFPBV
n
×−
×
=
PBV = population book value
RF = reliability factor (Table 9-14)
TM = tolerable misstatement
EM = expected misstatement
EF = expansion factor (Table 9-15)
25. Slide 9- 25
PPS Sampling
Sample Selection
Systematic selection is generally used with PPS sampling:
n
PBV
SI =
SI = sampling interval
PBV = population book value
n = sample size
26. Slide 9- 26
PPS Sampling
Evaluation of Sample Results
IABPPMULM ++=
ULM = upper limit on misstatement
PM = projected misstatement
BP = basic precision
IA = incremental allowance
Allowance for sampling risk
27. Slide 9- 27
PPS Sampling
Evaluation of Sample Results
Projected misstatement (PM)
If BV < SI, PM = TF x SI
TF = tainting factor = (BV – AV) / BV
» BV = book value
» AV = audit value
If BV > SI, PM = actual misstatement
28. Slide 9- 28
PPS Sampling
Evaluation of Sample Results
Allowance for sampling risk
Basic precision = SI x RF0
Incremental allowance
If no misstatements in sample found, IA = 0
If misstatements found:
For misstatements in which BV < SI, rank order
projected misstatements from largest to smallest,
multiply by corresponding incremental factor
(from Table 9-14) and sum to calculate IA.
29. Slide 9- 29
PPS Sampling
Evaluation of Sample Results
Compare ULM to TM:
If ULM < TM, conclude that population is not
misstated by more than TM at the specified
level of sampling risk.
If ULM > TM, conclude that the sample results
do not provide enough assurance that the
population misstatement is less than the TM
and balance adjustment may be warranted.
