Chapter 9
Audit Sampling – Part b
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Sampling to Test for Account Balance
Misstatements (Substantive Testing)
Basic steps:
1. Specify audit
objective of the test
2. Define misstatement
3. Define population
(and sampling units)
4. Choose sampling
method
5. Determine sample
size
6.
7.
8.
9.
10.
Select sample
Audit selected items
Evaluate sample
results
Perform follow-up
work as necessary
Document sampling
procedure and
results
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1. Define Specify Audit Objective
Sampling always relates to one specific procedure
usually testing one specific assertion
Specifying the audit objective determines the
population to test
 For example:
 If
objective is to determine existence, the sample should
be selected from recorded information
 - On the other hand, if the objective is to determine
completeness, the sample should be selected from a
complementary population such as source documents
(or cash disbursements if testing for unrecorded
payables)
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2. Define Misstatements

Misstatement is usually defined as
difference that affects the correctness of
the overall account balance

Misstatements should be defined before
sampling to:
 Preclude
auditor from rationalizing away
misstatements as isolated events
 Provide guidance to the audit team
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3. Define the Population

Group of items in an account balance that the
auditor wants to test. It does not include:
 Items

the auditor has decided to examine 100%
Items that will be tested separately
Important to properly define the population:
 Sample results can be projected only to the
group from which the sample is selected
 The population must be directly related to the
audit objective
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3. Define the Sampling Unit

Sampling units are the individual auditable
elements that make up the population

Example: sampling units for confirming
accounts receivable could be the
individual customer's balance or individual
unpaid invoices
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Identify Individually Significant Items


Many account balances are comprised of a few
large dollar items and many smaller items
Dividing a population into two or more
subgroups based on dollar amount can increase
audit efficiency
 Items
in excess of a specified dollar amount (top
stratum items) are examined 100%
 Items less than the specified amount (lower stratum
items) are sampled

This process (stratification) allows the auditor to
examine a significant portion ($ value) of an
account balance even though s/he examines a
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relatively few items
4. Choosing a Sampling Method

There are a number of sampling methods
an auditor may use
 Non-statistical
 Probability
proportional to size (PPS)
 Classical sampling methods (not covered in
this text/course)
Mean-per-unit
 Ratio estimation
 Difference estimation

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4. Choosing a Sampling Method
– Cont’d - Differences between methods)
A.
Measure of sampling risk


B.
Statistical methods provide an objective
measure of sampling risk
Non-statistical methods do not provide
such a measure
Tests for account balance


PPS is designed to test for overstatement
of an account balance
Classical methods test for both
overstatement and understatement
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4. Choosing a Sampling Method
– Cont’d (differences between methods)
C.
Statistical estimates


D.
PPS provides an estimate of the amount of
misstatement in the account
Classical methods provide an estimated range of
the account balance
Sample selection


PPS is a dollar-based approach; each dollar is a
sampling unit
Classical samples are selected using a variety of
sampling units e.g. balances or items
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4. Choosing a Sampling Method
– Cont’d
 Use of PPS would be appropriate if
Auditor
is testing for overstatements
in an account balance
 A dollar-based sampling approach
increases the probability of
selecting overstated items
Few or no misstatements expected
Individual book values (like a
subsidiary ledger) are available
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4. Choosing a Sampling Method
– Cont’d

One of the classical methods would be
appropriate if the auditor
 Is
concerned about understatements in an
account balance
 Expects numerous misstatements
 Is examining an account balance based on
estimates rather than a total of individual
items
 Is trying to estimate an account balance
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5 – 8. Determining Sample Size,
Selecting Sample, Evaluating Results




Sample size, method of selecting the sample, and the approach to
evaluating sample results all depend on the sampling method
used
Whichever sampling method is used, consideration must be given
to the risk of misstatement, sampling risk, and the auditor's
assessment of tolerable and expected misstatement
Tolerable misstatement
 Maximum misstatement an auditor will accept before deciding
the recorded account balance is materially misstated
Expected misstatement
 Based on results of other substantive tests and auditor's prior
experience with the client
 Expected misstatement should be less than tolerable
misstatement
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Steps in non-statistical sampling?

Determine sample size
 All significant items should be tested
 No way to mathematically control sampling

risk
Select the sample
 Sample must be representative of population
 Could use random-based method or haphazard

selection
Evaluate sample results
 Project misstatements to the population
 Consider sampling error
 Make judgment as to whether account is
materially misstated
likely to be
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Probability Proportional to Size
(PPS) Sampling




Dollar-based sampling approach where the
population is the number of dollars in the
account balance examined
Using dollars as sampling units means larger
dollar items in the account balance are more
likely to be selected in the sample
PPS is an effective sampling approach when the
auditor is testing for overstatements
Appropriate when few misstatements are
expected and individual book values are
available
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Probability proportional to size
(PPS) sampling: TD risk





To use PPS, the auditor must determine the allowable risk of the
sample failing to detect a material misstatement (test of details
risk) and tolerable and expected misstatements for the account
balance
Detection risk is the risk that the substantive audit procedures will
fail to detect material misstatements
There are two types of substantive audit procedures - those that
use sampling, and other (non-sampling) substantive procedures
Test of details (TD) risk is the part of detection risk related to
sampling; the risk that substantive sampling procedures will fail to
detect a material misstatement
Other substantive procedures risk (OSPR) is the risk that the
non-sampling procedures will fail to detect a material misstatement
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Probability Proportional to Size
(PPS) Sampling: TD risk– Cont’d:

The relation between TD risk and inherent
and control risks and OSPR is inverse
 High
inherent risk means the auditor is examining
transactions that are susceptible to misstatement
 High control risk means the client controls are
weak
 High OPSR means the non-sampling audit
procedures are not effective in detecting material
misstatements
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Probability Proportional to Size
(PPS) Sampling: TD risk– Cont’d:




In each of these situations, the auditor would
want to be more careful with his/her sampling
procedures
The auditor would want lower TD risk; less
chance of failing to detect material
misstatements with sampling procedures
Lower TD risk means the auditor wants a lower
risk of sampling procedures failing to detect
material misstatements
To achieve this lower risk of failing to detect, the
sample size must increase
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Probability Proportional to Size
(PPS) Sampling: Sample Size
PPS samples are usually selected using a fixed interval
sampling approach
 The sampling interval (I) is calculated as
I = TM - (EM x EEF)
RF
TM = Tolerable misstatement (in population)
EM = Expected misstatement (in population)
EEF = Error expansion factor (derived form tables)
RF = Reliability factor (derived form tables)
 Error expansion and reliability factors are based on TD risk

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Probability Proportional to Size
(PPS) Sampling: Sample Size

Sample size (n) is computed by dividing
the account book value by the sampling
interval
n = Population Book Value
Sampling Interval
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Probability Proportional to Size (PPS)
Sampling - Sample Selection
Sample items are often selected using a fixed interval approach
 Every nth dollar after a random start
 A random start is required to give every dollar in the population
an equal chance to be included in the sample
 The first sample item is the one that first causes the cumulative
total (cumulative book value + random start) to equal or exceed
the sampling interval
 Successive sample items are those first causing the cumulative
total to equal or exceed multiples of the interval
Sample composition:
 All top stratum items will be included in the sample
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 Lower stratum items will be sampled

Probability Proportional to Size: Zero or
Negative Balances

Zero balances
 Items
with zero balances have no chance of being
selected using PPS
 If evaluation is necessary, zero balance items should
be audited as a different population

Two approaches to deal with population items
with negative balances:
 Exclude
them from the selection process and test
them as a separate population
 Include them in the selection process and ignore the
negative sign
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Probability Proportional to Size:
Sample Evaluation

Based on sample results, the auditor computes
the upper misstatement limit
Upper misstatement limit (UML)
 Maximum dollar overstatement that might exist
in the population
 Given the misstatements detected in the sample,
at the specified TD risk level, UML is the sum of
three components:
 Basic
precision
 Most likely misstatement
 Incremental allowance for sampling error.
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Probability Proportional to Size:
Sample Evaluation – Cont’d
Evaluation:
 If the UML is less than the tolerable
misstatement, the account balance is
considered fairly presented
 If the UML exceeds the tolerable
misstatement, the account balance is not
fairly presented and further work is
necessary
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