Chapter 11
Audit sampling
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-1
Learning objective 1:
Definition and features
• Audit sampling: the application of an audit
procedure to less than 100% of the items within
a population to obtain audit evidence about
particular characteristics of the population.
• Audit sampling is important because it provides
information on:
–
–
–
How many items to examine
Which items to select
How sample results are evaluated and extrapolated
to the population in order to tell us something about
the population (e.g. level of misstatement).
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-2
Non-sampling and sampling risk
defined
• Sampling risk: the probability that the auditor
has reached an incorrect conclusion because
audit sampling was used rather than 100%
examination (ASA/ISA 530.05).
• Non-sampling risk: arises from factors,
other than sample size, that cause an auditor
to reach an incorrect conclusion, such as the
possibility that:
–
–
The auditor will fail to recognise misstatements included
in examined items
The auditor applies a procedure that is not effective in
achieving a specific objective.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-3
Characteristic of interest
• When sampling, the auditor identifies a particular
characteristic of the population to focus upon.
• For tests of control, the characteristic of interest is
the rate of deviation from an internal control policy
or procedure.
• For substantive tests, the characteristic of interest
is monetary misstatement in the balance.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-4
Learning objective 2:
Various means of gathering audit
evidence
• 100% examination: this is not a sampling
method.
• Selecting specific items: e.g. high value
or high risk — this is not a sampling method.
Items selected will not necessarily be
representative of the population.
• Audit sampling.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-5
Statistical and non-sampling sampling
•
Statistical sampling: an approach to sampling
that has the following characteristics:
–
–
–
Random sample selection
Use of probability theory to evaluate sample results
Major advantage is defensibility, thorough quantification of
sampling risk

•
Refer ASA/ISA 530.5(g)
Non-statistical sampling: sampling approaches
that do not have all the characteristics of statistical
sampling.
–
–
Major advantage is greater application of audit experience
The basic principles and essential procedures identified in
ASA/ISA 530 apply equally to both statistical and nonstatistical sampling.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-6
Current practice in Australia and
business risk assessment
• In Australia, there are some disparities with regard to
the practice of sampling within the large audit firms.
• Firms will usually use an unbiased approach but the
size of the sample they select will usually be
determined with the help of decision aids within the
firm.
• Sample sizes that are commonly used in practice are
around 20 items where a moderate level of testing is
required, or 30 items where more extensive levels of
testing are undertaken.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-7
Basic requirements of all audit samples
Whenever an auditor uses audit sampling (statistical
or non-statistical) the following requirements apply:
–
–
–
Planning and design: The auditor considers the relationship
of the sample to the relevant specific audit objective or
control objective and considers certain other factors that
should influence sample size.
Selection: Sample items are selected in such a way that the
sample can be expected to be representative of the
population.
Performing the procedure and evaluating results: The
auditor performs the required audit procedures on the items
selected, projects the results of the audit procedures
undertaken on the sample to the population and considers
sampling risk.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-8
Learning objective 3:
Planning and designing the sample
• Auditor must consider:
–
Objectives of the audit test (usually related
to an audit assertion of interest)
–
Population from which to sample
–
Possible use of stratification
–
Definition of the sampling unit.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-9
Defining the audit objective and
population
• Once the audit objective is specified, such as
reliance on controls or misstatement of account
balance, the auditor must consider what conditions
would constitute an error.
• The auditor must ensure that the population from
which the sample is to be selected is complete and
appropriate to the audit objective.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-10
Stratification
• Stratification: occurs when the auditor divides the
population into a series of sub-populations, each of
which has an identifying characteristic, such as
dollar value (ASA 530/ISA 530 Appendix 1,
paragraphs 1–4).
• Can assist with audit efficiency as it allows the
auditor to reduce the sample size by reducing
variability without increasing the sampling risk.
• Can direct auditor’s attention to areas of audit
interest, especially risky or material items.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-11
Defining the sampling unit
• The sampling unit is commonly the:
–
Transactions or balances making up the account
balance, or
–
Individual dollars that make up an account balance
or class of transactions, commonly referred to as
Monetary-Unit Sampling (MUS) or Dollar Unit
Sampling (DUS).
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-12
Learning objective 4:
Determining sample size
• Sample size is affected by the degree of sampling
risk the auditor is willing to accept.
• Auditor's major consideration in determining
sample size is whether, given expected results
from examining sample, sampling risk will be
reduced to an acceptably low level (ASA/ISA
530.07).
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-13
Factors that influence sample size
for tests of controls
• Appendix 2 to ASA/ISA 530 outlines the factors that
influence sample size for tests of controls as follows:
– The extent to which the auditor’s risk assessment
takes into account relevant controls (control risk
assessment)
– The tolerable rate of deviation
– The expected rate of deviation
– The auditor’s desired level of assurance
– The number of sampling units in the population.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-14
Factors that influence sample size
for substantive testing
• Appendix 3 to ASA/ISA 530 outlines the factors that
influence sample size for substantive testing as
follows:
–
–
–
–
–
–
–
The auditor’s assessment of risk of material misstatement
The use of other substantive procedures directed at the same
assertion
The auditor’s desired level of assurance that actual
misstatement is not greater than tolerable misstatement
The tolerable misstatement
The amount of misstatement the auditor expects to find in the
population (expected misstatement)
Stratification
The number of sampling units in the population.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-15
Learning objective 5:
Selecting the sample
• To draw conclusions about population or stratum,
the sample needs to be typical of characteristics
of population or stratum.
• Sample needs to be selected without bias so
that all sampling units in the population or stratum
have a chance of selection.
• Common sampling techniques are:
–
Random selection — random number generation
–
Systematic selection
–
Haphazard selection — select without conscious bias.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-16
Steps in systematic selection
For example, suppose the sample size is 20 and the number of
items in the population is 10 000:
•
Step 1:
Calculate the sample interval:
No. of items in population 10 000

 500
Sample size
20
•
Step 2:
•
Step 3:
Give every item in population chance of selection
by choosing a random number (random start)
within range of 1 and sampling interval (in this
example, 500), e.g. 217.
Continue to add sampling interval to random start,
and identify items to be sampled, e.g. item nos. 217,
717, 1217. . . 9217, 9717.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-17
Biases from haphazard sampling
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-18
Unacceptable sample selection
methods
• Block selection: the auditor selects all items of a
specified type processed on a particular day, week or
month.
• Judgmental selection (based on sample item
characteristics): the auditor selects large or unusual
items from the population or uses some other
judgmental criterion for selection.
–
This method has a conscious bias and cannot be considered
representative.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-19
Learning objective 6:
Performing the audit procedures
• To ensure conclusions arising from tests on audit
samples are appropriate, auditor must perform testing
on each item selected.
• If selected item is not appropriate for application
of testing procedure, a replacement item can be
selected (ASA/ISA 530.9–10).
• If auditor is unable to perform test on a selected item
(e.g. loss of documentation), it is considered to be an
error.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-20
Evaluating sample results
• To evaluate sample results, auditor determines
the level of misstatement found in sample and
directly projects this misstatement to relevant
population. For example: sample 20%, find
misstatement of $10 000. Therefore projected
misstatement = $50 000 ($10 000/20%).
• Projected misstatement is then compared with
tolerable misstatement for the audit procedure to
determine if characteristic of interest can be
accepted or rejected.
• Auditor should consider both the nature and
cause of any misstatement or deviations identified.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-21
Learning objective 7:
Sampling for tests of controls,
attribute sampling
• Audit sampling is useful for tests of controls,
especially involving inspection of source
documentation for specific attributes such as
evidence of authorisation (attribute sampling).
• Involves examination of documents for particular
attributes related to controls (e.g. authorisation).
• Results of attribute sampling can be used
to support or refute an initial assessment of
control risk.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-22
Planning and designing sample for
tests of controls
• Auditor should consider:
–
Audit objectives (assertions of audit interest)
–
Control risk assessment and tolerable deviation rate
–
Allowable risk of over-reliance — allowable risk
of assessing control risk too low
–
Expected error — amount of error the auditor
expects to find in the population.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-23
Audit objectives
• A sampling technique that is suitable for tests of
controls is attribute sampling.
• The following steps are necessary in considering the
relationship between the sample and the objective of
the test:
–
–
–
Identify relevant control objectives, policies and procedures
that are relevant to restricting substantive tests of the related
account balances.
Identify population and sample unit.
Define the characteristic of interest – so that an attribute
either exists or does not exist which means that a control
activity has either been complied with or not complied with.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-24
Control risk assessment and tolerable
deviation rate
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-25
Reliability factors for assessing
required confidence level
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-26
Sample size estimation for attribute
sampling
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-27
Sample size estimation for attribute
samples (alternative method)
An alternative method is to determine sample size by
reference to:
–
Table 11.3 (p. 566), for where allowable risk of overreliance (ARO) is 10% (90% confidence). This ARO is
common in practice.
–
Table 11.4 (p. 567), for where allowable risk of overreliance is 5% (95% confidence).
For example, where desired level of assurance is 90%,
(Table 11.3), tolerable deviation rate is 10%, and expected
deviation rate is 0, required sample size is 22.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-28
Selection of sample items for tests of
controls
• Having determined the appropriate sample size, it is
then a matter of determining which sample items to
select.
• The representative selection methods of random
selection and systematic selection generally apply to
both tests of controls and substantive tests.
• However, stratification is not usually applicable to tests
of controls.
• Systematic selection is often useful for tests of controls
because it helps to achieve the auditor’s internal
control objective of testing continuity of controls by
ensuring sampling is continuous throughout the year.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-29
Evaluation of attribute sample results
• Approach in practice is to use sample deviation
rate (SDR) as best estimate of population deviation
rate.
• For example, auditor selects 25 items, finds one
error => SDR rate is 4%.
• Auditor compares with tolerable deviation rate
(TDR). If SDR ≤ TDR, sample results support
auditor’s planned reliance on IC.
• If SDR > TDR, sample results do not support
auditor’s planned reliance on IC. Auditor will need
to consider reliance on IC and may consequentially
increase substantive testing.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-30
Learning objective 8:
Planning for substantive tests
• The following matters should be considered:
–
Relationship of sample to relevant audit objective (assertion
of audit interest)
–
Preliminary judgments about materiality levels
–
Auditor's allowable risk of incorrect acceptance
–
Characteristics of the population
–
Use of other substantive procedures directed at
same financial report assertion.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-31
Dollar-unit sampling
• Sample unit is individual dollar units, not physical
units (transactions or balances). A population
with $1 000 000 that contains 1000 physical
units or accounts is viewed as a population with
1 000 000 sample units.
• Individual dollar selected is attached to that
physical unit or account in which it is contained,
and the unit or account will then be tested.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-32
Advantages of dollar-unit sampling
(DUS)
• Directs auditor’s attention to material items.
For example, under traditional sampling,
debtor A (owing $10 000) and debtor B (owing
$1000) have equal chance of selection. Under DUS,
debtor A is ten times more likely to be selected and
tested.
• Directs auditor’s attention towards overstatement
errors.
• However, a disadvantage is that it directs auditor’s
attention away from understatement errors.
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-33
Determination of sample size for
substantive tests
For convenience, this is usually presented as:
n = BV xR
TE
E.g. account balance $1 000 000. Tolerable error $50 000.
Expected error is zero and risk of incorrect acceptance is 5%
 Reliability factor = 3 (Table 11.5, p. 572)
1 000 000 x 3
Sample Size 
 60
50 000
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-34
Illustration of DUS with systematic
selection
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-35
Illustration of DUS with systematic
selection (cont.)
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-36
Evaluation of sample results for
substantive testing
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-37
Learning objective 9:
Other statistical sampling approaches
• Mean per unit estimation
• Difference estimation
• Ratio estimation
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a Auditing and Assurance Services in Australia 4e by Grant Gay and Roger Simnett
Slides prepared by Roger Simnett
11-38