Chartered Accountants of
Audit
Conference in 2007
Fundamentals
Auditing
ASA 530 – Audit Sampling and Other Means of Testing
Michael Cain, FCA
Audit & Accounting Technical Director
Nexia International – Australia and New Zealand
charteredaccountants.com.au
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Sampling Experiment
Choose a Numbe r from 1 to 10
16
14
12
10
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
Sampling Experiment
Select an Invoice for Testing
12
10
8
6
4
2
0
1
2
3
4
5
6
7
8
Sampling Experiment – Same Birthday?
30
25
20
15
10
5
0
1
2
3
4
5
6
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.
Sampling
ASA 530: Sampling
> ASAs do not prescribe any particular
way of determining the sample size or
selecting the sample.
> AARF Audit Guide No 1 (available at
Institute library) outlines methods for
determining the sample size.
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.
> 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.
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 (ASA
530.06.
> 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).
Definition and features
> ASA 530: Sampling
> Key issue is to select a sample that is
representative of the population.
> Remember:
> % coverage is no guarantee of a
representative sample.
> The number of items in the population has
little effect on the sample size, unless the
population is small.
Sampling risk defined
>
Sampling risk: the probability that
the auditor has reached an incorrect
conclusion because audit sampling
was used rather than 100% examination
(i.e. correctly chosen sample was not
representative of the population).
Non-sampling risk defined
>
Non-sampling risk: arises from
factors, other than sample size, that
cause an auditor to reach an incorrect
conclusion, such as the possiblility
that:
•
The auditor will fail to recognise
misstatements included in examined
items.
•
The auditor will therefore apply a
procedure that is not effective in
achieving a specific objective.
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.
Statistical sampling defined
>
Statistical sampling: any approach to
sampling that has the following
characteristics:
•
Random sample selection.
•
Use of probability theory to evaluate
sample results, including measurement of
sampling risk.
>
Major advantage of statistical sampling over
non-statistical sampling methods is
defensibility, thorough quantification of
sampling risk.
>
Refer ASA 530.13
Non-statistical sampling
> Non-statistical sampling: sampling approaches
that do not have all the characteristics of statistical
sampling.
> Major advantage of non-statistical sampling is
greater application of audit experience.
> The basic principles and essential procedures
identified in ASA 530 apply equally to both
statistical and non-statistical sampling.
Plan the sample
1. State the objectives of the audit test
2. Decide whether audit sampling applies
3. Define attributes and deviation conditions
4. Define the population
5. Define the sampling unit
6. Specify the tolerable deviation/misstatement rate
7. Specify allowable risk of overreliance/incorrect
acceptance
8. Estimate population deviation/misstatement in the
population
9. Determine initial sample size
Select the sample and perform the
audit procedures
10.
Select the sample
11.
Perform the audit procedure
Evaluate the results
12.
Generalise from the sample to
the population
13.
Analyse the exceptions
14.
Decide the acceptability of the
population
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.
Planning and designing sample for
tests of controls
> Auditor should consider:
• Audit objectives (assertions of audit interest).
• Tolerable error — maximum error rate that
would till support control risk assessment.
• 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.
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.
Defining the sampling unit
> 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
Probability Proportionate to Size
Sampling (PPS) or Dollar Unit
Sampling (DUS).
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.
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.
Factors that influence sample size
for tests of controls
Determining the sample size –
test of controls
Judgemental considering statistical
sample sizes
Terminology
> Risk of overreliance
> Tolerable (error) rate
> Expected population deviation rate
Sample size estimation for attribute
sampling
Reliability factors for assessing
required confidence level
Determining the sample size –
test of controls
Example using Table 2
> 5% risk of overreliance.
> No errors are expected (= 0 deviation
rate)
> 10% tolerable error rate.
= Sample size of 29 items
Sample size estimation for attribute
samples (alternative method)
> An alternative method is to determine
sample size by reference to:
• Appendix, Table 3, for where allowable risk
of over-reliance (ARO) is 10% (90%
confidence). This ARO is common in
practice.
• Appendix, Table 2, for where allowable risk
of over-reliance is 5% (95% confidence).
Sampling 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.
Factors that influence sample
size for substantive testing
Determining the sample size
– substantive tests
Judgemental considering statistical
sample sizes
Terminology
>
Risk of incorrect acceptance
>
Tolerable error as a % of population
>
Expected error as a % of tolerable
error
Determining the sample size
– substantive tests
Example using Table 1
>
Acceptable risk of incorrect
acceptance is low.
>
Few errors are expected.
>
Tolerable error = 10% of
population.
= sample size of 23-30 items
Determining the sample size
– substantive tests
Judgemental using approximation of a
statistical technique
Terminology
>
Audit assurance (substantial,
moderate, little).
>
Expected error (little/no, or some).
>
Individually significant items.
>
Tolerable error.
Determining the sample size
– substantive tests
Example:
>
Recorded amount is $500,000.
>
No individually significant amounts.
>
Tolerable error = $50,000.
>
High degree of assurance required.
>
Few errors expected.
Determining the sample size
– substantive tests
Formula:
= Population recorded
amount/tolerable error x assurance
(reliability) factor = sample size.
= 500,000/50,000 x 3.0 = 30 items
Selecting the sample
> To draw conclusions about population or
strata, the sample needs to be typical of
characteristics of population or strata.
> Sample needs to be selected without bias
so that all sampling units in the population
or strata have a chance of selection.
> Common sampling techniques are:
• Random selection — random number generation
• Systematic selection
• Haphazard selection — select without conscious
bias
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:
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.
>
Step 3:
Continue to add sampling interval to random start,
and identify items to be sampled, e.g. item nos. 217,
717, 1217. . . 9217, 9717.
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.
> If auditor is unable to perform test on a
selected item (e.g. loss of documentation),
it is considered to be an error.
Analyse the exceptions
Tests of control
> Determine whether exceptions
are errors.
> Determine the no. of errors/error
rate.
> Compare to tolerable error.
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 revisit audit plan and reduce
reliance on IC and increase substantive
testing.
Analyse the misstatements
Substantive tests
> Determine any differences.
> Calculate projected error compare
to tolerable error.
Evaluating sample results
> To evaluate sample results, auditor determines the
level of error found in sample and directly projects
this error to relevant population. For example:
sample 20%, find misstatement of $10,000.
Therefore projected error = $50,000
($10,000/20%).
> Projected error is then compared with tolerable error
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 errors identified.
Decide the acceptability
Financial report overall
> Summary of audit differences
(mandatory requirement).
Dollar-unit sampling
> Sample unit is individual dollar units,
not physical units (transactions or
balances). A population with
$1,000,000 that contains 1,000
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, which will then
be tested.
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 $1,000) 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.
Illustration of DUS with systematic
selection
Determination of sample size for
substantive tests
n =
R
reliabilit y factor
=
TE  BV
tolerable error  book value
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
Sample Size 
1 000 000 x 3
 60
50 000
Illustration of DUS with systematic
selection
Evaluation of sample results for
substantive testing
Take Away
> Mandatory requirement to consider
> Defensible
> Focus on key areas
> Reduction in audit work? = < $$$
> Questions??