Michael Cain, FCA

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Chartered Accountants Audit Conference 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
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Sampling Experiment
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Sampling Experiment Same Birthday?
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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.

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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.

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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 auditors attention to areas of audit
  interest, especially risky or material items.

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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).

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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.

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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).

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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.

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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.

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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

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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.

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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

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Select the sample and perform the audit
procedures

• 10. Select the sample
• 11. Perform the audit procedure

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Evaluate the results

• 12. Generalise from the sample to
• the population
• 13. Analyse the exceptions
• 14. Decide the acceptability of the population

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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.

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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.

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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.

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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).

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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.

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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.

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Factors that influence sample size for tests of
controls
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Determining the sample size test of controls

• Judgemental considering statistical sample sizes
• Terminology
• Risk of overreliance
• Tolerable (error) rate
• Expected population deviation rate

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Sample size estimation for attribute sampling
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Reliability factors for assessing required
confidence level
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• 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

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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).

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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.

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Factors that influence sample size for
substantive testing
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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

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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

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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.

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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.

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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

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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

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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
• 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.

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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.

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Analyse the exceptions

• Tests of control
• Determine whether exceptions are errors.
• Determine the no. of errors/error rate.
• Compare to tolerable error.

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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 gt SDR rate is 4.
• Auditor compares with tolerable deviation rate
  (TDR). If SDR lt TDR, sample results support
  auditors planned reliance on IC.
• If SDR gt TDR, sample results do not support
  auditors planned reliance on IC, auditor will
  revisit audit plan and reduce reliance on IC and
  increase substantive testing.

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Analyse the misstatements

• Substantive tests
• Determine any differences.
• Calculate projected error compare
• to tolerable error.

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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.

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Decide the acceptability

• Financial report overall
• Summary of audit differences (mandatory
  requirement).

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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.

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Advantages of dollar-unit sampling (DUS)

• Directs auditors 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 auditors attention towards overstatement
  errors.
• However, a disadvantage is that it directs
  auditors attention away from understatement
  errors.

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Illustration of DUS with systematic selection
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Determination of sample size for substantive tests

• For convenience, this is usually presented as
• 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

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Illustration of DUS with systematic selection
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Evaluation of sample results for substantive
testing
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Take Away

• Mandatory requirement to consider
• Defensible
• Focus on key areas
• Reduction in audit work? lt
• Questions??