11-1Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Chapter 11

Audit Sampling

11-2Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Definition and Features

• Audit sampling: the application of an audit procedure to less than 100 per cent of the items within a population to obtain audit evidence about particular characteristics of the population.

• Ref.: AUS 514/ASA 530 (ISA 530).

Learning Objective 1:

11-3Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Importance of audit sampling

• 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

11-4Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Sampling risk defined

• Sampling risk: the probability that the auditor has reached an incorrect conclusion because audit sampling was used rather than 100 per cent examination (i.e. correctly chosen sample was not representative of the population).

11-5Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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 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.

11-6Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Characteristics 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.

11-7Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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.

Learning Objective 2:

11-8Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Statistical sampling defined

• Statistical Sampling: any approach to sampling that has the following characteristics:(a)Random sample selection; and

(b)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.

• Ref.: AUS 514.10/ASA 530.13 (ISA 530.10).

11-9Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Non-statistical sampling

• Non-statistical sampling: all 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 AUS 514/ASA 530 (ISA 530) apply equally to both statistical and non-statistical sampling.

11-10Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Planning and Designing the Sample

• Auditor must consider:– Objectives of the audit test;– Population from which to sample;– Possible use of stratification; and– Definition of the sampling unit.

Learning Objective 3:

11-11Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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.

11-12Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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.

11-13Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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).

11-14Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Determing 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.

Learning Objective 4:

11-15Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Factors that influence sample size for tests of controls

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Factors that influence sample size for substantive testing

11-17Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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

Learning Objective 5:

11-18Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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 selectionby choosing a random number (random start)within range of 1 and sampling interval (in thisexample, 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.

500 20

10000

size Sample

populationin items of No.

11-19Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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 selected item (e.g. loss of documentation), it is considered to be an error.

Learning Objective 6:

11-20Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Evaluating sample results

• To evaluate sample results, auditor determines the level of error found in sample and directly projects this error to relevant population. e.g. 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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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.

Learning Objective 7:

11-22Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Planning and designing sample for tests of controls

• Auditor should consider:– Audit objectives– Tolerable error – maximum error rate that would still

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

11-23Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Reliability factors for assessing required confidence level

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Sample size estimation for attribute sampling

11-25Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Sample size estimation for attribute samples (alternative method)

• An alternative method is to determine sample size by reference to:

– Table 11.5 (p. 532), for where allowable risk of over-reliance (ARO) is 10% (90% confidence). This ARO is common in practice.

– Table 11.6 (p. 532), for where allowable risk of over-reliance is 5% (95% confidence).

11-26Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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 internal control.

• This approach is consistent with standards and practice but is subject to criticism as it does not account for sample size or sample risk.

11-27Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Sampling for Substantive Tests

• The following matters should be considered:– Relationship of sample to relevant audit objective;– Preliminary judgments about materiality levels;– Auditor's allowable risk of incorrect acceptance;– Characteristics of the population; and– Use of other substantive procedures directed at same

financial report assertion.

Learning Objective 8:

11-28Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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.

11-29Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Advantages of dollar-unit sampling (DUS)

• Directs auditor’s attention to material items. E.g. 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.

11-30Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

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 (Table 11.4, p. 531)

n = RTE BV

= reliability factortolerable error book value

n = BV x RTE

60 000,50

3 x 1,000,000 Size Sample

11-31Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Illustration of DUS with systematic selection

11-32Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Illustration of DUS with systematic selection (Cont.)

11-33Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Evaluation of sample results for substantive testing

11-34Copyright 2006 McGraw-Hill Australia Pty Ltd Revised PPTs t/a Auditing and Assurance Services in Australia 3e by Grant Gay and Roger SimnettSlides prepared by Roger Simnett

Other statistical sampling approaches

• Mean per unit estimation;• Difference estimation; and• Ratio estimation.

Learning Objective 9: