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SESSION 19 – AUDIT SAMPLING OVERVIEW Objective To identify and describe audit sampling and other selective testing procedures GATHERING AUDIT EVIDENCE Selection ALL ITEMS (100%) Basic principles methods SPECIFIC ITEMS AUDIT SAMPLING Definitions Application Judgmental selection DESIGN Basic principle Sampling plan Sample size SELECTION Basic principle Common methods Other methods STATISTICAL v NONSTATISTICAL Statistical Non-statistical TESTING Essential procedure Basic principle Error projection Evaluation SAMPLE RESULTS 1901 SESSION 19 – AUDIT SAMPLING GATHERING AUDIT EVIDENCE 1.1 Basic principles 1.1.1 Selection methods Items should be selected for testing by appropriate means Any one or a combination of selecting all items (100% examination) selecting specific items audit sampling 1.1.2 Risk considerations Professional judgment should be used to: assess audit risk; and design audit procedures to reduce audit risk to an acceptable low level This requires consideration of: inherent, control and detection risk; sampling and non-sampling risk SELECTING ALL ITEMS Example Suggest circumstances in which a 100% check of a class of transactions or account balances check may be necessary Solution 1902 SESSION 19 – AUDIT SAMPLING SELECTING SPECIFIC ITEMS Example Suggest reasons why it is unnecessary for an auditor to carry out a complete check of all the transactions and balances of a business Solution 3.1 Judgmental selection 3.1.1 Factors to consider Knowledge of business Preliminary assessments of inherent and control risk Characteristics of the population being tested 3.1.2 Specific items High-value or key items All items over a certain amount Items to obtain information Items to test procedures 3.1.3 Main advantage Usually an efficient means of gathering audit evidence 3.1.4 Main disadvantage It is NOT audit sampling , therefore cannot validly project results to population 1903 SESSION 19 – AUDIT SAMPLING AUDIT SAMPLING [ISA 530] 4.1 Definitions Audit sampling – applying procedures to less than 100% of items such that all sampling units have a chance of selection in order to form a conclusion concerning the population Error (in Audit sampling) – either a control deviations (in tests of control) or a misstatement (in a substantive procedure) Anomalous error – an error that arises from an isolated event that has not recurred other than on specifically identifiable occasions and is therefore not representative of errors in the population Population − the entire set of data from which the auditor wishes to sample For example, all items in an account balance or a class of transactions A population may be divided into strata, or sub-populations, with each stratum being examined separately Sampling risk − arises from the possibility that the auditor’s conclusion, based on a sample, may be different from the conclusion that would be reached if the entire population were subjected to the same audit procedure Two types: (a) the risk the audit will conclude that control risk is lower than it actually is (for a test of control) or that a material error does not exist when in fact it does (for a substantive test) This type of risk affects audit effectiveness and is more likely to lead to an inappropriate audit opinion (b) the risk the auditor will conclude that control risk is higher than it actually is (for a test of control) or that a material error exists when in fact it does not (for a substantive test) This type of risk affects audit efficiency as it would usually lead to additional work to establish that initials conclusions were incorrect Confidence level – the mathematical complement of risk (e.g 5% risk ≡ 95% confidence) Non-sampling risk − arises from factors that cause the auditor to reach an erroneous conclusion for any reason not related to the size of the sample For example, the auditor might use inappropriate procedures or misinterpret evidence and thus fail to recognize an error Sampling unit − the individual items constituting a population, for example credit entries on bank statements, sales invoices, trade receivable balances, or a monetary unit (e.g $1) Statistical sampling – any approach to sampling that has the following characteristics (a) random selection of a sample; and (b) use of probability theory to evaluate sample results, including measurement of sampling risk 1904 SESSION 19 – AUDIT SAMPLING A sampling approach that does not have characteristics (a) and (b) is considered nonstatistical sampling Stratification − the process of dividing a population into subpopulations, each of which is a group of sampling units, which have similar characteristics (often monetary value) Tolerable error (or deviation rate) − the maximum error in the population that the auditor is willing to accept (and still conclude that the result from the sample has achieved the audit objective) For substantive tests, this “precision” may be expressed as a monetary amount (which is less than overall materiality) or a percentage of population value For tests of control, precision is the maximum rate of failure of an internal control that can be accepted in order to place reliance on it (and is therefore likely to be small) 4.2 Application Audit sampling can be applied using either non-statistical or statistical sampling methods (see later in this Session) Stages in the sampling process include: sample design sample selection performing audit procedures (“testing”) error evaluation DESIGN 5.1 Basic principle Matters to be considered when designing an audit sample are: Test objectives; and Attributes of the population 5.2 Sampling plan In practice a “Sampling plan” may be drawn up to cover audit objectives population and sampling unit (or attribute) definition of an error (or deviation) sample size method(s) of sample selection 1905 SESSION 19 – AUDIT SAMPLING Matters to consider Specific audit objectives Note Population and sampling unit and use of stratification Appropriate and complete Note Sampling unit Note Sample size Stratification (into sub-popns) Note Considerations Sampling risk (acceptably low?) Tolerable error (= maximum error/deviation rate willing to accept) Expected error Notes (1) For example, “customers exist” (2) Must be appropriate (may be a “reciprocal” population) and complete (3) An item number n (e.g GRN) (4) Involves dividing a population into subgroups (“strata”) to create relatively homogenous groups in which variations in characteristics are likely to be small 5.3 Sample size Example — Tests of control For each of the following factors, decide whether the effect on sample size is an increase, decrease or no effect: 1906 SESSION 19 – AUDIT SAMPLING Solution Effect on Sample Size (1) Increase in intended reliance on accounting and internal control systems (2) Increase in tolerable error (3) Increase in the rate of deviation expected (“expected error”) (4) Increase in confidence level (i.e decrease in risk) (5) Increase in number of sampling units in the population Example — Substantive procedures For each of the following factors, decide whether the effect on sample size is an increase, decrease or no effect: Solution Effect on Sample Size (1) Increase in inherent risk assessment (2) Increase in control risk assessment (3) Increase in use of other substantive procedures aimed at the same assertion (4) Increase in confidence level (i.e decrease in risk) (5) Increase in tolerable error (6) Increase in expected error (7) Stratification of the population (8) Increase in number of sampling units in the population 1907 SESSION 19 – AUDIT SAMPLING SELECTION 6.1 Basic principle Items should be selected in such a way that all sampling units have a chance of selection 6.2 Most commonly used methods Random number selection by use of random number tables or a computerised random number generator Systematic (also called “interval”) selection uses a constant interval between items selected (with a random start) Value-weighted selection is a method which uses monetary unit values, rather than the items, as the sampling population CAUTION: The sampling units must not be structured in such a way that the sampling interval corresponds with a pattern in the population Haphazard selection i.e without following a structured technique, may be an acceptable alternative (to random methods) provided that conscious bias and predictability are avoided 6.3 Other methods Block sampling (e.g all items on a particular page) is not generally appropriate because populations may be structured so that items in a sequence have similar characteristics to each other but different characteristics to items elsewhere in the population TESTING 7.1 Essential procedure Audit procedures appropriate to the test objective should be performed on each item selected If an inappropriate item is selected (e.g a document which has been made “void”) an appropriately chosen replacement must be tested instead If the planned procedure cannot otherwise be performed (e.g if a customer does not reply to a direct confirmation request) a suitable alternative should be performed (e.g examination of after-date cash receipts) If no suitable alternative test can be performed, assume that item to be an error 1908 SESSION 19 – AUDIT SAMPLING SAMPLE RESULTS 8.1 Basic principles The auditor should: consider the sample results; consider the nature and cause of any identified errors; and their potential effect on: − − the test objective other audit areas evaluate sample results to confirm or revise the preliminary assessment of the relevant characteristic of the population Consider qualitative aspects: ISOLATED Obtain corroborative evidence of anomalous error 8.2 COMMON FEATURE Identify sub-population Extend audit procedures in sub-stratum Error projection Monetary errors (i.e in respect of substantive procedures) should be projected The effect of projected error (on test objective and other audit areas) should be considered Compare: Projected error + Anomalous error vs Tolerable error Note that, for tests of control no projection is necessary (i.e sample error rate represents population error rate) (See Illustration below.) 1909 SESSION 19 – AUDIT SAMPLING Illustration Population of trade receivables: Sample value Errors (e.g overpricing of invoices) Tolerable error $ 800,000 274,330 4,311 40,000 (5% of population) Projected error (ratio method): Error in sample × Population value 800 ,000 = $12,572 = 4,311 × 274 ,330 Sample value Conclusion: Trade receivables are not materially overstated (as the potential error is less than the tolerable error of $40,000) 8.3 Evaluation of results If projected error plus uncorrected anomalous error exceeds tolerable error, reassess sampling risk 8.3.1 Tests of control If CR higher than originally assessed, modify planned procedures e.g extend sample size test an alternative control extend substantive procedures 1910 8.3.2 Substantive procedures If maximum potential and/or most likely error exceeds tolerable error request management adjust for identified errors re-evaluate unadjusted errors SESSION 19 – AUDIT SAMPLING Illustration — Evaluating the results of a test of controls Summary of deviations: No of despatch notes not found No of despatch notes without invoices * include authorised cancellations 4* (3) DN ref (13,685) (17,345) _ Actual deviations _ Deviation rate: = 0.016 125 If the tolerable error is 1% (say) the sample size could be extended (to at least 200) If no further errors were found the deviation rate would be acceptable STATISTICAL v NON-STATISTICAL SAMPLING 9.1 Statistical sampling Involves use of random sample selection AND probability theory to evaluate sample results, and measure the sampling risk Statistical sampling precludes the use of haphazard selection In practice, a high level of mathematical competence is required if valid conclusions are to be drawn from sample evidence Most firms draw up complex plans which can be operated by staff without statistical training 1911 SESSION 19 – AUDIT SAMPLING Main types 9.1.1 ATTRIBUTE SAMPLING 9.1.2 VARIABLES SAMPLING Sampling units either have a property (attribute) or they not Sampling units can take a value within a continuous range Concerns rates of occurrence of events not monetary amounts Used to provide conclusions on monetary values Therefore used in tests of controls Population value can be estimated by extrapolation Example Suggest relative advantages/disadvantages of statistical sampling Solution Advantages 9.2 Disadvantages Non-statistical sampling Any approach which does not fulfil ALL the conditions set out above in the definition of statistical sampling Includes not only non-random selection but evaluating errors on a “judgement” basis 1912 SESSION 19 – AUDIT SAMPLING Example Suggest the relative advantages/disadvantages of non-statistical sampling Solution Advantages Disadvantages FOCUS You should now be able to: define audit sampling and explain the need for sampling; identify and discuss the differences between statistical and non-statistical sampling; discuss and provide relevant examples of the application of the basic principles of statistical sampling and other selective testing procedures; discuss the results of statistical sampling including consideration of whether additional testing is required 1913 SESSION 19 – AUDIT SAMPLING EXAMPLE SOLUTION Solution — Why 100% Population consists of a small number of large value items Items to which monetary materiality does not apply Unusual, one-off, or exceptional items Any area where the auditor is put upon enquiry Exceptionally high risk areas When the repetitive nature of a CIS operation makes 100% examination cost-effective Solution — Why not 100% Cost – expensive audit resources Time – financial statements unnecessarily delayed Users of a/cs not require 100% accuracy Tedium – audit staff might miss errors Does not add value – few errors would normally be expected Solution — Tests of control: factors influencing sample size Factor Sample size Explanation (1) ↑ Reliance on accounting and internal control systems (i.e CR↓) Increase ↑ To support a lower assessment of CR, will require larger sample sizes for tests of control (2) ↑ Tolerable error Decrease ↓ If the auditor is prepared to accept, say, a 3% error rate rather than 1%, the amount of testing (and hence sample size) is reduced (3) ↑ Expected error Increase ↑ If more errors are expected (perhaps because they are suggested by prior period or other findings) more work (i.e greater sample size) is required Note that if error rates are expected to be high, CR would be 100% ∴ no tests of control (4) ↑ Confidence (i.e ↓ Risk) Increase ↑ More confidence requires more audit work i.e larger sample sizes 1914 SESSION 19 – AUDIT SAMPLING Factor (5) ↑ Population Sample size Explanation Negligible The size of a large population has little, if any, effect on the sample size (e.g a sample size may be 60 regardless of whether the population contains 1,600 items, 16,000 items or 160,000 items) For small populations, evidence is usually gathered by selective testing procedures other than audit sampling Solution — Substantive procedures: factors influencing sample size Factor Sample size Explanation (1) ↑ IR ↑ Increase Consider the audit risk model If IR is higher, DR must be rendered lower – by doing more substantive work (i.e greater sample sizes) (2) ↑ CR ↑ Increase If CR is higher (i.e less reliance on tests of controls) more evidence must be obtained from substantive procedures (to render DR lower) (3) ↑ Other substantive procedures ↓ Decrease If assurance is (to be) obtained by analytical procedures, less assurance is required from tests of detail (4) ↑ Confidence ↑ Increase As for Solution (5) ↑ Tolerable error ↓ Decrease As for Solution (6) ↑ Expected error ↑ Increase As for Solution (7) Stratification ↓ Decrease The aggregate of the sample sizes from the strata will usually be less than that of a single sample drawn from the whole population (8) ↑ Population Negligible As for Solution However, an increase in the monetary value of a population may increase sample size unless materiality is increased proportionately 1915 SESSION 19 – AUDIT SAMPLING Solution — Statistical sampling Advantages Disadvantages Imposes more formal discipline to planning audit of a population Expense of implementation Objectively determines sample sizes Sample sizes may be “too large” Evaluates test results more precisely May be time-consuming (e.g manually determining cumulative monetary amounts) Quantifies sampling risk Staff training Use of judgement is not precluded (as it is required to set objectives and evaluate results) In tests of control, qualitative aspects of error evaluation cannot be statistically analysed Solution — Non-statistical sampling Advantages Disadvantages Approach used for many years, is well understood and refined by experience Sample sizes may be too small to satisfy stated objectives Can use greater judgement and expertise Sampling risk cannot be quantified Non-random selection may be quicker/more cost effective Statistical sampling may be cheaper if CAATs used No special knowledge of statistics required Sample sizes may be unnecessarily large Less expensive to apply (usually) Personal bias in sample selection may be unavoidable (e.g if using haphazard selection) 1916 ... management adjust for identified errors re-evaluate unadjusted errors SESSION 19 – AUDIT SAMPLING Illustration — Evaluating the results of a test of controls Summary of deviations: No of despatch notes... tests of detail (4) ↑ Confidence ↑ Increase As for Solution (5) ↑ Tolerable error ↓ Decrease As for Solution (6) ↑ Expected error ↑ Increase As for Solution (7) Stratification ↓ Decrease The... to obtain information Items to test procedures 3.1.3 Main advantage Usually an efficient means of gathering audit evidence 3.1.4 Main disadvantage It is NOT audit sampling , therefore cannot
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