Presentation on theme: "Audit Sampling for Tests of Controls and Substantive Tests of Transactions Chapter 15."— Presentation transcript:
1 Audit Sampling for Tests of Controls and Substantive Tests of Transactions Chapter 15
2 Learning Objective 1Explain the concept of representative sampling.
3 Representative Samples A representative sample is one in whichthe characteristics in the sample of auditinterest are approximately the same asthose of the population.In practice, an auditor can increase thelikelihood of a representative sample byusing care in designing the samplingprocess and selection, and evaluatingthe results.
4 Sampling Risks Sampling risk is the risk that an auditor reaches an incorrect conclusion becausethe sample is not representative of thepopulation.Sampling risk is an inherent part of sampling that results from testingless than the entire population.Nonsampling risk is the risk that audittests do not uncover existing exceptionsin the sample.
5 Minimizing Sampling Risk Sampling Risk MeterStep 1Step 2Adjust sample sizeUse appropriate sample selectionmethodIncreasing sample size reduces sampling risk and vice versa.Using an appropriate sample selection method increases the likelihood of representativeness.
6 Learning Objective 2Distinguish between statistical and nonstatistical sampling and between probabilistic and nonprobabilistic sample selection.
7 Statistical Versus Nonstatistical Sampling Similarities of both approaches:Step 2Step 1Select the sample and perform the testsStep 3Plan the sampleEvaluate the resultsThe purpose of planning the sample is to make sure that the audit tests are performed in a manner that provides the desired sampling risk and minimizes the likelihood of nonsampling error.Selecting the sample involves deciding how a sample is selected from the population.Evaluating the results is drawing conclusions based on the audit tests.
8 Statistical Versus Nonstatistical Sampling Differences in approach:Statistical sampling allows the quantificationof sampling risk in planning the sample (Step 1)and evaluating the results (Step 3)In nonstatistical sampling those items thatthe auditor believes will provide the mostuseful information are selected
9 Probabilistic Versus Nonprobabilistic Sample Selection Probabilistic sample selection is a methodof selecting a sample such that eachpopulation item has a known probabilityof being included in the sample.Nonprobabilistic sample selection is amethod in which the auditor uses professionaljudgment rather than probabilistic methods.
11 Probabilistic Versus Nonprobabilistic Sample Selection Probabilistic selection methods:1. Simple random sample selection2. Systematic sample selection3. Probability proportional to size sample selection4. Stratified sample selection
12 Nonprobabilistic Sample Selection Methods Directed sample selection is the selection ofeach item based on auditor’s judgmental criteria.Items most likely to contain misstatementsItems containing selected population characteristicsLarge dollar coverageAuditors are often able to identify which population items are most likely to be misstated. Examples include accounts receivable outstanding for a long time, purchases from and sales to officers and affiliated companies and unusually large or complex transactions.The auditor can sometimes select a sample that includes a large portion of total population dollars, and thereby reduce the risk of drawing an improper conclusion by not examining small items.
13 Nonprobabilistic Sample Selection Methods Block sample selection is the selectionof several items in sequence.Haphazard sample selection is theselection of items without any consciousbias on the part of the auditor.It is ordinarily acceptable to use block samples only if a reasonable number of blocks is used.The most serious shortcoming of haphazard sample selection is the difficulty of remaining completely unbiased in the selection.
15 Probabilistic Sample Selection Methods A simple random sample is one in whichevery possible combination of elementsin the population has an equal chanceof constituting the sample.Random number tablesComputer generation of random numbersoffers several advantagestime savingsreduced risk of errorautomatic documentationAuditors use random sampling when there is no need to emphasize one or more types of population items. An application of this concept is when selecting a sample for testing cash disbursements.
16 Random Sample Selection Tools Random number tablesComputer generation of randomnumbers offers several advantagestime savingsreduced risk of errorautomatic documentationRandom numbers are a series of digits that have equal probabilities of occurring over long runs and which have no identifiable pattern.Auditors usually prefer to use computer generation of random numbers over other probabilistic selection methods.
17 Probabilistic Sample Selection Methods Systematic sample selection:The auditor calculates an interval andthen selects the items for the samplebased on the size of the interval.The advantage of systematic selection is its ease of use. A systematic sample can be drawn quickly and the approach automatically puts the numbers in sequence.The interval is determined by dividingthe population size by the number ofsample items desired.
18 Probabilistic Sample Selection Methods Probability proportional to size:A sample is taken where the probabilityof selecting any individual population itemis proportional to its recorded amount (PPS).In many auditing situations it is advantageous to select samples that emphasize population items with larger recorded amounts. One such audit area is in the selection of customer accounts for confirmation. In this area, the auditor may select larger balances that may be susceptible to error or adjustment.
19 Learning Objective 4Define and describe audit sampling for exception rates.
20 Sampling for Exception Rates The occurrence rate, or exception rate,is the percent of items in the populationcontaining the characteristic or specificattribute of interest to the total numberof population items.For example, if the auditor determines that the exception rate for the internal verification of sales invoices is approximately 3%, then on average 3 of every 100 invoices are not properly verified.
21 Sampling for Exception Rates Following are types of exceptions inpopulations of accounting data:1. Deviations from client’s established controls2. Monetary misstatements in populationsof transaction data3. Monetary misstatements in populations ofaccount balance detailsKnowing the exception rate in a sample is used to estimate the exception rate in the entire population. Exceptions refer to both deviations from the client’s procedures and amounts that are not monetarily correct.
22 Learning Objective 5Use nonstatistical sampling in tests of controls and substantive tests of transactions.
23 Terms Used in Audit Sampling Terms related to planning:Characteristic or attributeAcceptable risk of assessing control risk toolow (ARACR)Tolerable exception rate (TER)Estimated population exception rate (EPER)Initial sample sizeAttribute is the characteristic being tested in the application.ARACR is the risk that the auditor is willing to take of accepting a control as effective or a rate of monetary misstatements as tolerable when the true population exception rate is greater than the tolerable exception rate.TER is the exception rate that the auditor will permit in the population and still be willing to conclude the control is operating effectively and/or the amount of monetary misstatements in the transactions established during the planning is acceptable.EPER is the exception rate that the auditor expects to find in the population before testing begins.Initial sample size is the sample size decided after considering the above factors in planning.
24 Terms Used in Audit Sampling Terms related to evaluating results:ExceptionSample exception rate (SER)Computed upper exception rate (CUER)Exception – deviation from the attribute in a sample item.Sample exception rate -- Number of exceptions in the sample divided by the sample size.CUER -- The highest estimated exception rate in the population at a given ARACR.
25 I: Plan the Sample State the objectives of the audit test. Step 1Step 2Step 3State the objectives of the audit test.Decide whether audit sampling applies.Define attributes and exception conditionsObjectives might be:Test the operating effectiveness of controlsDetermine whether the transactions contain monetary misstatementsWhen sampling is used, auditors must carefully define the characteristics being tested and the exception conditions.The population is those items about which the auditor wishes to generalize. The sample must be selected from the entire population as it has been defined.The sampling unit is defined by the auditor based on the definition of the population and objective of the audit test.Step 5Step 4Define the sampling unitDefine the population
26 I: Plan the SampleStep 7Step 6Specify acceptable risk of assessing control risk too lowSpecify the tolerable exception rate.TER represents the highest exception rate the auditor will permit in the control being tested and still be willing to conclude the control is operating effectively.For audit sampling in tests of controls and tests of transactions, that risk is called the acceptable risk of assessing control risk too low (ARACR). ARACR measures the risk the auditor is willing to take of accepting a control as effective when the true population exception rate is greater than TER.A combination of two factors has the greatest effect on sample size: TER minus EPER. The difference is precision of the initial sample estimate.Population size is not a significant factor and typically can be ignored especially for large populations.Auditors should make an advance estimate of the population exception rate to plan the appropriate sample size. If the EPER is low, a relatively small sample size will satisfy the auditor’s tolerable exception rate because a less precise estimate is required.Four factors determine the initial sample size for audit sampling: population size, TER, ARACR, and EPERStep 8Step 9Estimate the population exception rate.Determine the initial sample size
27 II: Select the Sample and Perform the Audit Procedures Step 11Step10Perform the audit proceduresSelect the sample
28 III: Evaluate the Results Step 12Step 14Generalize from the sample to the populationStep 13Decide the acceptability of the populationAnalyze exceptionsThe sample exception rate can be easily calculated from the actual sample results. SER equals the actual number of exceptions divided by the actual sample size.
30 Guidelines for ARACR and TER Tests of Transactions
31 Effect on Sample Size of Changing Factors Effect on initialType of change sample sizeIncrease acceptable risk ofassessing control risk too lowIncrease tolerable risk rateIncrease estimated populationexception rateIncrease population size (minor)
32 Actions When Population is Not Acceptable Revise TER or ARACRExpand the sample sizeRevise assessed control riskCommunicate with the auditcommittee or managementRevising the TER of ARACR is an alternative that should only be followed when the auditor has concluded that the original specifications were too conservative.An increase in sample size has the effect of decreasing the sampling error if the actual sample exception rate does not increase.If the results of the tests do not support the preliminary assessed control risk, the auditor should revise the assess control risk upward.
33 Summary of Audit Sampling Steps Plan the sample(Steps 1-9)To/FromStep 6Select the sample(Step 10)CompareComputedupperexceptionrateNumber ofexceptionsin sampleand actualsample sizePerform the tests(Step 11)Step 12FromEvaluate the results(Steps 12-14)To Step 14To Step 12
34 Learning Objective 6Define and describe attributes sampling and a sampling distribution.
35 Statistical Audit Sampling The statistical sampling method mostcommonly used for tests of controlsand substantive tests of transactionsis attributes sampling.
36 Sampling Distribution It is a frequency distribution of the resultsof all possible samples of a specified sizethat could be obtained from a populationcontaining some specific parameters.Attributes sampling is based on thebinomial distribution.
38 Learning Objective 7Use attributes sampling in tests of controls and substantive tests of transactions.
39 Application of Attributes Sampling Use of the tables:Select the table corresponding to the ARACRLocate the TER on the top of the tableLocate the EPER in the far left columnRead down the appropriate TER column untilit intersects with the appropriate EPER rowin order to get the initial sample size
40 Application of Attributes Sampling Effect of population size:Population size is a minor considerationin determining sample sizeRepresentativeness is ensured by the sampleselection process more than by sample size
41 Application of Attributes Sampling Select the samplePerform the audit proceduresEvaluate the results