Presentation on theme: "What is Audit Sampling? Applying a procedure to less than 100% of a population To estimate some characteristic of the population Qualitative Quantitative."— Presentation transcript:
2What is Audit Sampling?Applying a procedure to less than 100% of a populationTo estimate some characteristic of the populationQualitativeQuantitative
3RiskSampling riskrisk that the auditors’ conclusions based on a sample may be different from the conclusion they would reach if they examined every item in the populationNonsampling riskrisk pertaining to nonsampling errorsCan be reduced to low levels through effective planning and supervisions of audit engagements
4Nonstatistical Sampling The auditor estimates sampling risk by using professional judgment rather than statistical techniquesProvides no means of quantifying sampling riskSample may be larger than necessary or auditors may unknowingly accept a higher than acceptable degree of sampling risk
5Advantages of Statistical Sampling Allows auditors to measure and control sampling risk which helps:Design efficient samplesMeasure sufficiency of evidenceObjectively evaluate sample results2
6Selection of Random Sample Random sample results in a statistically unbiased sample that may not be a representative sampleRandom sample techniquesRandom number tablesRandom number generatorsSystematic selection3
8Other Methods of Sample Selection Haphazard selectionSelect items on an arbitrary basis, but without any conscious biasBlock selectionBlock sample consists of all items in a selected time period, numerical sequence or alphabetical sequenceStratificationTechnique of dividing population into relatively homogeneous subgroups
11Dual Purpose TestTested used both as a test of control and substantiating the dollar amount of an account balanceEx. Test to evaluate the effectiveness of a control over recording sales transactions and to estimate the total overstatement or understatement of the sales account
12Allowance for Sampling Risk Amount used to create a range, set by + or – limits from the sample results, within which the true value of the population characteristic being measured is likely to liePrecisionWider the interval, more confident but less precise conclusionCan be used to construct a dollar interval
13Sample SizeSignificant effect on allowance for sampling risk and sampling riskSample size increase -> sampling risk and allowance for sampling risk decreaseSample size affected by characteristics of populationGenerally as Population increases -> sample size increase
14Requirements of Audit Sampling Plans When planning the sample consider:The relationship of the sample to the relevant audit objectiveMateriality or the maximum tolerable misstatement or deviation rateAllowable sampling riskCharacteristics of the populationSelect sample items in such a manner that they can be expected to be representative of the populationSample results should be projected to the populationItems that cannot be audited should be treated as misstatements or deviations in evaluating the sample resultsNature and cause of misstatements or deviations should be evaluated55
15Sampling Risks--Tests of Controls Actual Extent of Operating Effectivenessof the Control Procedure isAdequate InadequateThe Test of ControlsSample Indicates:Extent of OperatingEffectiveness isAdequateEffectivenessInadequateCorrectDecisionIncorrectDecision(Risk of AssessingControl RiskToo Low)IncorrectDecision(Risk of AssessingControl RiskToo High)CorrectDecision66
16Audit Sampling Steps for Tests of Controls Determine the objective of the testDefine the attributes and deviation conditionsDefine the population to be sampledSpecify:The risk of assessing control risk too lowThe tolerable deviation rateEstimate the population deviation rateDetermine the sample sizeSelect the sampleTest the sample itemsEvaluate the sample resultsDocument the sampling procedure77
17Attributes Sampling: Relationship Between the Planned Assessed Level of Control Risk and the Tolerable Deviation Rate
18Illustration of Attributes Sampling--Determining Sample Size Risk of Assessing Control Risk Too Low—5 percentTolerable Deviation Rate—9 percentExpected Population Deviation Rate—2 percent
19Figure 9.4: Statistical Sample Sizes for Tests of Controls at 5 Percent Risk of Assessing Control Risk Too Low
20Sample Size Sample size using Figure 9-4 (next slide) =68 (2) This means the auditor should select a sample of 68 items. We will discuss the (2) in a few slides.
21Attributes Sampling Evaluation of Results 2 possible approaches:Use the bracketed number from Table If you find that number or less deviations, conclude that you have accomplished your audit objective.Use Table 9.5 for a more precise conclusion.
22Example A--No Deviations Identified (Evaluating Attributes Sampling Results) Approach 1—You have met your audit objective (because the bracketed number was (2), you meet objective when you identify 0, 1 or 2 deviations). What can you say?“I believe that the deviation rate in the population is less than 9 percent.” You will be wrong 5 percent of the time when the deviation is exactly 9 percent. If the deviation rate is in excess of 9 percent you will be wrong even less than 5 percent of the time. The planned assessed level of control risk is achieved.Approach 2You have tested 68 items, a number not on Table 9-5 (next slideTo be conservative go to next lowest number on table (65) and use it for your conclusions (we could, but won't interpolate for a more precise answer).You have met your audit objective. Table 9-5 gives us an answer of 4.6 percent. What can you say?"I believe that the deviation rate in the population is less than 4.6 percent.” You will be wrong 5 percent of the time when the deviation rate is exactly 4.6 percent. If the deviation rate is in excess of 4.6 percent you will be wrong even less than 5 percent of the time. The planned assessed level of control risk is achieved.
23Figure 9.5 Statistical Sampling Results Evaluation Table for Tests of Controls: Achieved Upper Deviation Rate at 5 Percent Risk of Assessing Control Risk Too Low
24Example B--3 Deviations Identified (Evaluating Attributes Sampling Results) Approach 1—You have not met your audit objective. What can you say?“The achieved upper deviation rate is higher than 9 percent.” The planned assessed level of control risk is not achieved. You need to consider increasing the assessed level of control risk above the planned assessed level.Accordingly, you may not “rely” on internal control to the extent planned. Thus, the auditor will need to increase the scope of substantive procedures (the nature, timing, and/or extent).Approach 2—You have not met your audit objective. Table 9-5 provides us an answer of 11.5 percent“I believe that the deviation rate in the population is less than 11.5 percent.” You will be wrong 5 percent of the time when the deviation rate is exactly 11.5 percent. But this is not good enough as you wanted 9 percent rather than 11.5 percent. The planned assessed level of control risk is not achieved. You need to consider increasing the assessed level of control risk above the planned assessed level.As per Approach 1, an increase in the scope of substantive procedures is appropriate.
25Other Statistical Attributes Sampling Approaches Discovery samplingPurpose is to detect at least one deviation, with a predetermined risk of assessing control risk too low if the deviation rate in population is greater than specified tolerable deviation rateUseful in suspected fraudSequential (Stop-or-Go) SamplingAudit sample taken in several stages
26Sampling Risks--Substantive Tests The Population Actually isNot Materially MateriallyMisstated MisstatedThe SubstantiveProcedure SampleIndicatesMisstatement inAccount ExceedsTolerable AmountAccount Is LessThan TolerableAmountCorrectDecisionIncorrectDecision(Risk of IncorrectRejection)IncorrectDecision(Risk of IncorrectAcceptance)CorrectDecision88
27Audit Sampling Steps for Substantive Tests Determine the objective of the testDefine the population and sampling unitChoose an audit sampling techniqueDetermine the sample sizeSelect the sampleTest the sample itemsEvaluate the sample resultsDocument the sampling procedure99
28Population Variability—Why it Matters Item Population A Population B, ,000,, ,000,,Mean , ,100Standarddeviation ,395The variability determines how much information each of the items in the population tells you about the other items in the population.211
33Determining Sample Size--MPU (2 of 2) = Accounts
34Variables Sampling Illustration--MPU Adjusted allowancefor sampling risk =Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.)misstatement Sample sizeThis formula “adjusts” the allowance for sampling risk to consider the standard deviation of the audited values in the sample. It holds the risk of incorrect acceptance at its planned level.413
35Variables Sampling Illustration--MPU Using the text example with a standard deviation of audited values of $16Adjusted allowancefor sampling risk =Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.)misstatement Sample size= $364, _ ($100,000 * 1.64 * $16)225= $189,067We would still “accept” the book balance because the $6,250,000 (book value) falls within this intervalEstimate of total Adjusted allowanceaudited value for sampling risk$6,100, $189,067[$5,910, to $6,289,067]
37Difference Estimation Use sample to estimate the avg. difference between the audited value and book value of items in populationProjected = Sample Net Misstatement * Pop. ItemsMisstatement Sample itemsMost appropriate when size of misstatements does not vary significantly in comparison to book value
38Ratio EstimationUse a sample to estimate the ratio of misstatement in a sample to its book value and project it to populationProjected = Sample Net Misstatement * Pop. Book ValueMisstatement Book Value of SamplePreferred when the size of misstatements is nearly proportional to the book values of the itemsLarge accounts have large misstatements
39Nonstatistical Variables Sampling Illustration Plan Sample:Population:Size = 363 itemsBook value = $200,000Tolerable misstatement = $10,000Risk assessments:Inherent and control risk = Slightly below maximumOther substantive tests = Moderate815
40Nonstatistical Sampling--Determination of Sample Size Sample size = Population book value X Reliability factorTolerable misstatement= $200,000 X 2.0 = 40 items$10,000916
41Nonstatistical Sampling--Evaluation of Sample Results 40 accounts in sample$350 net overstatement$60,000 book value of sample itemsProjected misstatement:= [Sample net misstatement] X Book value of population[ Book value of sample ]= [ $350 ] X $200,000[$60,000]= $1,167Since the projected misstatement is only 11.7 percent ($1,167/$10,000) of tolerable misstatement, it is likely that the auditors would conclude that the account balance is materially correct.1017
42PPS Sampling Illustration Population book value = $6,250,000Other Information:Tolerable misstatement = $364,000Sampling risk--Incorrect acceptance = 5%Expected misstatement = $50,000Use Figures 9-14 and 9-15 to obtain a “reliability factor” and an “expansion factor”--next slide618
48Comparison of statistical sampling techniques for substantive procedures
49Audit Risk AR = IR x CR x DR where AR=The allowable audit risk that a material misstatement might remain undetected for the account balance and related assertions.IR= Inherent risk, the risk of a material misstatement in an assertion, assuming there were no related controls.CR= Control risk, the risk that a material misstatement that could occur in an assertion will not be prevented or detected on a timely basis by internal control.DR= Detection risk, the risk that the auditors’ procedures will fail to detect a material misstatement if it exists.