E-1 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Overview of Sampling There are three kinds of lies: lies, damned lies,

E-2 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Audit Sampling The application of an audit procedure to less than 100 percent of the items within an account balance or class of transactions for the purpose of evaluating some characteristic of the balance or class

E-3 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. How Audit Sampling Differs from Sampling in Other Professions Generally evaluates whether amount is misstated rather than determine value. Distribution is skewed. Other evidence is gathered

E-4 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. When is Sampling Used? Study and evaluation of internal control –Selecting control procedures to verify compliance –Attribute sampling Substantive procedures –Selecting components or transactions of account balances for verification –Variables sampling Dual Purpose tests

E-5 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Sampling Risk Risk that the decision made based on the sample differs from the decision that would have been made by examining the population Cause is a nonrepresentative sample Controlled by: –Determining an appropriate sample size –Ensuring that all items have an equal opportunity of selection –Mathematically evaluating sample results

E-6 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Sampling Approaches Statistical sampling methods use the laws of probability to: –Select sample items –Evaluate sample results Statistical sampling methods control the auditor’s exposure to sampling risk Nonstatistical sampling violates one or both of the above criteria Both statistical sampling and nonstatistical sampling can be used in a GAAS audit

E-7 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Sampling 1.Determine sample plan and method of selection 2.Determine the objective 3.Define characteristic of interest 4.Define the population 5.Determine sample size 6.Select the sample 7.Measure sample items 8.Evaluate sample results Planning Performing Evaluating

E-9 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Precision and Reliability Precision (Allowance for sampling risk) –Closeness of sample estimate to true population value Reliability (Confidence) –Likelihood of achieving a given level of precision

E-11 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Example of Evaluating Sample Results (Continued) A 90% probability exists that the true average age is between 33 and 53 years (sample estimate  precision) A 10% probability exists that the true average age is less than 33 years or greater than 53 years

E-12 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Example of Evaluating Sample Results (Continued) Precision Interval 33 yrs 43 yrs 53 yrs Estimate EstimateEstimate - Precision+ Precision

E-13 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Example of Evaluating Sample Results (Continued) Precision Interval 33 yrs 43 yrs 53 yrs Estimate EstimateEstimate - Precision+ Precision 90%

E-14 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Attribute Sampling There are five kinds of lies: lies, damned lies, statistics, politicians quoting statistics, and novelists quoting politicians on statistics – Stephen K. Tagg

E-15 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Attribute Sampling Used to estimate the extent to which a characteristic exists within a population Used in the auditor’s study of internal control Goal: Estimate the rate at which the client’s internal control is failing to function effectively and compare to an allowable level (tolerable deviation rate)

E-16 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Decisions in Attribute Sampling SampleTolerableRely on Deviation  Deviationcontrols as RateRateplanned SampleTolerableReduce Deviation  Deviationplanned reliance RateRateon controls

E-18 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Summary of Sampling Risks Effectiveness Losses –Risk of assessing control risk too low (overreliance) –Risk of incorrect acceptance Efficiency Losses –Risk of assessing control risk too high (underreliance) –Risk of incorrect rejection

E-19 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Attribute Sampling 1.Determine the objective 2.Define deviation conditions 3.Define the population 4.Determine sample size 5.Select the sample 6.Measure sample items 7.Evaluate sample results Planning Performing Evaluating

E-20 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Attribute Sampling: Planning 1.Determine the objective of sampling Identify key controls that the auditor intends to rely upon 2.Define deviation conditions Instance in which control is not functioning as intended 3.Define the population Should reflect all potential applications of the control during the period being examined

E-21 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Attribute Sampling: Performing 4.Determine sample size Sampling risk (Risk of assessing control risk too low) Expected deviation rate Tolerable deviation rate Population size (not applicable in most instances) 5.Select sample items 6.Measure sample items

E-23 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. How to Determine Sample Size? Select AICPA Sample Size table corresponding to desired risk of assessing control risk too low Identify row related to appropriate expected deviation rate (EDR) Identify column related to appropriate tolerable deviation rate (TDR) Determine sample size at junction of row for EDR and column for TDR

E-24 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Sample Size Example Parameters –Risk of assessing control risk too low = 5% –Expected deviation rate = 2% –Tolerable deviation rate = 7%

E-25 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Sample Size Example (Continued) From AICPA Table (5% risk) Tolerable Deviation Rate EDR2%3%4%5%6%7% 1.00%**156937866 2.00%***181127 3.00%****195129 88

E-26 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Attribute Sampling: Performing 4.Determine sample size 5.Select sample items For statistical sampling, use unrestricted random selection or systematic random selection Haphazard selection or block selection are not appropriate for statistical sampling 6.Measure sample items

E-27 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Attribute Sampling: Performing 4.Determine sample size 5.Select sample items 6.Measure sample items Perform appropriate test of controls Calculate sample deviation rate = No. deviations  sample size

E-28 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Attribute Sampling: Evaluating 7.Evaluate sample results Problem with sample deviation rate is that it may result from a nonrepresentative sample Need to “adjust” sample deviation rate to control for the risk of assessing control risk too low Calculate a Computed Upper Limit (CUL)

E-29 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Evaluating Exceptions Voided Documents Unused or inapplicable documents Misstatement in estimating sequence Consider qualitative effect of deviations

E-30 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Computed Upper Limit (CUL) There is a (1 minus risk of assessing control risk too low) probability that the true population deviation rate is less than or equal to the CUL There is a (risk of assessing control risk too low) probability that the true population deviation rate exceeds the CUL Example: CUL = 6%, Risk of assessing control risk too low = 5% 95% probability 5% probability 0% 6%

E-31 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Components of the CUL CUL XXX Sample Deviation Rate(XXX) Allowance for Sampling Risk XXX or Sample Deviation Rate XXX Allowance for Sampling Risk XXX CUL XXX

E-32 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. How to Determine the CUL Select AICPA Sample Evaluation Table corresponding to desired risk of assessing control risk too low Identify row related to appropriate sample size –If cannot locate exactly, round down to next lowest sample size Identify column related to number of deviations noted Determine CUL at junction of row for sample size and column for deviations

E-33 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. CUL Example Parameters –Sample size = 50 –Risk of assessing control risk too low = 5% –No. of deviations = 3 Sample deviation rate 3  50 = 6%

E-34 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. CUL Example (Continued) From AICPA Table (5% risk) No. of deviations found n 012345 407.311.415.018.3** 505.99.212.117.419.9 604.97.710.212.514.716.8 14.8

E-36 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Making the Decision If CUL > Tolerable Deviation Rate: –Conclude that internal control is not functioning effectively –Options Increase sample size in hopes of supporting planned level of control risk Increase level of control risk, leading to more effective substantive procedures (lower detection risk)

E-37 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Making the Decision If CUL  Tolerable Deviation Rate –Conclude that the internal control is functioning effectively –Options Maintain planned level of control risk, leading to planned effectiveness of substantive tests Consider a further reduction in control risk, leading to less effective substantive procedures (higher detection risk)

E-38 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Sequential (Stop-or-Go Sampling) Select initial (smaller) sample and consider results Decision –Rely on control; discontinue sampling –Cannot rely on control Select additional items; make decision Discontinue sampling Advantage is that evidence may support reliance on control with a relatively small sample size Disadvantage is that auditor may continually extend the sample, creating inefficiencies

E-39 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Discovery Sampling Used when deviations from control are expected to be infrequent but very critical Allows the auditor to –Determine the necessary sample size to find at least one example of a deviation if such deviations exist –Determine the probability that the rate of occurrence of a deviation is less than a specific (low) level

E-41 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Variables Sampling USA Today has come out with a new survey- apparently three out of every four people make up 75% of the population – David Letterman

E-42 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Variables Sampling Used to estimate the amount (or value) of a population Substantive procedures –Estimate the account balance or misstatement –Compare account balance or misstatement to recorded amount or tolerable error Types of variables sampling approaches –Probability proportional to size (PPS) sampling –Classical variables sampling –Non Statistical Sampling

E-43 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Decisions in Variables Sampling SampleTolerableAccount Estimate of  Error balance is Error(Materiality)not misstated SampleTolerableAccount Estimate of  Errorbalance is Error(Materiality)misstated

E-45 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Nonstatistical Sampling Does not control the auditor’s exposure to sampling risk Permitted under generally accepted auditing standards Differences –Does not consider sampling risk in determining sample size or evaluating sample results –May use a nonprobabilistic selection technique (block or haphazard selection)

E-46 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Basic Procedure for Nonstatistical Sampling Select sample –Does not explicitly consider sampling risk in determining sample size –May use block or haphazard selection methods Measure sample items Evaluate sample results –Does not consider sampling risk in projected results to population –Compare determined misstatement to tolerable error

E-47 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Nonstatistical Sampling for Substantive Tests of Details Identify individually significant items Determine sample size Consider variation within the population

E-48 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Factors Influencing Sample Size Assessment of inherent risk Assessment of control risk Assessment of risk from other substantive tests Tolerable misstatement Expected errors and variance of population Number of items in population

E-50 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Example Recorded amount $190,000 Examine 100 percent—12 items totaling $70,000 Tolerable misstatement $4,000 Inherent risk and control risk “slightly below the maximum” Risk that other substantive procedures will fail to detect material misstatement—moderate Sample Size= 60 ($120,000x2/$4,000)

E-51 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Stratification Increases efficiency If not stratified—increase sample GroupsItemsRecorded Amount Sample $100-$1,000150$86,00040 < $1001,500$34,00020

E-52 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Projecting Misstatement Two acceptable methods –Project by dollar amount –Project average difference Consider sampling risk Compare to tolerable misstatement

E-53 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Probability Proportional to Size (PPS) Sampling Defines the sampling unit as individual dollar in an account balance Auditor will select individual dollars for examination Auditor will verify entire “logical unit” containing the selected dollar –Accounts receivable: Customer account –Inventory: Inventory item

E-54 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Advantages of PPS Sampling Results in smaller sample sizes Includes transactions or components reflecting larger dollar amounts Effective for overstatement errors Generally simpler to use than classical variables sampling

E-55 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Disadvantages of PPS Sampling Provides a conservative (higher) estimate of misstatement Not effective for understatement or omission errors Expanding a PPS sample is difficult if the initial conclusion is to reject account balance Requires special consideration for accounts with zero or negative balances

E-56 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Variables Sampling 1.Determine the objective 2.Define characteristic of interest 3.Define the population 4.Determine sample size 5.Select the sample 6.Measure sample items 7.Evaluate sample results Planning Performing Evaluating

E-57 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Variables Sampling: Planning 1.Determine the objective of sampling Select assertion: existence or occurrence, completeness, valuation 2.Define characteristic of interest Instance in which audited value of component differs from recorded value 3.Define the population PPS sampling: Dollars comprising account balance Classical variables sampling: Individual components or transactions comprising account balance

E-58 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Variables Sampling: Performing 4.Determine sample size Sampling risk (risk of incorrect acceptance) Expected error Tolerable error Population size (recorded account balance) 5.Select sample items 6.Measure sample items

E-61 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. PPS Sampling Formulae Sample size Recorded Balance x Reliability Factor Tolerable Error - (Expected Error x Expansion Factor) Sampling Interval Population Size (Recorded Balance) Sample Size Controls exposure to Sampling risk

E-62 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Reliability and Expansion Factors Risk of Incorrect Acceptance 1%5%10%15%20% Reliability Factors4.613.002.311.901.61 (0 Errors) Expansion Factors1.901.601.501.401.30 When incorporated into formula, factors are consistent with inverse relationship between risk of incorrect acceptance and sample size.

E-63 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Variables Sampling: Performing 4.Determine sample size 5.Select sample items Select random starting point in population Bypass number of dollars equal to sampling interval Select dollar and identify entire logical unit containing selected dollar Large items may account for more than one selection 6.Measure sample items

E-64 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Variables Sampling: Performing 4.Determine sample size 5.Select sample items 6.Measure sample items Perform appropriate substantive procedure Calculate actual misstatement –Audited value – Recorded value

E-65 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Major Steps in Variables Sampling: Evaluating 7.Evaluate sample results Problem with actual misstatement is that it may result from a nonrepresentative sample Need to “adjust” actual misstatement to control for the risk of incorrect acceptance Calculate an Upper Error Limit

E-66 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Upper Error Limit Has a (1 – risk of incorrect acceptance) probability of equaling or exceeding the true amount of misstatement A (risk of incorrect acceptance) probability exists that the true amount of misstatement exceeds the upper error limit

E-67 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Upper Error Limit If upper error limit is $50,000 and risk of incorrect acceptance is 5% –There is a 5% probability that the true misstatement exceeds $50,000 –There is a 95% probability that the true misstatement is less than or equal to $50,000 95%5% $0$50,000

E-68 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Components of Upper Error Limit Projected misstatement Incremental allowance for sampling risk Basic allowance for sampling risk

E-69 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Projected Misstatement Assumes the entire sampling interval contains the same percentage of misstatement as the item examined by the auditor Tainting % = Amount of Misstatement Recorded Balance of Item Projected = Sampling Interval x Tainting % Misstatement

E-70 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Incremental Allowance for Sampling Risk “Adjusts” the projected misstatement to control auditor’s exposure to sampling risk Procedure –Rank all projected misstatements less than sampling interval in descending order –Determine incremental reliability factor for each misstatement –Multiply projected misstatement by incremental reliability factor minus 1.00

E-71 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Basic Allowance for Sampling Risk Provides a statistical measure of the misstatement that may be included in sampling intervals in which a misstatement was not detected Basic Allowance for Sampling Risk = Sampling interval x Reliability factor

E-73 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. PLANNING Determine the test objective(s). Define the population. Define the sampling unit. Choose an audit sampling technique.

E-74 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. PLANNING Determine sample size. –Consider the variation within the population. –Determine the acceptable risk of incorrect acceptance. –Determine the tolerable misstatement. –Determine the expected amount of misstatement. –Consider the population size.

E-77 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. NONSTATISTICAL SAMPLING FOR TESTS OF ACCOUNT BALANCES The only differences between a nonstatistical sampling application and a statistical sampling application occur in the following steps: –Identifying individually significant items. –Determining the sample size. –Calculating the sample results.

E-80 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. NONSTATISTICAL SAMPLING AN EXAMPLE - CALABRO Jones has made the following decisions: –Based the results of the tests of controls, a low assessment is made for inherent and control risk. –Tolerable misstatement allocated to accounts receivable is $40,000. The expected amount of misstatement is $15,000. –There is moderate risk that other auditing procedures will fail to detect material misstatements. –All customer account balances greater than $25,000 are to be audited.

E-82 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. NONSTATISTICAL SAMPLING: CALCULATING SAMPLE RESULTS The AICPA's guidance describes two acceptable methods for projecting the amount of misstatement found in a nonstatistical sample: –Project the amount of misstatement by dividing the amount of misstatement by the percentage of the dollars of the population included in the sample. –Project the average misstatement found in the sample to the population.

E-85 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. MONETARY-UNIT SAMPLING (MUS) MUS uses attribute sampling theory to express a conclusion in monetary amounts rather than as a rate of occurrence.

E-86 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. ADVANTAGES OF MUS When the auditor expects no misstatements, MUS will normally result in a smaller sample size than classical variable methods. notThe calculation of sample size and the evaluation of the sample results are not based on the variation between items in the population. When applied using a PPS sample selection procedure MUS automatically results in a stratified sample

E-87 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. DISADVANTAGES OF MUS The selection of zero or negative balances generally requires special design consideration. The general approach to MUS assumes that the audited amount of the sample item is not in error by more than 100 percent. When more than one or two misstatements are detected using a MUS approach, the sample results calculations may overstate the allowance for sampling risk.

E-88 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. APPLYING MUS Defining the sampling unit (Step 3). Determining the sample size (Step 5). Selecting the sample (Step 6) - See Figure 9-1. Calculating sample results (Step 8). –No misstatements detected. –Misstatements detected.

E-95 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. CASE 3 - CONSIDERATION OF UNDERSTATEMENT ERRORS The net ULM is $107,072 ($110,566 - $3,494). When the ULM is adjusted for understatement errors, the risk of incorrect acceptance for the test is no longer 5 percent.

E-96 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. CLASSICAL VARIABLES SAMPLING Classical variables sampling uses normal distribution theory to evaluate the characteristics of a population based on sample data.

E-98 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. ADVANTAGES OF CLASSICAL VARIABLES SAMPLING When the auditor expects a large number of differences between book and audited values, classical variables sampling will normally result in a smaller sample size than monetary unit sampling. Classical variables sampling techniques are effective for both overstatements and understatements. The selection of zero balances generally does not require special sample design considerations since the sampling unit will not be an individual dollar but rather an account, transaction, or line item.

E-99 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. DISADVANTAGES OF CLASSICAL VARIABLES SAMPLING The auditor must estimate the standard deviation of the audited value to determine sample size. If few misstatements are detected in the sample data, the true variance tends to be underestimated and the resulting projection of the misstatements to the population is not likely to be reliable.

E-100 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. APPLYING CLASSICAL VARIABLES SAMPLING Defining the sampling unit Selecting the sample Determining sample size See example in the Appendix

E-103 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. The Auditor’s Decision Upper error limit  Tolerable error Accept account balance as fairly recorded Upper error limit > Tolerable error Conclude that account balance is not fairly recorded

E-104 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Classical Variables Sampling (Sample Size) Sample size N x [R(IR) + R(IA)] x SD 2 TE - EE Differences from PPS sampling –Standard deviation –Risk of incorrect rejection

E-105 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Reliability Factors for Classical Variables Sampling Sampling Risk 1%5%10%15%20% Risk of Incorrect Acceptance2.331.651.281.040.84 Risk of Incorrect Rejection2.581.961.651.441.28 When incorporated into formula, factors are consistent with inverse relationship between sampling risk and sample size.

E-106 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Classical Variables Sampling (Evaluating Results) Precision: Closeness of a sample estimate to the true value Precision Interval Estimate EstimateEstimate - Precision+ Precision

E-107 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Classical Variables Sampling (Evaluating Results) Precision interval has a (1 – risk of incorrect acceptance) probability of including the true balance Decision –If recorded account balance falls within the precision interval, accept as fairly recorded –If recorded account balance falls outside of the precision interval, conclude that the account is misstated

E-108 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. PPS Sampling vs. Classical Variables Sampling PPS is more appropriate when: –Overstatement errors are of greater concern –The standard deviation is difficult or impractical to estimate –No or few misstatements are anticipated –The auditor wishes to begin sampling during an interim period

E-109 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. PPS Sampling vs. Classical Variables Sampling Classical variables sampling is more appropriate when: –The auditor is concerned with both overstatement and understatement errors –The standard deviation can be estimated –Some levels of misstatement are anticipated –The auditor does not begin sampling until after year-end

E-1 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Overview of Sampling There are three kinds of lies: lies, damned lies,

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E-1 McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Overview of Sampling There are three kinds of lies: lies, damned lies,

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