Module G

1. Module G 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

2. Learning Objectives • Define variables sampling and understand when variables sampling is used in the audit examination. • Understand the basic process underlying probability proportional to size (PPS) sampling as well as when PPS sampling should be used. • Identify the factors affecting the size of a PPS sample and calculate the sample size for a PPS sampling application. • Evaluate the sample results for a PPS sample by calculating the projected misstatement, incremental allowance for sampling risk, and basic allowance for sampling risk.

3. 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

4. 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

5. 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

6. 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

7. Major Steps in Variables Sampling • Determine the objective • Define characteristic of interest • Define the population • Determine sample size • Select the sample • Measure sample items • Evaluate sample results Planning Performing Evaluating

8. Major Steps in Variables Sampling: Planning • Determine the objective of sampling • Determine whether account balance is fairly stated under GAAP • Define characteristic of interest • Instance in which audited value of component differs from recorded value • Define the population • PPS sampling: Dollars comprising account balance

9. Major Steps in Variables Sampling: Performing • Determine sample size • Sampling risk (risk of incorrect acceptance) • Expected error • Tolerable error • Population size (recorded account balance) • Select sample items • Measure sample items

10. Effect of Factors on Sample Size in PPS Sampling

11. Sampling Risks in Variables Sampling

12. 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

13. Reliability and Expansion Factors Risk of Incorrect Acceptance 1% 5% 10% 15% 20% Reliability Factors 4.61 3.00 2.31 1.90 1.61 (0 Errors) Expansion Factors 1.90 1.60 1.50 1.40 1.30 • When incorporated into formula, factors are consistent with inverse relationship between risk of incorrect acceptance and sample size.

14. Major Steps in Variables Sampling: Performing • Determine sample size • 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 • Measure sample items

15. Major Steps in Variables Sampling: Performing • Determine sample size • Select sample items • Measure sample items • Perform appropriate substantive procedure • Calculate actual misstatement • Audited value – Recorded value

16. Major Steps in Variables Sampling: Evaluating • 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

17. 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

18. 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

19. Components of Upper Error Limit • Projected misstatement • Incremental allowance for sampling risk • Basic allowance for sampling risk

20. 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

21. Basic Allowance for Sampling Risk • Basic Allowance for Sampling Risk = Sampling interval x Reliability factor

22. Incremental Allowance for 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

23. The Auditor’s Decision