Audit Sampling Concepts

1. Audit Sampling Concepts

2. Importance of Sampling • Auditor does not look at everything • How does this affect the opinion? • Auditor CANNOT look at everything • Why?

3. Purpose of Sampling • The auditor examines only a portion of the population in order to estimate • How much is a portion?

4. When to Do Sampling When: • The nature and materiality of the balance or class of transactions does not demand a 100% audit • A decision must be made about the balance or class of transactions. • The time and cost to audit 100% of the population would be too great

5. When is Sampling Used? To conduct: • Walk through tests • For tests of controls • Tests of details

6. Representative Sampling • Having a representative sample is important • What does representative mean?

7. Non-sampling risk: • Sampling risk:

8. Statistical Sampling • Uses the laws of probability for selecting and evaluating a sample from a population • Selected at random • Statistical calculations are used

9. Statistical vs. Non-Statistical Similarities • Both require a structured process • The use of stratification Differences • Sampling risk cannot be quantified

10. Non-Probabilistic Sample Selection Methods • Directed sample selection • When used? • Auditor often able to identify items likely to contain errors • Items containing selected characteristics • Large dollar item coverage

11. Block sample selection • A selection of several items in a sequence • Reasonable number of blocks must be chosen • Haphazard sample selection • Auditor goes through the population and haphazardly selects items

12. Probabilistic Sample Selection Methods • Sampling risk requires • Simple random sample selection • Every member of the population has an equal chance of being selected • Systematic sample selection • Auditor calculates an interval and use the interval to select sample

13. Major problem with systematic sampling is bias • Once the first item is chosen • No problem if • But some characteristics

14. Probability Proportionate-to-Size Sampling Methodology • A key statistical methodology • also known as • the sampling unit is • MUS allows the result to be stated

15. Attribute Sampling Methodology • Another key statistical methodology • very useful for tests of controls • The main question to be answered is • If the auditor can allow 5% deviations

16. Advantages of Statistical Sampling Provides: • for quantitative evaluation of the sample results • a more defensible expression of the test results • It is more objective

17. Disadvantages of Statistical Sampling • Requires random sample selection which may be more costly and time consuming. • Might require additional training costs for staff members to use statistics or specialized software

18. Advantages of non-statistical sampling • Allows the auditor to inject his or her subjective judgment in determining the sample size • May be designed so that it is equally effective and efficient as statistical sampling while being less costly

19. Disadvantages of non-statistical sampling • Cannot draw objectively valid statistical inferences from the sample results • Cannot quantitatively measure and express sampling risk.

20. The Main Phases of the Sampling Process Both statistical and non-statistical methods 1. Planning the sample 2. Selecting the sample • Performing the tests • Evaluating the results

21. Sampling Process • Fourteen steps in the sampling process. • Look at tests of controls versus tests of details

22. 1. State the Objectives of the Test Test of control: • Are the controls working as specified? • Are there monetary errors or fraud or other irregularities Test of detail: • Auditor wants to determine the maximum amount of overstatement and understatement that could exist based on the sample

23. 2. Decide if Audit Sampling Applies • Test of control: • some controls can be sampled • others cannot be • Test of detail: • sampling test of details depends on the nature of the population • high volume can be

24. 3. Define attributes and exception or error conditions

25. 4. Define the population • Population can be defined in a way to suit the audit tests • Must sample from the entire population as defined • In testing controls over sales, what is the population? • In testing details in accounts receivable it is the recorded dollar population • Most populations can be stratified, if needed.

26. 5. Define the sampling unit Tests of controls: • Usually a physical unit Test of detail: • If MUS • If non-statistical sampling

27. 6. Specify tolerable exception rate (TER) or specify materiality • Test of control • TER` • As TER increases • Test of detail • Materiality is used • These decisions require the use of

28. 7. Specify ARACR or ARIA • Test of control • What is ARACR? • Acceptable Risk of Assessing Control Risk Too Low • Test of detail • What is ARIA? • Acceptable Risk of Incorrect Acceptance

29. Test of control • Assume • TER 6% • ARACR 10% • But unknown to the auditor the true error rate is 8% • Test of detail • If ARIA changes from 10% to 5% • Since assurance required increases • When controls are good

30. 8. Estimate population exception rate or misstatements • Test of control • Estimated population error rate (EPER) • The lower the EPER, the smaller the sample size • Test of detail • Provide an advance estimate of the total dollar error, i.e. misstatements, in the population

31. 9. Determine the initial sample size • For non-statistical or judgmental sampling, professional judgment is used to calculate the sample size • For statistical sampling, mathematical formulae are used, either in specially prepared tables or using software designed for audit sampling • For stratified sampling, the sample is allocated among the strata

32. 10. Select the sample • Using the number of items determined in Step #9, choose the items from the population using the sampling unit defined in Step #5 • Use probabilistic or non-probabilistic methods • To enable quantification of sampling risk, probabilistic, i.e. statistical, methods must be used

33. 11. Perform the audit procedures • For test of controls, examine each item for the attribute defined in Step #3, recording all exceptions found • For test of details, apply the audit procedures designed in the audit program

34. 12. Generalize from the sample to the population • Test of controls sample error rate (SER) • But that is not necessarily equal to the actual population rate • In practice, auditors tend to test controls when they expect no exceptions • But ultimately, the method of generalization depends on the sampling methodology used

35. When generalizing tests of details, auditors deal with • Misstatements found are projected from the sample results to the population • Auditor must calculate a point estimate

36. To calculate the point estimate: • (Client Misstatement / Recorded Value of Sample) x Recorded Book Value of the Population • Thus for a misstatement of $500 in A/R with a sample value of $10,000 and a total book value of $25,000 • Note that if the population is divided into strata • The total point estimate may not be an adequate result for the population • The auditor must consider this fact

37. Calculating Point Estimate for a population

38. 13. Analyze exceptions or misstatements • Test of control • What breakdown in internal controls caused the exceptions? • Should additional substantive testing be conducted because of these results? • Test of detail • Were the misstatements caused by control exceptions? • Is additional substantive testing required?

39. 14. Decide the acceptability of the population • Test of control • If TER is sufficiently larger than SER • If TER – SER is too small • Test of detail • Compare the difference between the projection to the population • If projection is greater than materiality level

40. What if the auditor decides the population is NOT acceptable? What to do? • 1. Revise TER (tolerable error rate), ARACR, or ARIA (the risks of accepting incorrect populations) • 2. Expand the sample size. • 3. Revise assessed control risk. • 4. Report weaknesses in management letter.

41. Problem 11-22, p. 357 For the examination of the financial statements of Scotia Inc., Rosa Schellenberg, a public accountant, has decided to apply non-statistical audit sampling in the tests of sales transactions. Based on her knowledge of Scotia’s operations in the area of sales, she decides that the estimated population deviation rate is likely to be 3 percent and that she is willing to accept a 5 percent risk the true population rate is not greater than 6 percent. Given this information, Rosa selects a random sample of 150 sales invoices from the 5,000 prepared during the year and examines them for exceptions. She notes the following exceptions in her working papers. There is no other documentation. REQUIRED Which of the invoices in the table should be defined as an exception? Explain why it is inappropriate to set a single acceptable TER and EPER for the combined exceptions. State the appropriate analysis of exceptions for each of the exceptions in the sample.

42. Problem 11-25, page 358 You have just completed the accounts receivable confirmation process in the audit of Danforth paper Company Ltd., a paper supplier to retail shops and commercial users. Following are the data related to the process: Accounts receivable recorded balance $2,760,000 Number of accounts 7,320 A non-statistical sample was taken as follows: All accounts over $10,000 (23 accounts) $465,000 77 accounts under $10,000 $81,500 Materiality $100,000 Inherent and control risk are both high No relevant analytical procedures were performed. The table below gives the results of the confirmation procedures REQUIRED Evaluate the results of the non-statistical sample. Consider both the direct implications of the misstatements found and the effect of using a sample.

44. Problem 11-23 (p.357) You have been asked to do planning for statistical testing of the audit of cash receipts. Following is a partial audit program for the audit of cash receipts. • Review the cash receipts journal for large and unusual transactions. • Trace entries from the prelisting of cash receipts to the cash receipts journal to determine whether each is recorded. • Compare customer name, date, and amount on the prelisting with the cash receipts journal. • Examine the related remittance advice for entries selected from the prelisting to determine whether cash discounts were approved. • Trace entries from the prelisting to the deposit slip to determine whether each has been deposited. REQUIRED • Identify which audit procedures can be tested using attribute sampling. Justify your response. • State the appropriate sampling unit for each of the tests in part (a). • Define the attributes that you would test for each of the tests in part (a). State the audit object associated with each of the attributes. • Define exception conditions for each of the attributes that you have described in part (c). • Which of the exceptions would be indicative of potential fraud? Justify your response.

45. Problem 12-24, page 404 Lenter Supply Corp. is a medium sized distributor of wholesale hardware supplies in southern Manitoba. It has been a client of yours for several years and has instituted excellent internal control for the control of sales, at your recommendation. In providing control over shipments, the client has prenumbered “warehouse removal slips” that are used for every sale. It is company policy never to remove goods from the warehouse without an authorized warehouse removal slip. After shipment, two copies of the warehouse removal slip are sent to billing for the computerized preparation of a sales invoice. One copy is stapled to the duplicate copy of the prenumbered sales invoice, and the other copy is filed numerically. In some cases more than one warehouse removal slip is used for billing one sales invoice. The smallest warehouse removal slip number for the year is 14682 and the largest is 37521. The smallest invoice number is 47821 and the largest is 68507. In the audit of sales, one of the major concerns is the effectiveness of the control in making sure all shipments are billed. The auditor has decided to use attribute sampling in testing internal control.

46. State an effective audit procedure for testing whether shipments have been billed. What is the sampling unit for the audit procedure? • Assuming the auditor expects no deviations in the sample but is willing to accept a TDR of 3%, at a 10% ARACR, what is the appropriate sample size?

48. EPDR

49. n = n’ 1 + n’/N Effect of population size -Initial sample size only -Possible to make adjustment to initial sample size based on overall population size -Finite correction factor n = revised sample size n’ = initial sample size N = population size

50. From the problem 12-24 Population is n’ = Thus revised sample size is