1. Auditing: The Art and Science of Assurance Engagements Chapter 13: Audit Sampling Concepts Copyright © 2011 Pearson Canada Inc.

2. Auditing, Canadian Eleventh Edition Chapter 13 Learning Objectives 1.Define sampling. State when an auditor would use statistical rather than non-statistical sampling. 2.Explain the three different ways that an auditor can select a statistical sample. 3.Describe the 14 steps in planning and selecting a sample, performing the tests, and evaluating the sample. 13-2 Copyright © 2011 Pearson Canada Inc.

3. Auditing, Canadian Eleventh Edition Importance of Sampling to Auditors The auditor doesn’t look at everything… just pieces. The auditor CANNOT look at everything. 13-3 Copyright © 2011 Pearson Canada Inc.

4. Auditing, Canadian Eleventh Edition Purpose of Sampling Sampling is a method of obtaining information that will permit an estimate of the value or quality of a population by examining only a portion of the population. 13-4 Copyright © 2011 Pearson Canada Inc.

5. Auditing, Canadian Eleventh Edition Use of Sampling 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. 13-5 Copyright © 2011 Pearson Canada Inc.

6. Auditing, Canadian Eleventh Edition Sampling is Used to Conduct Walk through tests (to understand internal controls) Tests of controls Tests of details 13-6 Copyright © 2011 Pearson Canada Inc.

7. Auditing, Canadian Eleventh Edition Representative Sampling Definition: The characteristics in the sample of audit interest are approximately the same as those of the population. (Continued) 13-7 Copyright © 2011 Pearson Canada Inc.

8. Auditing, Canadian Eleventh Edition Representative Sampling (Continued) Non-representativeness can occur due to: -Non-sampling risk: Audit test do not uncover the exceptions in the sample due to failure to recognize them, or due to ineffective procedures -Sampling risk: Results from testing less than the entire population 13-8 Copyright © 2011 Pearson Canada Inc.

9. Auditing, Canadian Eleventh Edition Statistical Sampling Sampling that uses the laws of probability for selecting and evaluating a sample from a population for the purposes of reaching a conclusion about the population –selected at random –statistical calculations are used to measure and express the results 13-9 Copyright © 2011 Pearson Canada Inc.

10. Auditing, Canadian Eleventh Edition Statistical vs. Non-Statistical Similarities Both require a structured process involving planning, selection, conducting, evaluating Any type can be stratified Differences Sampling risk can be quantified in statistical sampling using mathematical formulae 13-10 Copyright © 2011 Pearson Canada Inc.

11. Auditing, Canadian Eleventh Edition Non-Probabilistic (Judgmental) Sample Selection Methods Directed sample selection, useful for: –Items likely to contain errors –Items containing selected characteristics (e.g. old amounts –Large dollar item coverage Block sample selection (e.g. sequences) Haphazard sample selection 13-11 Copyright © 2011 Pearson Canada Inc.

12. Auditing, Canadian Eleventh Edition Probabilistic Sample Selection Methods Simple random sample selection Systematic sample selection Probability proportionate-to-size sample selection (also known as MUS monetary unit sampling) 13-12 Copyright © 2011 Pearson Canada Inc.

13. Auditing, Canadian Eleventh Edition Advantages of Statistical Sampling Provides for quantitative evaluation of the sample results. Provides a more defensible expression of the test results. Provides for more objective recommendations for management. 13-13 Copyright © 2011 Pearson Canada Inc.

14. Auditing, Canadian Eleventh Edition 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. 13-14 Copyright © 2011 Pearson Canada Inc.

15. Auditing, Canadian Eleventh Edition Advantages of Non-statistical Sampling Allows the auditor to inject his or her subjective judgment in determining the sample size and selection process to audit items of greatest value and highest risk. May be designed so that it is equally effective and efficient as statistical sampling while being less costly. 13-15 Copyright © 2011 Pearson Canada Inc.

16. Auditing, Canadian Eleventh Edition Disadvantages of Non-Statistical Sampling Disadvantages Cannot draw objectively valid statistical inferences from the sample results. Cannot quantitatively measure and express sampling risk. 13-16 Copyright © 2011 Pearson Canada Inc.

17. Auditing, Canadian Eleventh Edition Professional Judgment Problem 13-25, p. 440 Making decisions about sampling Does the implementation method matter? 13-17 Copyright © 2011 Pearson Canada Inc.

18. Auditing, Canadian Eleventh Edition Sampling Process For both statistical and non-statistical methods, the four main parts are: 1.Planning the sample 2.Selecting the sample 3.Performing the tests 4.Evaluating the results 13-18 Copyright © 2011 Pearson Canada Inc.

19. Auditing, Canadian Eleventh Edition Steps in Sampling Process We are going to look at the fourteen steps in the sampling process, comparing the process for tests of controls versus tests of details. 13-19 Copyright © 2011 Pearson Canada Inc.

20. Auditing, Canadian Eleventh Edition 1. State the Objectives of the Test Test of controls: Are the controls applied? 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 13-20 Copyright © 2011 Pearson Canada Inc.

21. Auditing, Canadian Eleventh Edition 2. Decide if Audit Sampling Applies Some controls can be sampled (e.g. is a shipping document attached?) while others cannot be (e.g. separation of duties) Ability to sample for test of details depends on the nature of the population (e.g. capital assets may not be sampled, depending upon volume, while A/R confirmations will be 13-21 Copyright © 2011 Pearson Canada Inc.

22. Auditing, Canadian Eleventh Edition 3. Define Attributes and Exception or Error Conditions Term related to planning: Test of control (e.g. attribute sample) Test of detail (e.g. for MUS sample) Define the item of interest Identify the characteristic or attribute of interest Individual dollars Define exceptions or errors Define the control deviation (an exception) Normally, any monetary difference (error) 13-22 Copyright © 2011 Pearson Canada Inc.

23. Auditing, Canadian Eleventh Edition 3. Define Attributes and Exception or Error Conditions- Sales and A/R Term related to planning: Test of controls (e.g. attribute sample) Sales Test of details (e.g. for MUS sample) Accounts Rec’bl Define the item of interest Are sales approved for credit? Individual dollars Define exceptions or errors Sale made that causes customer balance to exceed credit limit Confirmed amount different from amount in customer account 13-23 Copyright © 2011 Pearson Canada Inc.

24. Auditing, Canadian Eleventh Edition 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 population is likely recorded sales invoices. In testing details in accounts receivable it is the recorded dollar population. Most populations can be stratified, if needed. 13-24 Copyright © 2011 Pearson Canada Inc.

25. Auditing, Canadian Eleventh Edition 5. Define the Sampling Unit Test of controls: Usually a physical unit, e.g. invoice, shipping document, purchase order Test of details: If MUS, would be the individual dollar For non-statistical sampling, it is likely the unit making up the balance, e.g. an unpaid invoice 13-25 Copyright © 2011 Pearson Canada Inc.

26. Auditing, Canadian Eleventh Edition 6. Specify Tolerable Exception Rate (TER) or Specify Materiality Test of controls TER is the exception rate the auditor will permit in the population and still be willing to use the assessed control risk As TER increases, the sample size decreases Test of details Materiality is used to determine the tolerable misstatement amount for the audit of each account These decisions require the use of professional judgment. 13-26 Copyright © 2011 Pearson Canada Inc.

27. Auditing, Canadian Eleventh Edition 7. Specify ARACR or ARIA Test of controls Acceptable Risk of Assessing Control Risk Too Low (ARACR) is the risk that the auditor will take of accepting controls as effective when population error rates are actually greater Test of details Acceptable Risk of Incorrect Acceptance (ARIA) is the risk the auditor will take of accepting a balance as correct when the true misstatement is greater than materiality (Continued) 13-27 Copyright © 2011 Pearson Canada Inc.

28. Auditing, Canadian Eleventh Edition 7. Specify ARACR or ARIA (Continued) Test of controls Assumes TER 6%, ARACR 10%, true error rate 8% True error rate exceeds TER, so population is NOT acceptable, but auditor does not know! Test of details If ARIA changes from 10% to 5%, sample size increases, since assurance required increases When controls are good (control risk is low), ARIA can be increased 13-28 Copyright © 2011 Pearson Canada Inc.

29. Auditing, Canadian Eleventh Edition 8. Estimate Population Exception Rate or Misstatements Test of controls Estimated population error rate (EPER) is an advance estimate of the percentage of exceptions in the population The lower the EPER, the smaller the sample size Test of details Provide an advance estimate of the total dollar error (misstatements) in the population Use prior year data and professional judgment. 13-29 Copyright © 2011 Pearson Canada Inc.

30. Auditing, Canadian Eleventh Edition 9. Determine the Initial Sample Size For non-statistical (also called 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. 13-30 Copyright © 2011 Pearson Canada Inc.

31. Auditing, Canadian Eleventh Edition 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 (statistical) methods must be used. 13-31 Copyright © 2011 Pearson Canada Inc.

32. Auditing, Canadian Eleventh Edition 11. Perform the Audit Procedures For test of controls, examine each item for the attribute defined in Step #3, recording all exceptions found (e.g. all sales approved for credit). For test of details, apply the audit procedures to each item to determine whether it is correct or contains a misstatement (e.g. send and reconcile confirmations, conduct alternative procedures). 13-32 Copyright © 2011 Pearson Canada Inc.

33. Auditing, Canadian Eleventh Edition 12. Generalize from the Sample to the Population For test of controls the sample error rate (SER) equals actual number of exceptions divided by actual sample size –But that is not necessarily equal to the actual population rate: a potential range must be calculated In practice, auditors tend to test controls when they expect no exceptions Method of generalization depends on the sampling methodology used (Continued) 13-33 Copyright © 2011 Pearson Canada Inc.

34. Auditing, Canadian Eleventh Edition 12. Generalize from the Sample to the Population (Continued) When generalizing tests of details, auditors deal with dollar amounts rather than with exceptions Misstatements found are projected from the sample results to the population Need to consider sampling error and sampling risk (ARIA) 13-34 Copyright © 2011 Pearson Canada Inc.

35. Auditing, Canadian Eleventh Edition 13. Analyze Exceptions or Misstatements Test of controls What breakdown in internal controls caused the exceptions? (does it affect control risk?) Should additional substantive testing be conducted because of these results? Test of details Were the misstatements caused by control exceptions? (need to reassess control risk? Is additional substantive testing required? 13-35 Copyright © 2011 Pearson Canada Inc.

36. Auditing, Canadian Eleventh Edition 14. Decide the Acceptability of the Population Test of controls If TER (Tolerable Error Rate) is sufficiently larger than SER (sample error rate) will normally accept the population Test of details Compare the difference between the projection to the population and materiality Use decision rule for statistical sampling (Continued) 13-36 Copyright © 2011 Pearson Canada Inc.

37. Auditing, Canadian Eleventh Edition 14. Decide the Acceptability of the Population (Continued) 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) - not easily defensible –2. Expand the sample size. Will decrease the sampling error OR you could end up with the same result. –3. Revise assessed control risk. This will likely mean an increase in tests of detail. –4. Report weaknesses in management letter. 13-37 Copyright © 2011 Pearson Canada Inc.