1. Copyright © 2007 Pearson Education Canada 1 Chapter 12: Audit Sampling Concepts

2. Copyright © 2007 Pearson Education Canada 12-2 Chapter 12 objectives  Define sampling  Discuss the advantages and disadvantages of statistical and non-statistical sampling  Identify three ways that a statistical sampling method can be selected  Describe the 14 steps in planning, selecting, performing the tests and evaluating a sample

3. Copyright © 2007 Pearson Education Canada 12-3 Importance of sampling to auditors  The auditor doesn’t look at everything… just pieces. The auditor CANNOT look at everything.

4. Copyright © 2007 Pearson Education Canada 12-4 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.

5. Copyright © 2007 Pearson Education Canada 12-5 Auditors sample 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

6. Copyright © 2007 Pearson Education Canada 12-6 Sampling is used to conduct  Walk through tests (to understand internal controls)  Tests of controls  Tests of details

7. Copyright © 2007 Pearson Education Canada 12-7 Representative sampling  Definition: The characteristics in the sample of audit interest are approximately the same as those of the population

8. Copyright © 2007 Pearson Education Canada 12-8 Practice question 12-17, p. 364  Sampling multiple choice  Concept check

9. Copyright © 2007 Pearson Education Canada 12-9 Representative sampling (cont’d)  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

10. Copyright © 2007 Pearson Education Canada 12-10 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

11. Copyright © 2007 Pearson Education Canada 12-11 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

12. Copyright © 2007 Pearson Education Canada 12-12 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. Copyright © 2007 Pearson Education Canada 12-13 Probabilistic sample selection methods  Simple random sample selection  Systematic sample selection  Probability proportionate-to-size sample selection (also known as MUS monetary unit sampling)

14. Copyright © 2007 Pearson Education Canada 12-14 Statistical sampling Advantages -- Provides  for quantitative evaluation of the sample results.  a more defensible expression of the test results.  for more objective recommendations for management.

15. Copyright © 2007 Pearson Education Canada 12-15 Statistical Sampling ( cont’d) Disadvantages  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.

16. Copyright © 2007 Pearson Education Canada 12-16 Non-statistical Sampling (Judgmental) Advantages  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.

17. Copyright © 2007 Pearson Education Canada 12-17 Non-statistical Sampling (Judgmental) (cont’d) Disadvantages  Cannot draw objectively valid statistical inferences from the sample results.  Cannot quantitatively measure and express sampling risk.

18. Copyright © 2007 Pearson Education Canada 12-18 Practice problem 12-23 (p. 366)  Making decisions about sampling  Does the implementation method matter?

19. Copyright © 2007 Pearson Education Canada 12-19 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

20. Copyright © 2007 Pearson Education Canada 12-20 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

21. Copyright © 2007 Pearson Education Canada 12-21 1. State the objectives of the test Test of control:  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

22. Copyright © 2007 Pearson Education Canada 12-22 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

23. Copyright © 2007 Pearson Education Canada 12-23 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)

24. Copyright © 2007 Pearson Education Canada 12-24 3. Define attributes and exception or error conditions (cont’d) - Sales and A/R Term related to planning: Test of control (e.g. attribute sample) Sales Test of detail (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

25. Copyright © 2007 Pearson Education Canada 12-25 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 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.

26. Copyright © 2007 Pearson Education Canada 12-26 5. Define the sampling unit Tests of controls:  Usually a physical unit, e.g. invoice, shipping document, purchase order Test of detail:  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

27. Copyright © 2007 Pearson Education Canada 12-27 6. Specify tolerable exception rate (TER) or specify materiality  Test of control  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 detail  Materiality is used to determine the tolerable misstatement amount for the audit of each account These decisions require the use of professional judgment.

28. Copyright © 2007 Pearson Education Canada 12-28 7.Specify ARACR or ARIA  Test of control  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 detail  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

29. Copyright © 2007 Pearson Education Canada 12-29 7.Specify ARACR or ARIA (cont’d) examples ARACR and ARIA are measures of sampling risk.  Test of control  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 detail  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

30. Copyright © 2007 Pearson Education Canada 12-30 8. Estimate population exception rate or misstatements  Test of control  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 detail  Provide an advance estimate of the total dollar error (misstatements) in the population Use prior year data and professional judgment.

31. Copyright © 2007 Pearson Education Canada 12-31 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

32. Copyright © 2007 Pearson Education Canada 12-32 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 (statistical) methods must be used

33. Copyright © 2007 Pearson Education Canada 12-33 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)

34. Copyright © 2007 Pearson Education Canada 12-34 12. Generalize from the sample to the population  For test of controls 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

35. Copyright © 2007 Pearson Education Canada 12-35 12.Generalize from the sample to the population (cont’d)  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)

36. Copyright © 2007 Pearson Education Canada 12-36 13.Analyze exceptions or misstatements  Test of control  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 detail  Were the misstatements caused by control exceptions? (need to reassess control risk?  Is additional substantive testing required?

37. Copyright © 2007 Pearson Education Canada 12-37 14.Decide the acceptability of the population  Test of control  If TER (Tolerable Error Rate) is sufficiently larger than SER (sample error rate) will normally accept the population  Test of detail  Compare the difference between the projection to the population and materiality  Use decision rule for statistical sampling

38. Copyright © 2007 Pearson Education Canada 12-38 14.Decide the acceptability of the population (cont’d)  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.