1. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 1 Audit Sampling for Tests of Controls and Substantive Tests of Transactions Chapter 15

2. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 2 Learning Objective 1 Explain the concept of representative (probabilistic) sampling.

3. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 3 What does this have to do with representative sampling and sampling risk?

4. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 4 Representative Samples A representative sample (probabilistic) is one in which the characteristics in the sample of audit interest are approximately the same as those of the population. Nonsampling risk is the risk that audit tests do not uncover existing exceptions in the sample. Competence, Budget, Boredom, Power-ticking. Matching task to worker, realistic budgets, review. Modesto, CA, students, and a media hungry Professor

5. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 5 Representative Samples Sampling risk is the risk that an auditor reaches an incorrect conclusion for population because the sample is not representative of the population. Sampling risk is an inherent part of sampling that results from testing less than the entire population. How to reduce/measure? Increase sample size / appropriate (statistical) sampling methods

6. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 6 Learning Objective 2 Distinguish between statistical and nonstatistical sampling (n?) and between probabilistic and nonprobabilistic sample selection (which n?).

7. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 7 Statistical Versus Nonstatistical Sampling Step 1 Plan the sample: obj., attributes, exception, population, sampling unit, stat or non-stat to get n. Step 2 Select the sample: (prob or non-prob?) and perform the tests. Step 3 Evaluate the results: SER generalize to pop., more sampling? Similarities

8. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 8 Statistical Versus Nonstatistical Sampling Statistical sampling allows the quantification of sampling risk (ARACR) in planning the sample (Step 1) and evaluating the results (Step 3). Plus must use Probabilistic sampling methods In nonstatistical sampling Sampling risk is not quantified. More discretion with sampling, more judgmental. Can use either Prob. or non. Prob. Why use?? Differences

9. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 9 Sample Selection Methods 1. Directed sample selection 2. Haphazard sample selection Only use w/ nonstat. sampling Nonprobabilistic/nonrepresentative

10. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 10 Sample Selection Methods 1. Simple random sample selection 2.Systematic sample selection 3.Probability proportional to size sample selection Use with either stat. or nonstat. sampling. Probabilistic/representative

11. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 11 Nonprobabilistic Sample Selection Methods Item selection based on auditor judgmental criteria Items most likely to contain misstatements: risk-based Items containing selected population characteristics: 5 shipping docs from each month or 30% of sample from one division Large dollar coverage Directed Sample Selection

12. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 12 Nonprobabilistic Sample Selection Methods Auditor randomly selects sample items. Haphazard Sample Selection

13. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 13 Learning Objective 3 Select representative samples.

14. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 14 Probabilistic Sample Selection Methods – see handout Simple Random Sample Selection Every possible combination of elements in the population has an equal chance of constituting the sample. Computer generation of random numbers

15. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 15 Probabilistic Sample Selection Methods Systematic Sample Selection The auditor calculates an interval and then selects the items for the sample based on the size of the interval. The interval is determined by dividing the population size by the number of sample items desired.

16. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 16 Probabilistic Sample Selection Methods Probability Proportional to Size Sample Selection Probability Proportional to Size Sample Selection A sample is taken where the probability of selecting any individual population item is proportional to its recorded amount.

17. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 17 Learning Objective 4 Define and describe audit sampling for exception rates.

18. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 18 Sampling for Exception Rates The exception rate is the ratio of the items NOT containing the specific attribute to the total number of population items (e.g. invoice data not traced to shipping doc. (ToT-occurrence)), daily batch total of qty shipped NOT compared with qty billed (I/C-occurrence)). SER: 3 exceptions / 100 sample = 3%

19. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 19 Sampling for Exception Rates Following are types of exceptions in populations of accounting data: – deviations from client’s established controls – monetary misstatements in populations of transaction data – no shipping doc for invoice – monetary misstatements in populations of account balance details – A/R not confirmed

20. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 20 Learning Objective 5 Use nonstatistical sampling in tests of controls and substantive tests of transactions.

21. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 21 Terms Used in Audit Sampling Terms Related to Planning: Table 15-1 p. 485 Characteristic or attribute (test) Acceptable risk of assessing control risk too low or accept ToT results (ARACR) = sampling risk! Tolerable exception rate (TER) Estimated population exception rate (EPER) Initial sample size: determined by all 3 above

22. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 22 Terms Used in Audit Sampling Terms Related to Evaluating Results Exception Sample exception rate (SER) Computed upper exception rate (CUER) Mathematically incorporates (adds) sampling risk or ARACR to SER (only related to stat. sampling)

23. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 23 I: Plan the Sample - Fig 15-2 p. 490 Step 1 State the objectives of the audit test – Ex. ToT accuracy – Attribute 5. Step 2Decide whether audit sampling applies. Step 3Define attributes and exception conditions. Ex. Table 15-3 p. 492, attribute 5. Step 4Define the population– all sales invoices in year Step 5Define the sampling unit – sales invoice

24. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 24 I: Plan the Sample - Fig 15-2 p. 490 Specify acceptable risk of assessing control risk too low or accepting ToT. Key – qual. w/ non-stat. quant. w/ stat. Estimate the population exception rate. How? Determine the initial sample size – use professional judgment, w/ statistical sampling use tables/computers. TER-EPER = precision  smaller = bigger sample Step 7 Step 8 Step 9 Specify the tolerable exception rate. How?Step 6

25. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 25 II: Select the Sample and Perform the Tests Select the sample = prob. or non prob. Perform the audit procedures. Fig 15-3 p. 498. Attribute 5: 4 ex. / 100 sample- SER = 4% Step 10 Step 11

26. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 26 III: Evaluate the Results-Fig 15-4 p. 496 Generalize from the sample to the population. SER sig. < TER: CR OK, ToT provides no adjustment: reduce AP and detail testing. SER≥TER: inc. CR, ToT – adj proposed (project to pop. or isolate w/ more sampling): do more AP/detailed tests. Too close to call? → Conservative (not an issue w/ stat) Analyze exceptions – isolated or distributed? Decide the acceptability of the population. Step 12 Step 13 Step 14

27. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 27 Guidelines for ARACR and TER for Tests of Control Factors: Preliminary assessed control risk (lower) – ARACR/Sampling Risk (lower) Significance of the transactions and related account balances that the internal controls are intended to affect (higher) – TER (lower)

28. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 28 Guidelines for ARACR and TER for Tests of Control Judgment Lowest assessed control risk Moderate assessed control risk Higher assessed control risk 100% assessed control risk Highly significant balances Significant balances Less significant balances Guideline ARACR of low ARACR of med. ARACR of high ARACR is N/A TER of 4% TER of 5% TER of 6%

29. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 29 Guidelines for ARACR and TER of Tests of Transactions Planned Reduction in ARACR forTER for Substantive Tests of Substantive TestsSubstantive Tests Details of Balances of Transactionsof Transactions Large Low Low ModerateMedium Medium Small HighHigh

30. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 30 Effect on Sample Size of Changing Factors Table 15-6 p. 493 Type of ChangeEffect on Initial Sample Size Increase ARACRDecrease or sampling risk (usually constant) Increase tolerable exception rateDecrease Increase estimated population exception rateIncrease Increase population sizeIncrease (minor)

31. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 31 Decide the Acceptability of the Population Revise TER or ARACR – no-no Expand the sample size–isolate exceptions (known mist) Revise assessment control risk, SOX 404? ToT – book adj. and inc. AP and detail testing Is SER > TER???

32. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 32 Learning Objective 6 Define and describe attributes (statistical) sampling and a sampling distribution.

33. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 33 Statistical Audit Sampling The statistical sampling method most commonly used for tests of controls and substantive tests of transactions is attributes sampling.

34. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 34 Sampling Distribution Attributes (statistical) sampling is based on the binomial distribution (think 2 columns). And since we quantify sampling risk and use only representative samples, we can use tables (like the normal distribution table you have used for z or t-tests in stat classes)!

35. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 35 Learning Objective 7 Use attributes sampling in tests of controls and substantive tests of transactions.

36. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 36 Application of Attributes Sampling EPER and TER the same as non-statistical testing – see p. 496. Still judgments! 2 We quantify sampling risk (ARACR) = 5%, We want to be 95% confident in our conclusion. 3How did we get initial sample size of 93? We judg- mentally selected a sample size of 100 on p. 496 1 See Fig 15-8 p. 506 – Attribute 5 where did all this come from? See Fig 15-8 p. 506 – Attribute 5 where did all this come from?

37. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 37 Application of Attributes Sampling Select the table corresponding to the ARACR. 2Locate the TER on the top of the table. 3Locate the EPER on the far left column. 4 1 Read down the appropriate TER column until it intersects with the appropriate EPER row in order to get the initial sample size = 93! Get 93 invoices via a REPRESENTATIVE sample. Use of the Tables – Table 15-8 (Sample Size) p. 504

38. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 38 Application of Attributes Sampling Samples rounded up to even number–not necessary! 2 # exceptions same as p. 500, SER = 4% 3Do not compare SER to TER like p. 496, go to Table 15-9 p. 505 to get Computed Upper Exception Rate (CUER) – compare CUER to TER. CUER > TER: I/C - increase CR, ToT – book adjustment and/or increase AP and detail testing 1 Back to Figure 15-8 p. 506

39. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 39 Application of Attributes Sampling Use table that corresponds to your ARACR 2 Locate the SER on the top of the table. 3Locate the Sample Size on the far left column. 4 1 Read down the appropriate TER column until it intersects with the appropriate EPER row in order to get the CUER – we are 95% confident that PER for no. 5 is ≤ 9.0, but 9.0 > TER = 5! Use of the CUER tables – Generalize To Population – Table 15-9 p. 505 Use of the CUER tables – Generalize To Population – Table 15-9 p. 505

40. ©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 40 End of Chapter 15