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# Audit sampling for tests of controls and substantive tests of transactions

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### Audit sampling for tests of controls and substantive tests of transactions

1. 1. Audit Sampling for Tests of Controls and Substantive Tests of Transactions Chapter 14©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 1
2. 2. Representative Samples A representative sample 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, resulting in nonsampling errors.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 2
3. 3. Representative Samples Sampling risk is the risk that an auditor reaches an incorrect conclusion because the sample is not representative of the population, resulting in sampling error. Sampling risk is an inherent part of sampling that results from testing less than the entire population. Note: A 95% confidence level = 5% sampling risk.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 3
4. 4. Representative Samples Reducing Nonsampling Risk – Careful design of audit procedures, Proper instruction, supervision, and review. Reducing Sampling Risk – Adjust sample size, Use appropriate method for selecting sample items.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 4
5. 5. Statistical Versus Nonstatistical Sampling Similarities Similarities Step 1 Plan the sample. Select the sample Step 2 and perform the tests. Step 3 Evaluate the results.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 5
6. 6. Statistical Versus Nonstatistical Sampling Differences Differences Statistical sampling allows the quantification of sampling risk in planning the sample (Step 1) and evaluating the results (Step 3). In nonstatistical sampling those items that the auditor believes will provide the most useful information are selected. Conclusions are judgmental = judgmental sampling©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 6
7. 7. Probabilistic Versus Nonprobabilistic Sample Selection Probabilistic Sample Selection – Selecting a sample such that each population item has a known probability of being included in the sample and the sample is selected by a random process. Nonprobabilistic Sample Selection – Selecting a sample in which the auditor uses professional judgment rather than probabilistic methods to select sample items.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 7
8. 8. Sample Selection Methods Nonprobabilistic Nonprobabilistic 1. Directed sample selection 2. Block sample selection 3. Haphazard sample selection©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 8
9. 9. Sample Selection Methods Probabilistic Probabilistic 1. Simple random sample selection 2. Systematic sample selection 3. Probability proportional to size sample selection 4. Stratified sample selection©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 9
10. 10. Nonprobabilistic Sample Selection Methods Directed Sample Selection Directed Sample Selection Item selection based on auditor judgmental criteria Items most likely to contain misstatements Items containing selected population characteristics Large dollar coverage©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 10
11. 11. Nonprobabilistic Sample Selection Methods Block Sample Selection Block Sample Selection Selection of several items in sequence forming “blocks” of items Haphazard Sample Selection Haphazard Sample Selection Selection without regard to size, source, or Distinguishing characteristics©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 11
12. 12. Probabilistic Sample Selection Methods Simple Random Sample Selection Simple Random Sample Selection Every possible combination of elements in the population has an equal chance of constituting the sample. Random number tables Computer generation of random numbers©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 12
13. 13. Probabilistic Sample Selection Methods Systematic Sample Selection 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.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 13
14. 14. Probabilistic Sample Selection Methods Systematic Sample Selection Example Systematic Sample Selection Example Population of sales invoices 652 – 3151 Desired sample size = 125 Interval = (3151 – 651) / 125 = 20 Select a random start between 1 & 19 (ex. 9) First item in sample is invoice # 661 (652 + 9) Remaining 124 items = 681 (661+20), 701 (681+20), 721 (701+20) etc.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 14
15. 15. Probabilistic Sample Selection Methods Probability Proportional to Size Probability Proportional to Size Sample Selection – for emphasis on Sample Selection – for emphasis on large dollar items large dollar items A sample is taken where the probability of selecting any individual population item is proportional to its recorded amount (PPS). Evaluated using monetary unit sampling Discussed in Chapter 16©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 15
16. 16. Probabilistic Sample Selection Methods Stratified Sample Selection Stratified Sample Selection For emphasis on large dollar items For emphasis on large dollar items The population is divided into subpopulations by size and larger samples are taken of the larger subpopulations. Evaluated using variables sampling Discussed in Chapter 16©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 16
17. 17. Sampling for Tests of Controls and Substantive Tests of Transactions Estimate the proportion (ratio) of items in a population containing a characteristic or attribute of interest. The occurrence rate, or exception rate, is the ratio of the items containing the specific attribute to the total number of population items. Ex. invoices are not properly verified 3 percent of the time©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 17
18. 18. 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 – monetary misstatements in populations of account balance details (requires a dollar estimate)©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 18
19. 19. Sampling for Exception Rates Exceptions versus Deviations Difference between sample exception rate and population exception rate is Sampling Error Reliability of sampling error estimate is Sampling Risk Ex. Find a 3% sample exception rate and sampling error of 1% With a sampling risk of 10%. We conclude that the population Exception rate is between 2 – 4% at a 10% risk of being wrong (or 90% chance of being right)©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 19
20. 20. I: Plan the Sample Step 1 State the objectives of the audit test. Step 2 Decide whether audit sampling applies. Step 3 Define attributes and exception conditions. Step 4 Define the population. Step 5 Define the sampling unit.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 20
21. 21. I: Plan the Sample Step 6 Specify the tolerable exception rate. Specify acceptable risk of assessing Step 7 control risk too low. Step 8 Estimate the population exception rate. Step 9 Determine the initial sample size.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 21
22. 22. II: Select the Sample and Perform the Tests Step 10 Select the sample. Step 11 Perform the audit procedures.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 22
23. 23. III: Evaluate the Results Generalize from the sample Step 12 to the population. Step 13 Analyze exceptions. Step 14 Decide the acceptability of the population.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 23
24. 24. Plan the Sample: TER, ARACR, EPER  TER = Tolerable Exception Rate  The exception rate that the auditor will permit in the population and still be willing to use the assessed control risk (CR) and/or amount of monetary misstatements in the transactions (tolerable materiality).  Result of auditor judgment; affected by materiality.  What amount of exceptions is material to reject a control?  More controls operating for an audit objective results in higher TER.  High TER => low sample size; low TER => high sample size©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 24
25. 25. Plan the Sample: TER, ARACR, EPER  ARACR = Acceptable Risk of Assessing Control Risk too low  The risk the auditor is willing to take of accepting a control as effective (or monetary amount as tolerable) when the true population exception rate is greater than TER.  ARACR = measure of sampling risk  The lower the assessed control risk => the lower the ARACR => the fewer tests of detailed balances.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 25
26. 26. Plan the Sample: TER, ARACR, EPER  EPER = Expected Population Error Rate  A judgmental estimate based on knowledge of client.  Used to determine appropriate sample size.  Low EPER => low sample size  As EPER approaches TER, more precision is needed and larger sample size is needed.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 26
27. 27. Guidelines for ARACR and TER Tests of Control Judgment Guideline • Lowest assessed control risk • ARACR of low • Moderate assessed control risk • ARACR of med. • Higher assessed control risk • ARACR of high • 100% assessed control risk • ARACR is N/A • Highly significant balances • TER of 4% • Significant balances • TER of 5% • Less significant balances • TER of 6%©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 27
28. 28. Effect on Sample Size of Changing Factors Type of Change Effect on Initial Sample Size Increase acceptable risk of assessing control risk too low Decrease Increase tolerable exception rate Decrease Increase estimated population exception rate Increase Increase population size Increase (minor)©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 28
29. 29. Generalize Sample to Population  SER = Sample exception rate = exceptions/sample size  Subtract SER from TER = sampling error  If sampling error is sufficiently large, then true population exception rate is acceptable.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 29
30. 30. Decide the Acceptability of the Population Revise TER or ARACR Expand the sample size Revise assessment control risk Communicate with the audit committee or management (good for all 3 options)©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 30
31. 31. Statistical Audit Sampling The statistical sampling method most commonly used for tests of controls and substantive tests of transactions is attributes sampling.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 31
32. 32. Sampling Distribution It is a frequency distribution of the results of all possible samples of a specified size that could be obtained from a population containing some specific parameters. Attributes sampling is based on the binomial distribution.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 32
33. 33. Application of Attributes Sampling Use of the Tables Use of the Tables 1 Select the table corresponding to the ARACR. 2 Locate the TER on the top of the table. 3 Locate the EPER on the far left column. 4 Read down the appropriate TER column until it intersects with the appropriate EPER row in order to get the initial sample size.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 33
34. 34. Application of Attributes Sampling Effect of Population Size Effect of Population Size Population size is a minor consideration in determining sample size. Representativeness is ensured by the sample selection process more than by sample size.©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 34
35. 35. Application of Attributes Sampling Use of the Tables Use of the Tables 1 Select the table corresponding to the ARACR. 2 Locate the actual number of exceptions on the top of the table. 3 Locate the sample size on the far left column. 4 Read down the appropriate exceptions column until it intersects with the appropriate sample size row in order to get the CUER (calculated upper exception rate).©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 35
36. 36. End of Chapter 14©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 36