1. Chapter 15 Audit Sampling for Tests of Controls and Substantive Tests of Transactions

2. Presentation Outline Representative Sample
Statistical vs. Nonstatistical Sampling
Terms Used in Sample Planning
Terms Related to Evaluating Results
Steps in Sampling

3. I. Representative Sample
A representative sample is one in which the characteristics in the sample of audit interest are approximately the same as those of the population. Two things cause a sample to be nonrepresentative:
Nonsampling risk
Sampling risk

4. A. Nonsampling Risk
Nonsampling risk is the risk that the audit tests do not uncover existing exceptions in the sample. Two causes of this risk are:
Auditor failure to recognize exceptions
Inappropriate or ineffective audit procedures

5. B. Sampling Risk
Sampling risk is the risk that an auditor reaches an incorrect conclusion because the sample is not representative of the population. This can be controlled by:
Adjusting the sample size
Using an appropriate method of selecting sample items

6. II. Statistical vs. Nonstatistical Sampling
Probabilistic Sample Selection
Nonstatistical Sampling
Nonprobabilistic Sample Selection
Although statistical sampling uses either sampling with or without
replacement, auditors normally sample without replacement.

7. A. Statistical Sampling
Mathematical rules allow the quantification of sampling risk in planning the sample. For example, a 95% confidence level provides a 5% sampling risk. Statistical sampling requires probabilistic sample selection.

8. B. Probabilistic Sample Selection
Probabilistic sample selection selects a sample in a way that each population item has a known probability of being included in the sample and the sample is randomly selected.
Simple random number selection – all items of the population have an equal chance of being selected. Can use random number tables and random number generators (see Fig on p. 448).
Systematic sample selection – Auditor determines an interval and selects items on the basis of the interval (see example on page 449)
Probability Proportional to Size – Probability of selecting an item is proportional to its recorded amount.
Stratified sample – Divided population into subpopulations and use different selection criteria for each subpopulation.
Note: It is acceptable to make nonstatistical evaluations by using
probabilistic selection, but it is never acceptable to evaluate a
nonprobabilistic sample as if it were a statistical sample.

9. Stratification Illustrated
The process of dividing a population into subpopulations that have similar characteristics. Strata must be defined so that each sampling unit can only be in one stratum.
Accounts Receivable Stratification
Stratum
Size
Composition of Stratum
Sample Selection 2 22
All accounts over $5,000
100%
examination
121
All accounts between $1,000 and $5,000
Random-number table 3 85
All accounts under $1,000
Systematic selection 4 14
All accounts with credit balances

10. C. Nonstatistical Sampling
In nonstatistical sampling, the auditor does not quantify sampling risk. Instead, those sample items that the auditor believes will provide the most useful information are selected. Since conclusions are based on a judgmental basis, nonprobabilistic sample selection is normally conducted.

11. D. Nonprobabilistic Sample Selection
Nonprobabilistic sample selection is a method of selecting a sample where the auditor uses professional judgment rather than probabilistic methods to select sample items.
Directed sample selection – auditor selects items based on a judgmental criteria such as likelihood of misstatement, characteristics such as different time periods, or large dollar amounts.
Block sample selection – selection of a number of items in sequence. Auditor must use several blocks to obtain a representative sample.
Haphazard sample selection – selection of items without any conscious bias on the part of the auditor.
Note: It is acceptable to make nonstatistical evaluations by using
probabilistic selection, but it is never acceptable to evaluate a
nonprobabilistic sample as if it were a statistical sample.

12. III. Terms Used in Sample Planning
Characteristics or Attribute
Acceptable Risk of Assessing Control Risk Too Low (ACACR)
Tolerable Exception Rate (TER)
Estimated Population Exception Rate (EPER)

13. A. Characteristics or Attribute
The characteristic being tested in the population.

14. B. Acceptable Risk of Assessing Control Risk Too Low (ARACR)
The risk that the auditor is willing to take of accepting a control as effective or a rate of monetary misstatement as tolerable, when the true population exception rate is greater than the tolerable exception rate.

15. C. Tolerable Exception Rate
Exception rate that the auditor will permit in the population and still be willing to use the assessed control risk and/or the amount of monetary misstatements in the transactions established during planning.

16. D. Estimated Population Exception Rate
Exception rate that the auditor expects to find in the population before testing begins.

17. IV. Terms Related To Evaluating Results
Exception
Sample Exception Rate (SER)
Computed Upper Exception Rate

18. A. Exception The term exception should be understood to refer to both:
deviations from prescribed controls and
situations where amounts are not monetarily correct.

19. B. Sample Exception Rate (SER)
Number of exceptions in the sample size divided by the sample size.

20. C. Computed Upper Exception Rate (CUER)
The upper limit of the probable population exception rate; the highest exception rate in the population at a given ARACR.

21. V. Steps in Sampling Planning the Sample (Steps 1-9)
Select the Sample and Perform the Tests (Steps 10-11)
Evaluate the Results (Steps 12-14)

22. A. Planning 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.

23. A. Planning the Sample
Step 6
Specify the tolerable exception rate.
Step 7
Specify acceptable risk of assessing
control risk too low.
Step 8
Estimate the population exception rate.
Step 9
Determine the initial sample size.

24. B. Select the Sample and Perform the Tests
Step 10
Select the sample.
Step 11
Perform the audit procedures.

25. C. Evaluate the Results
Step 12
Generalize from the sample
to the population.
Step 13
Analyze exceptions.
Step 14
Decide the acceptability of the population.

26. Summary
Effect of Sampling Risk and Nonsampling Risk a Representative Sample
Statistical Sampling Must Use Probabilistic Sample Selection
Simple Random Sample Selection
Systematic Sample Selection
Probability Proportional to Size Sample Selection
Stratified Sample Selection
Nonstatistical Sampling Often Uses Nonprobabilitic Sample Selection
Directed Sample Selection
Block Sample Selection
Haphazard Sample Selection
Sampling Terms
The 14 Steps of Sampling