2. STATISTICAL TOOLS FOR AUDITING
Part Four

3. CHAPTER 9
AUDIT SAMPLING: AN APPLICATION TO SUBSTANTIVE TESTS OF ACCOUNT BALANCES
Chapter 9

4. A SAMPLING PLAN FOR SUBSTANTIVE TESTING
Planning
Performance
Evaluation

5. PLANNING Determine the test objective(s). Define the population.
Define the sampling unit.
Choose an audit sampling technique.

6. PLANNING Determine sample size.
Consider the variation within the population.
Determine the acceptable risk of incorrect acceptance.
Determine the tolerable misstatement.
Determine the expected amount of misstatement.
Consider the population size.

7. PERFORMANCE Determine the method of selecting the sample items.
Perform the audit procedures.

8. EVALUATION Calculate the sample results. Perform error analysis.
Draw final conclusions.

9. TWO SAMPLING TECHNIQUES
Monetary-unit sampling
Classical variables sampling

10. MONETARY-UNIT SAMPLING (MUS)
MUS uses attribute sampling theory to express a conclusion in monetary amounts rather than as a rate of occurrence.

11. ADVANTAGES OF MUS
When the auditor expects no misstatements, MUS will normally result in a smaller sample size than classical variable methods.
The calculation of sample size and the evaluation of the sample results are not based on the variation between items in the population.
When applied using a PPS sample selection procedure MUS automatically results in a stratified sample

12. DISADVANTAGES OF MUS
The selection of zero or negative balances generally requires special design consideration.
The general approach to MUS assumes that the audited amount of the sample item is not in error by more than 100 percent.
When more than one or two misstatements are detected using a MUS approach, the sample results calculations may overstate the allowance for sampling risk.

13. APPLYING MUS Defining the sampling unit (Step 3).
Determining the sample size (Step 5).
Selecting the sample (Step 6) - See Figure 9-1.
Calculating sample results (Step 8).
No misstatements detected.
Misstatements detected.

14. AN EXTENDED EXAMPLE

15. CASE 1 - EVIDENCE SUPPORTS FAIR PRESENTATION

16. CASE 1 - EVIDENCE SUPPORTS FAIR PRESENTATION

17. CASE 2 - EVIDENCE DOES NOT SUPPORT FAIR PRESENTATION

18. CASE 3 - CONSIDERATION OF UNDERSTATEMENT ERRORS

19. CASE 3 - CONSIDERATION OF UNDERSTATEMENT ERRORS

20. CASE 3 - CONSIDERATION OF UNDERSTATEMENT ERRORS
The net ULM is $107,072 ($110,566 - $3,494).
When the ULM is adjusted for understatement errors, the risk of incorrect acceptance for the test is no longer 5 percent.

21. NONSTATISTICAL SAMPLING FOR TESTS OF ACCOUNT BALANCES
The only differences between a nonstatistical sampling application and a statistical sampling application occur in the following steps:
Identifying individually significant items.
Determining the sample size.
Calculating the sample results.

22. NONSTATISTICAL SAMPLING: DETERMINING SAMPLE SIZE

23. NONSTATISTICAL SAMPLING: CALCULATING SAMPLE RESULTS
The AICPA's guidance describes two acceptable methods for projecting the amount of misstatement found in a nonstatistical sample:
Project the amount of misstatement by dividing the amount of misstatement by the percentage of the dollars of the population included in the sample.
Project the average misstatement found in the sample to the population.

24. NONSTATISTICAL SAMPLING AN EXAMPLE - CALABRO

25. NONSTATISTICAL SAMPLING AN EXAMPLE - CALABRO
Jones has made the following decisions:
Based the results of the tests of controls, a low assessment is made for inherent and control risk.
Tolerable misstatement allocated to accounts receivable is $40,000. The expected amount of misstatement is $15,000.
There is moderate risk that other auditing procedures will fail to detect material misstatements.
All customer account balances greater than $25,000 are to be audited.

26. NONSTATISTICAL SAMPLING AN EXAMPLE - CALABRO
Sample Size = ($3,167,900/$40,000) x 1.2 = 95
Results

27. NONSTATISTICAL SAMPLING AN EXAMPLE - CALABRO
Projected Misstatement

28. CLASSICAL VARIABLES SAMPLING
Classical variables sampling uses normal distribution theory to evaluate the characteristics of a population based on sample data.

29. CLASSICAL VARIABLES SAMPLING ESTIMATORS
Mean-per-unit
Difference
Ratio
Regression

30. ADVANTAGES OF CLASSICAL VARIABLES SAMPLING
When the auditor expects a large number of differences between book and audited values, classical variables sampling will normally result in a smaller sample size than monetary unit sampling.
Classical variables sampling techniques are effective for both overstatements and understatements.
The selection of zero balances generally does not require special sample design considerations since the sampling unit will not be an individual dollar but rather an account, transaction, or line item.

31. DISADVANTAGES OF CLASSICAL VARIABLES SAMPLING
The auditor must estimate the standard deviation of the audited value to determine sample size.
If few misstatements are detected in the sample data, the true variance tends to be underestimated and the resulting projection of the misstatements to the population is not likely to be reliable.

32. APPLYING CLASSICAL VARIABLES SAMPLING
Defining the sampling unit
Selecting the sample
Determining sample size
See example in the Appendix

33. CHAPTER 9
AUDIT SAMPLING: AN APPLICATION TO SUBSTANTIVE TESTS OF ACCOUNT BALANCES
Chapter 9

34. CHAPTER 9
AUDIT SAMPLING: AN APPLICATION TO SUBSTANTIVE TESTS OF ACCOUNT BALANCES
Chapter 9