1. Chapter 9
Audit Sampling 1

2. What is Audit Sampling?
Applying a procedure to less than 100% of a population
To estimate some characteristic of the population
Qualitative
Quantitative

3. Advantages of Statistical Sampling
Design efficient samples
Measure sufficiency of evidence
Objectively evaluate sample results 2

4. Selection of Random Sample
Random number tables
Random number generators
Systematic selection 3

5. Random Number Table

6. Types of Statistical Sampling Plans
Attributes sampling
Discovery sampling
Classical variables sampling
Probability-proportional-to-size sampling 4

7. Requirements of Audit Sampling Plans
When planning the sample consider:
The relationship of the sample to the relevant audit objective
Materiality or the maximum tolerable misstatement or deviation rate
Allowable sampling risk
Characteristics of the population
Select sample items in such a manner that they can be expected to be representative of the population
Sample results should be projected to the population
Items that cannot be audited should be treated as misstatements or deviations in evaluating the sample results
Nature and cause of misstatements or deviations should be evaluated 5 5

8. Sampling Risks--Tests of Controls
Actual Extent of Operating Effectiveness
of the Control Procedure is
Adequate Inadequate
The Test of Controls
Sample Indicates:
Extent of Operating
Effectiveness is
Adequate
Effectiveness
Inadequate
Correct
Decision
Incorrect
Decision
(Risk of Assessing
Control Risk
Too High)
Incorrect
Decision
(Risk of Assessing
Control Risk
Too Low)
Correct
Decision 6 6

9. Audit Sampling for Tests of Controls
Determine the objective of the test
Define the attributes and deviation conditions
Define the population to be sampled
Specify:
The risk of assessing control risk too low
The tolerable deviation rate
Estimate the population deviation rate
Determine the sample size
Select the sample
Test the sample items
Evaluate the sample results
Document the sampling procedure 7 7

10. Sampling Risks--Substantive Tests
The Population Actually is
Not Materially Materially
Misstated Misstated
The Substantive
Procedure Sample
Indicates
Misstatement in
Account Exceeds
Tolerable Amount
Account Is Less
Than Tolerable
Amount
Correct
Decision
Incorrect
Decision
(Risk of Incorrect
Rejection)
Incorrect
Decision
(Risk of Incorrect
Acceptance)
Correct
Decision 8 8

11. Audit Sampling for Substantive Tests
Determine the objective of the test
Define the population and sampling unit
Choose an audit sampling technique
Determine the sample size
Select the sample
Test the sample items
Evaluate the sample results
Document the sampling procedure 9 9

12. Population Variability—Why it Matters
Item Population A Population B
, ,000 ,
, ,000 , ,
Mean , ,100
Standard
deviation ,395
The variability determines how much information each of the items in the population tells you about the other items in the population. 2 11

13. Factors Affecting Sample Size

14. Determining Sample Size--MPU2

15. Determining Sample Size--MPU Sampling
Planned allowance
for sampling risk
Tolerable misstatement
______________________ =
Incorrect acceptance coef.
1 +
Incorrect rejection coef. 12

16. Variables Sampling Illustration--MPU
Adjusted allowance
for sampling risk =
Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.)
misstatement Sample size
This formula “adjusts” the allowance for sampling risk to consider the standard deviation of the audited values in the sample. It holds the risk of incorrect acceptance at its planned level. 4 13

17. Variables Sampling Illustration--MPU
Using the text example with a standard deviation of audited values of $16
Adjusted allowance
for sampling risk =
Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.)
misstatement Sample size
= $364, _ ($100,000 * 1.64 * $16)
225
= $189,067
We would still “accept” the book balance because the $6,250,000 (book value) falls within this interval
Estimate of total Adjusted allowance
audited value for sampling risk
$6,100, $189,067
[$5,910, to $6,289,067]

18. Acceptance Interval Figure 9-12

19. Nonstatistical Variables Sampling Illustration
Plan Sample:
Population:
Size = 363 items
Book value = $200,000
Tolerable misstatement = $10,000
Risk assessments:
Inherent and control risk = Slightly below maximum
Other substantive tests = Moderate 8 15

20. Nonstatistical Sampling--Determination of Sample Size
Sample size = Population book value X Reliability factor
Tolerable misstatement
= $200,000 X 2.0 = 40 items
$10,000 9 16

21. Nonstatistical Sampling--Evaluation of Sample Results
40 accounts in sample
$350 net overstatement
$60,000 book value of sample items
Projected misstatement:
= [Sample net misstatement] X Book value of population
[ Book value of sample ]
= [ $350 ] X $200,000
[$60,000]
= $1,167
Since the projected misstatement is only 11.7 percent ($1,167/$10,000) of tolerable misstatement, it is likely that the auditors would conclude that the account balance is materially correct. 10 17

22. PPS Sampling Illustration
Population book value = $6,250,000
Other Information:
Tolerable misstatement = $364,000
Sampling risk--Incorrect acceptance = 5%
Expected misstatement = $50,000
Use Figures 9-14 and 9-15 to obtain a “reliability factor” and an “expansion factor.” 6 18

23. PPS Sample Size Computation
Recorded amount of population * Reliability factor
Tolerable misstatement - (Expected misstatement * Expansion factor)
= $6,250,000 * = 66
$364,000 - ($50,000 * 1.6)
Sampling interval = Book value of the population
Sample size
= $6,250, = $95,000 (approximately) 66 7 19

24. PPS Evaluation of Results
Upper Limit on misstatement =
Projected misstatement
+ Basic precision (Rel. factor x interval)
+ Incremental allowance

25. Calculation of Upper Limit on Misstatement