1. ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.
Module E
Overview of Sampling
“There are three kinds of lies: lies, damned lies, and statistics.”
– Benjamin Disraeli
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

2. ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
Understand the basic principles of sampling, including the differences between statistical and nonstatistical sampling and sampling and nonsampling risk.
Understand the basic steps and procedures used in conducting a sampling plan.
Identify the two situations in which sampling is used in an audit examination.
Understand how the basic steps and procedures used in a sampling plan apply to an audit engagement.
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

3. ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.
When is Sampling Used?
Study and evaluation of internal control
Selecting control procedures to verify compliance
Attribute sampling
Substantive procedures
Selecting components or transactions of account balances for verification
Variables sampling
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

4. ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.
Sampling Risk
Risk that the decision made based on the sample differs from the decision that would have been made by examining the population
Cause is a nonrepresentative sample
Controlled by:
Determining an appropriate sample size
Ensuring that all items have an equal opportunity of selection
Mathematically evaluating sample results
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

5. ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.
Sampling Approaches
Statistical sampling methods use the laws of probability to:
Select sample items
Evaluate sample results
Statistical sampling methods control the auditor’s exposure to sampling risk
Nonstatistical sampling violates one or both of the above criteria
Both statistical sampling and nonstatistical sampling can be used in a GAAS audit
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

6. Major Steps in Sampling
Determine the objective
Define characteristic of interest
Define the population
Determine sample size
Select the sample
Measure sample items
Evaluate sample results
Planning
Performing
Evaluating
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

7. Steps in Sampling: Planning
Determine the objective of sampling
Drawing conclusion about some population of interest (e.g., amateur golfers)
Define the characteristic of interest
Question of interest to person conducting sampling plan (e.g., does brand of golf ball provide increased distance?)
Define the population
Item(s) about which question is asked
Must be sure to completely and carefully define
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

8. Steps in Sampling: Performing
Determine sample size
Under statistical sampling, sample size considers exposure to sampling risk
Select sample items
Measure sample items
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

9. Steps in Sampling: Performing
Determine sample size
Select sample items
Unrestricted random selection: Select items based on random numbers matched to items in population
Systematic random selection: Bypass a fixed number of items in population, selecting every nth item
Block selection: Select contiguous units
Haphazard selection: Select items in a nonsystematic manner
Measure sample items
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

10. Steps in Sampling: Performing
Determine sample size
Select sample items
Measure sample items
Perform procedure and make appropriate evaluation/measurement
Determine sample estimate
Nonsampling risk can occur if incorrect procedures are performed or mistakes in evaluation or measurement are made
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

11. Steps in Sampling: Evaluating
Evaluate sample results
In statistical sampling, evaluating sample results controls exposure to sampling risk
Parameters
Sample estimate
Precision
Reliability
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

12. Precision and Reliability
Precision (Allowance for sampling risk)
Closeness of sample estimate to true population value
Reliability (Confidence)
Likelihood of achieving a given level of precision
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

13. Example of Evaluating Sample Results
Parameters
Sample estimate = 43 years
Reliability = 10 years
Confidence = 90% (Sampling risk = 10%)
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

14. Example of Evaluating Sample Results (Continued)
Precision Interval
Estimate Estimate Estimate
- Precision Precision
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

15. Example of Evaluating Sample Results (Continued)
Precision Interval
33 yrs yrs yrs
Estimate Estimate Estimate
- Precision Precision
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

16. Example of Evaluating Sample Results (Continued)
Precision Interval
33 yrs yrs yrs
Estimate Estimate Estimate
- Precision Precision
90%
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

17. Example of Evaluating Sample Results (Continued)
A 90% probability exists that the true average age is between 33 and 53 years (sample estimate  precision)
A 10% probability exists that the true average age is less than 33 years or greater than 53 years
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

18. ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.
Attribute Sampling
Used to estimate the extent to which a characteristic exists within a population
Used in the auditor’s study of internal control
Goal: Estimate the rate at which the client’s internal control is failing to function effectively and compare to an allowable level (tolerable deviation rate)
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

19. Decisions in Attribute Sampling
Sample Tolerable Rely on
Deviation  Deviation controls as
Rate Rate planned
Sample Tolerable Reduce
Deviation  Deviation planned reliance
Rate Rate on controls
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

20. Risks Associated with Attribute Sampling
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

21. ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.
Variables Sampling
Used to estimate the amount (or value) of some characteristic of a population
Used in the auditor’s substantive procedures
Goal: Estimate the amount of error in an account balance or class of transactions and compare to an allowable level (tolerable error)
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

22. Decisions in Variables Sampling
Sample Tolerable Account
Estimate of  Error balance is
Error (Materiality) not misstated
Estimate of  Error balance is
Error (Materiality) misstated
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

23. Risks Associated with Variables Sampling
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

24. Summary of Sampling Risks
Effectiveness Losses
Risk of assessing control risk too low (overreliance)
Risk of incorrect acceptance
Efficiency Losses
Risk of assessing control risk too high (underreliance)
Risk of incorrect rejection
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

25. Factors Affecting Sample Size
McGraw-Hill/Irwin
©2005 by the McGraw-Hill Companies, Inc. All rights reserved.