McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
Module G Variables Sampling
Learning Objectives
1.
2.
3.
4.
5.
6.
Define variables sampling and understand when variables sampling
is used in the audit.
Understand the basic process underlying monetary unit sampling
(MUS) and when to use it.
Identify the factors affecting the size of an MUS sample and
calculate the sample size for an MUS application.
Evaluate the sample results for an MUS sample by calculating the
projected misstatement, incremental allowance for sampling risk,
and basic allowance for sampling risk.
Understand the basic process underlying classical variables
sampling and the use of classical variables sampling in an audit.
Understand the use of nonstatistical sampling for variables
sampling.
Mod G-2
Variables Sampling
• Used to estimate the amount (or value) of a
population
• Substantive procedures
• Types of variables sampling approaches
– Monetary unit sampling (MUS)
– Classical variables sampling
Mod G-3
Monetary Unit Sampling (MUS)
• Defines the sampling unit as individual dollar (or
Euro, Yen, Yuan, etc.) in an account balance
• Auditor will select individual dollars for
examination
• Auditor will verify entire ―logical unit‖ containing
the selected dollar
Mod G-4
When to use MUS
• ADVANTAGES OF MUS
• DISADVANTAGES OF MUS
Mod G-5
Major Steps in Variables
Sampling: Planning
1. Determine the objective of sampling
2. Define characteristic of interest
3. Define the population
Mod G-6
Major Steps in Variables
Sampling: Performing
4. Determine sample size
5. Select sample items
6. Measure sample items
Mod G-7
Using AICPA MUS Tables
• Ratio of Expected to Tolerable Misstatement
• Tolerable Misstatement as a Percentage of Population
•
Find appropriate Risk of Incorrect Acceptance
•
Find Appropriate Ratio of Expected to Tolerable Misstatement
•
Read across to ―Tolerable Misstatement as a Percentage of Population‖ column
Mod G-8
Major Steps in Variables Sampling:
Evaluating
7.
Evaluate sample results
Upper Limit on Misstatements
Mod G-9
Upper Limit on Misstatements
• If Upper Limit on Misstatements is $50,000
and risk of incorrect acceptance is 5%
– There is a 5% probability that the true
misstatement exceeds $50,000
– There is a 95% probability that the true
misstatement is less than or equal to $50,000
95%
$0
5%
$50,000
Mod G-10
Projected Misstatement
• Assumes the entire sampling interval contains the
same percentage of misstatement as the item
examined by the auditor
• Do not calculate if balance > sampling interval
• Tainting %
= Amount of Misstatement
Recorded Balance of Item
• Projected
= Sampling Interval x Tainting %
Misstatement
Mod G-11
Basic Allowance for Sampling Risk
Incremental Allowance for Sampling Risk
Mod G-12
Evaluate Results
• If upper limit on misstatements < tolerable
misstatement
• If upper limit on misstatements > tolerable
misstatement
Mod G-13
MUS Sampling vs. Classical
Variables Sampling
•
MUS is more appropriate when:
•
Classical variables sampling is more appropriate when:
Mod G-14
Mean per Unit Sampling
(Sample Size)
• Sample size
N x [R(IR) + R(IA)] x SD 2
TE - EE
• Differences from MUS sampling
Mod G-15
Evaluating Results
• Precision = N X R(IA) X (SD ÷ √n )
• Project sample average to population estimate
• Add/subtract precision to get precision interval
• Determine difference between account balance
and furthest bound of precision interval
• If greater than tolerable misstatement—reject
balance
• Determine cause of all misstatements
Mod G-16
Other Approaches
• Stratified sampling
• Difference estimation
• Ratio estimation
Mod G-17
Nonstatistical Sampling
• Does not measure the auditor’s exposure to
sampling risk
• Permitted under generally accepted auditing
standards
• Differences
– Does not consider sampling risk in determining
sample size or evaluating sample results
– May use a nonprobabilistic selection technique
Mod G-18
BASIC PROCEDURE
• Select sample
– Does not explicitly consider sampling risk in
determining sample size
– May use block or haphazard selection methods
• Measure sample items (same as statistical sampling)
Mod G-19
Evaluate Sample Results
• Difference estimation
• Ratio estimation
• Use judgment to allow for sampling risk
• Normally reject if projected misstatement
exceeds expected misstatement
Mod G-20
Documentation
•
•
•
•
•
•
•
Objective and assertions evaluated
Sampling technique used and definition of a misstatement
Method and parameters used to determine sample size
Sample size
Selection method
Description of audit procedures
Determination of upper limit on misstatement, precision, or
projected misstatement
• Conclusion—effect on audit opinion
Mod G-21