1. Audit Sampling: An Overview and Application to Tests of Controls
Chapter 8
Audit Sampling: An Overview and Application to Tests of Controls
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

2. LO# 1
Introduction
Auditors need to rely on sampling to some degree because it’s not always possible to analyze the entire population:
Many control processes require human involvement.
Many testing procedures require the auditor to physically examine an asset.
In many cases auditors are required to obtain and evaluate evidence from third parties.
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3. Definitions and Key Concepts
LO# 1 and 2
Definitions and Key Concepts
On the following slides we will define:
Audit Sampling.
Sampling Risk.
Confidence Level.
Tolerable and Expected Error.
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4. LO# 1
Audit Sampling
Here are at least two ways (there are more) to define Audit Sampling:
Analysis of part of a population, instead of the entire population
Using inferential statistics in an audit
Why is this (not terribly accurate description) phrase “Audit Sampling” used?
Custom and tradition.
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5. LO# 2
Sampling Risk
Sampling risk exists whenever inferential statistics are used. There are two types of sampling risk. We worry more about Type II risk, as that can cause an audit failure
Risk of incorrect rejection (Type I) – in a test of internal controls, it is the risk that the sample indicates the control is not operating effectively when, in fact, it is operating effectively. In substantive testing, it is the risk that the sample indicates that the recorded balance is materially misstated when, in fact, it is not.
Risk of incorrect acceptance (Type II) – in a test of internal controls, it is the risk that the sample indicates the control is operating effectively when, in fact, it is not operating effectively. In substantive testing, it is the risk that the sample indicates the recorded balance is correct when it is, in fact, materially misstated.
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6. Determining the “right” sample size in attribute sampling and substantive sampling
Because sampling risk is always present, the auditor must decide how much to expose himself to.
The auditor would like to avoid any significant sampling risk, but that would cost him a huge amount of time and effort
He’d have to draw huge samples
He’d lose the benefit of small samples
Bottom line: this is a cost/benefit decision

7. Desired confidence level or risk of incorrect acceptance
Factors to Determine right Sample Size in Attribute (ACL calls it “Record”) Sampling (compare text Table 8-5 to ACL GUI)
Desired confidence level or risk of incorrect acceptance
The ACL GUI calls this Confidence
Tolerable deviation rate (or tolerable error)
ACL calls this Upper Error Limit %
Expected population deviation rate
ACL calls this Expected Error Rate %
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8. Desired Confidence Level Sample Size Actual Number of Deviations Found
Evaluation of Results of Attribute (“Record” in ACL) Sampling Terms: Text Table 8-8 vs. ACL
Desired Confidence Level
ACL calls this Confidence
Sample Size
ACL also calls this Sample Size
Actual Number of Deviations Found
ACL calls this Number of Errors
Computed Upper Deviation Rate
ACL calls it upper error limit frequency

9. Confidence level is the complement of sampling risk.
LO# 2
Confidence Level
Confidence level is the complement of sampling risk.
The auditor may set sampling risk for a particular sampling application at 5%, which results in a confidence level of 95%.
Thus, these 2 phrases are substantively the same thing.
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10. Sometimes we use Audit Sampling and sometimes not…
LO# 3
Sometimes we use Audit Sampling and sometimes not…
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11. Audit Evidence – To Sample or Not?
LO# 3
Audit Evidence – To Sample or Not?
Inspection of tangible assets. Auditors typically attend the client’s year-end inventory count. When there are a large number of items in inventory, the auditor will select a sample to physically inspect and count.
Inspection of records or documents. Certain controls may require the matching of documents. The procedure may take place many times a day. The auditor may gather evidence on the effectiveness of the control by testing a sample of the document packages.
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12. Audit Evidence – To Sample or Not?
LO# 3
Audit Evidence – To Sample or Not?
Reperformance. To comply with PCAOB standards, publicly traded clients must document and test controls over important assertions for significant accounts. The auditor may reperform a sample of the tests performed by the client.
Confirmation. Rather than confirm all customer account receivable balances, the auditor may select a sample of customers.
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13. Testing All Items with a Particular Characteristic
LO# 3
Testing All Items with a Particular Characteristic
When an account or class of transactions is made up of a few large items, the auditor may examine all the items in the account or class of transaction.
When a small number of large transactions make up a relatively large percent of an account or class of transactions, auditors will typically test all the transactions greater than a particular dollar amount.
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14. Types of Audit Sampling
LO# 4
Types of Audit Sampling
Auditing standards recognize and permit both statistical and nonstatistical methods of audit sampling.
Statistical sampling uses the laws of probability to 1) compute sample size and 2) evaluate results. The auditor is able to use the most efficient sample size and quantify sampling risk.
In nonstatistical sampling, the auditor does not use the laws of probability in one or both of these tasks
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15. Types of Audit Sampling
LO# 4
Advantages of statistical sampling:
Design an efficient sample.
Measure the sufficiency of evidence obtained.
Quantify sampling risk.
Disadvantage of statistical sampling:
It has been found, as a practical matter, in litigation, to be harder for the CPA firm to defend itself, if it used statistical sampling rather than nonstatistical sampling.
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16. Statistical Sampling Techniques
LO# 4
Statistical Sampling Techniques
Attribute Sampling (used for IC testing – Ch. 8).
Monetary-Unit Sampling (used to decide if auditor can accept as materially correct $$ in a Balance Sheet or IS account – Ch. 9).
Classical Variables Sampling (ditto MUS)

17. Attribute Sampling Applied to Tests of Controls
LO#
5, 6, & 7
Attribute Sampling Applied to Tests of Controls
In conducting a statistical sample for a test of controls, auditing standards require the auditor to properly plan, perform, and evaluate the sampling application and to adequately document each phase of the sampling application.
Plan
Perform
Evaluate
Document
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18. LO#
5, 6, & 7
Planning
The objective of attribute sampling when used for tests of controls is to evaluate the operating effectiveness of the internal control.
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19. LO#
5, 6, & 7
Planning
All of the items that constitute the class of transactions make up the sampling population.
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20. LO#
5, 6, & 7
Planning
Each sampling unit makes up one item in the population. The sampling unit should be defined in relation to the specific control being tested.
In the Calabro audit the sampling unit is the sales or lease contract (p. 282)
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21. LO#
5, 6, & 7
Planning
A deviation is a departure from adequate performance of the internal control.
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22. LO#
5, 6, & 7
Planning
Confidence level is the desired level of assurance that the sample results will support a conclusion that the control is functioning effectively. When the auditor has decided to rely on controls, the confidence level is traditionally set at 90% or 95%. This means the auditor is willing to accept a 10% or 5% risk of accepting the control as effective when it is not.
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23. Example Suggested Tolerable Deviation Rates:
LO#
5, 6, & 7
Planning
The tolerable deviation rate is the maximum deviation rate from a prescribed control that the auditor is willing to accept and still consider the control effective.
Example Suggested Tolerable Deviation Rates:
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24. LO#
5, 6, & 7
Planning
The expected population deviation rate is the rate the auditor expects to exist in the population. The larger the expected population deviation rate, the larger the sample size must be, all else equal.
EXAMPLE: Assume a desired confidence level of 95%, and a large population, the effect of the expected population deviation rate on sample size is shown right:
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25. Population Size: Attributes Sampling
LO#
5, 6, & 7
Population Size: Attributes Sampling
Population size is not often important in determining sample sizes for attributes sampling, so we skip Advanced Module 1. Below is shown the impact of the 3 factors that matter.
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26. LO#
5, 6, & 7
Performance
This is the preferred method. Every item in the population has the same probability of being selected as every other item.
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27. LO#
5, 6, & 7
Performance
For example, assume a sales invoice should not be prepared unless there is a related shipping document. If the shipping document is present, there is evidence the control is working properly. If the shipping document is not present, a control deviation exists.
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28. LO#
5, 6, & 7
Performance
Unless the auditor finds something unusual about either of these items, they should be replaced with a new sample item.
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29. LO#
5, 6, & 7
Performance
If the auditor is unable to examine a document or to use an alternative procedure to test the control, the sample item is a deviation for purposes of evaluating the sample results.
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30. LO#
5, 6, & 7
Performance
If a large number of deviations are detected early in the tests of controls, the auditor should consider stopping the test, as soon as it is clear that the results of the test will not support the planned assessed level of control risk.
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31. LO#
5, 6, & 7
Evaluation
The auditor summarizes the deviations and evaluates the results. For example, if the auditor discovered two deviations in a sample of 50, the sample deviation rate is 4% (2 ÷ 50). But what matters is the computed upper deviation rate (CUDR), the sum of the sample deviation rate plus an allowance for sampling risk. You get this from ACL or text Table 8-8.
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32. LO#
5, 6, & 7
Evaluation
The auditor compares the tolerable deviation rate (TDR) to the computed upper deviation rate (CUDR).
If the CUDR > TDR the results indicate IC is not as effective as planned and cannot be relied upon to the extent planned.
If the CUDR <= TDR the results indicate IC is as effective as planned and can be relied upon.
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33. Attribute Sampling Example
LO#
5, 6, & 7
Attribute Sampling Example
The auditor has decided to test a control at Calabro Wireless Services. The test is to determine that the sales and service contracts are properly authorized for credit approval. A deviation in this test is defined as the failure of the credit department personnel to follow proper credit approval procedures for new and existing customers. Here is information relating to the test:
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34. Attribute Sampling Example
LO#
5, 6, & 7
Attribute Sampling Example
Part of the table used to determine sample size when the auditor specifies a 95% desired confidence level.
If there are 125,000 items in the population numbered from 1 to 125,000, the auditor can use Excel to generate random selections from the population for testing.
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35. Attribute Sampling Example
LO#
5, 6, & 7
Attribute Sampling Example
The auditor examines each selected contract for credit approval and determines the following:
Let’s see how we get the computed upper deviation rate.
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36. Attribute Sampling Example
LO#
5, 6, & 7
Attribute Sampling Example
Part of the table used to determine the computed upper deviation rate at 95% desired confidence level:
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37. Attribute Sampling Example
LO#
5, 6, & 7
Attribute Sampling Example
Tolerable Deviation Rate (6%)
Computed Upper Deviation Rate (8.2%)
<
Auditor’s Decision:
Does not support reliance on the control.
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38. End of Chapter 8
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