mcgraw-hill/irwin © the mcgraw-hill companies 2010 audit sampling: an overview and application to...

McGraw-Hill/Irwin © The McGraw-Hill Companies 2010

Audit Sampling: An Overview and

Application to Tests of Controls

Chapter Eight


Introduction

Auditing standards recognize and permit both statistical and non-statistical methods of audit sampling.

Auditing standards recognize and permit both statistical and non-statistical methods of audit sampling.

Two technological advances have reduced the number of times auditors need to apply sampling techniques to

gather audit evidence:

1Development ofwell-controlled,

automated accounting

systems.

1Development ofwell-controlled,

automated accounting

systems.

2Advent of powerful

PC audit software todownload andexamine client

data

2Advent of powerful

PC audit software todownload andexamine client

data


IntroductionHowever, technology will never eliminate the need for auditors to rely on sampling to some degree because:1. Many control processes require human involvement.

2. Many testing procedures require the auditor to physically examine an asset.

3. In many cases auditors are required to obtain and examine evidence from third parties.


Definitions and Key Concepts

On the following slides we will define:

1. Audit Sampling

2. Sampling Risk

3. Confidence Level

4. Tolerable and Expected Error

On the following slides we will define:

1. Audit Sampling

2. Sampling Risk

3. Confidence Level

4. Tolerable and Expected Error


Audit Sampling

The application of audit procedures to less than 100 per cent of items within a population of audit relevance such that

all sampling units have a chance of selection in order to provide the auditor

with a reasonable basis on which to draw conclusions about the entire

population.

The application of audit procedures to less than 100 per cent of items within a population of audit relevance such that

all sampling units have a chance of selection in order to provide the auditor

with a reasonable basis on which to draw conclusions about the entire

population.


Sampling RiskSampling risk is the element of uncertainty that enters

into the auditor’s conclusions anytime sampling is used. There are two types of sampling risk.

Risk of incorrect rejection (Type I) – in a test of internal controls, it is the risk that the sample supports a conclusion that 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 rejection (Type I) – in a test of internal controls, it is the risk that the sample supports a conclusion that 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 supports a conclusion that the control is operating effectively when, in fact, it is not operating effectively. In substantive testing, it is the risk that the sample supports the recorded balance when it is, in fact, materially misstated.


Sampling Risk

Three Important Factors in Determining Sample Size

1.1. The desired level of assurance in the results (or confidence level),

2. Acceptable defect rate (or tolerable error), and

3. The historical defect rate (or expected error).

1.1. The desired level of assurance in the results (or confidence level),

2. Acceptable defect rate (or tolerable error), and

3. The historical defect rate (or expected error).


Confidence Level

Confidence level is the complement of sampling risk.

The auditor may set sampling risk for a particular sampling

application at 5 per cent, which results in a

confidence level of 95 per cent.

The auditor may set sampling risk for a particular sampling

application at 5 per cent, which results in a

confidence level of 95 per cent.


Tolerable and Expected Error

Once the desired confidence level is established, the sample size is determine largely by how much

the tolerable error exceeds expected error.

PrecisionPrecision, at the , at the planning stage of planning stage of audit sampling, is audit sampling, is the difference the difference between the between the expected and expected and tolerable deviation tolerable deviation rates.rates.

PrecisionPrecision, at the , at the planning stage of planning stage of audit sampling, is audit sampling, is the difference the difference between the between the expected and expected and tolerable deviation tolerable deviation rates.rates.

The term allowance for sampling

riskis used to reflect theconcept of precision

in a sampling application.


Audit Evidence – To Sample or Not?

Relationship between Evidence Types and Audit Sampling

Type of Evidence Audit Sampling Commonly Used

Inspection of tangible assets YesInspection of records or documents YesReperformance YesRecalculation YesConfirmation YesAnalytical procedures NoScanning NoInquiry NoObservation No



• 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 activity 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.

• 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 activity 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.



Reperformance. 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.

Reperformance. 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.


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 per cent of an account or class of

transactions, auditors will typically test all the transactions greater than a particular monetary amount.


Testing Only One or a Few Items

Highly automated information systems process transactions consistently unless the system or

programs are changed.

The auditor may test the The auditor may test the general controls over the general controls over the system and any program system and any program

changes, but test only a few changes, but test only a few transactions processed by transactions processed by

the IT system.the IT system.

The auditor may test the The auditor may test the general controls over the general controls over the system and any program system and any program

changes, but test only a few changes, but test only a few transactions processed by transactions processed by

the IT system.the IT system.


Types of Audit Sampling

Auditing standards recognize and permit both statistical Auditing standards recognize and permit both statistical and non-statistical methods of audit sampling.and non-statistical methods of audit sampling.

Auditing standards recognize and permit both statistical Auditing standards recognize and permit both statistical and non-statistical methods of audit sampling.and non-statistical methods of audit sampling.

In non-statistical sampling, the auditor does not use statistical techniques to determine sample size, select the sample items, or measure sampling risk.

Statistical sampling, uses Statistical sampling, uses the laws of probability to the laws of probability to compute sample size and compute sample size and evaluate the sample results. evaluate the sample results. The auditor is able to use The auditor is able to use the most efficient sample the most efficient sample size and quantify sampling size and quantify sampling risk.risk.

Statistical sampling, uses Statistical sampling, uses the laws of probability to the laws of probability to compute sample size and compute sample size and evaluate the sample results. evaluate the sample results. The auditor is able to use The auditor is able to use the most efficient sample the most efficient sample size and quantify sampling size and quantify sampling risk.risk.


Types of Audit Sampling

Advantages of statistical sampling

1. Design an efficient sample.

2. Measure the sufficiency of evidence obtained.

3. Quantify sampling risk.

Advantages of statistical sampling

1. Design an efficient sample.

2. Measure the sufficiency of evidence obtained.

3. Quantify sampling risk.Disadvantages of statistical sampling

1. Training auditors in proper use.

2. Time to design and conduct sampling application.

3. Lack of consistent application across audit engagement teams.

Disadvantages of statistical sampling

1. Training auditors in proper use.

2. Time to design and conduct sampling application.

3. Lack of consistent application across audit engagement teams.


Statistical Sampling Techniques

1. Attribute Sampling.

2. Monetary-Unit Sampling.

3. Classical Variables Sampling.


Attribute Sampling

Used to estimate the proportion of a population that possess a specified

characteristic. The most common use of attribute sampling is for tests of controls.

Our client’s controls require that sales are authorized for credit

approval.

Our client’s controls require that sales are authorized for credit

approval.

Yes, I know. We are planning a test of that control using attribute

sampling.

Yes, I know. We are planning a test of that control using attribute

sampling.


Monetary-Unit Sampling

Monetary-unit sampling uses attribute sampling theory to estimate the monetary (e.g. in €) amount of

misstatement for a class of transactions or an account balance.

This technique is used extensively because it has a number of advantages over classical variables

sampling


Classical Variables Sampling

Auditors sometimes use variables sampling to estimate the monetary value of a class of

transactions or account balance. It is more frequently used to determine whether an account is

materially misstated.


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.

PlanPlan PerformPerform EvaluateEvaluate DocumentDocument


Planning

Planning1. Determine the test objectives.2. Define the population characteristics. • Define the sampling population. • Define the sampling unit. • Define the control deviation conditions.3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. • The tolerable deviation rate. • The expected population deviation rate.

The objective of attribute sampling when used for tests of controls is to evaluate the operating

effectiveness of the internal control.


Planning

Planning2. Define the population characteristics. • Define the sampling population. • Define the sampling unit. • Define the control deviation conditions.3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. • The tolerable deviation rate. • The expected population deviation rate.

All of the items that constitute the class of transactions make up the sampling population.


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.


Planning


A deviation is a departure from adequate performance of the internal control.


PlanningPlanning

3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. • The tolerable deviation rate. • The expected population deviation rate.

The confidence level is the desired level of assurance that the sample results will support a conclusion that the control is functioning effectively. Generally, when

the auditor has decided to rely on controls, the confidence level is 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.


PlanningPlanning

3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. • The tolerable deviation rate. • The expected population deviation rate.

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:

Assessed Importance of a Control

Tolerable Deviation

Rate

Highly important 3–5%

Moderately important 6–10%


Planning

Planning3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. • The tolerable deviation rate. • The expected population deviation rate.

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. Expected Population

Deviation Rate Sample

Size

1.0% 93

1.5% 124

2.0% 181

3.0% ‡

‡ Sample size too large to be cost-effective.

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:


Population Size: Attributes Sampling

Population size is not an important factor in determining sample size for attributes sampling. The population size has little or no effect on the sample size, unless the population is relatively small, say less than 500 items.

Factor Relationship to

Sample Size Change in

Factor Effect on

Sample Size Lower DecreaseHigher IncreaseLower IncreaseHigher DecreaseLower DecreaseHigher Increase

Decreases sample size only when populationis small (fewer than 500 items)

Population size

Direct

Inverse

Direct

Examples

Desired confidence level

Tolerable deviation rate

Expected population deviation rate


Performance

Performance and Evaluation4. Select sample items. • Random-Number Selection. • Systematic Selection.5. Perform the Audit Procedures. • Voided documents. • Unused or inapplicable documents • Inability to examine a sample item. • Stopping the test before completion.6. Calculate the Sample Deviation and Upper Deviation Rates7. Draw Final Conclusions

Every item in the population has the same probability of being selected as every other

sampling unit in the population.


Performance

Performance and Evaluation4. Select sample items. • Random-Number Selection. • Systematic Selection.5. Perform the Audit Procedures. • Voided documents. • Unused or inapplicable documents • Inability to examine a sample item. • Stopping the test before completion.6. Calculate the Sample Deviation and Upper Deviation Rates7. Draw Final Conclusions

The auditor determines the sampling interval by dividing the population by the sample size. A starting number is selected

in the first interval and every nth item is selected.


Performance

Performance and Evaluation5. Perform the Audit Procedures. • Voided documents. • Unused or inapplicable documents • Inability to examine a sample item. • Stopping the test before completion.6. Calculate the Sample Deviation and Upper Deviation Rates7. Draw Final Conclusions

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.


Performance


Unless the auditor finds something unusual about either of these items, they should be replaced with a new sample item.


Performance

Performance and Evaluation5. Perform the Audit Procedures. • Voided documents. • Unused or inapplicable documents • Inability to examine a sample item. • Stopping the test before completion.6. Calculate the Sample Deviation and Upper Deviation Rates.7. Draw Final Conclusions.

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.


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.


EvaluationEvaluation

6. Calculate the Sample Deviation and Upper Deviation Rates7. Draw Final Conclusions

After completing the audit procedures, the auditor summarizes the deviations for each control tested and evaluates the results. For

example, if the auditor discovered two deviations in a sample of 50, the deviation rate

in the sample would be 4% (2 ÷ 50).The upper deviation rate is the sum of the sample deviation rate and an appropriate

allowance for sampling risk.


Evaluation

Evaluation6. Calculate the Sample Deviation and Upper Deviation Rates7. Draw Final Conclusions

Auditor's Decision Based on Sample Evidence Reliable Not Reliable

True State of Internal Control

Correct decision

Risk of incorrect rejection (Type I)

Supports the planned level of control risk

Does not support the planned level of control risk

Risk of incorrect acceptance (Type II)

Correct decision

The auditor compares the tolerable deviation rate to the computed upper deviation rate.


Attribute Sampling Example

The auditor has decided to test a control at Calabro Wireless Services. The test is to determine 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:

Desired confidence level 95%Tolerable deviation rate 6%Expected population deviation rate 1%Sample size 78



ExpectedPopulationDeviation

Rate 2% 3% 4% 5% 6% 7%0.00% 149 99 74 59 49 42 0.25% 236 157 117 93 78 66 0.50% 157 117 93 78 66 0.75% 208 117 93 78 66 1.00% 156 93 78 66 1.25% 156 124 78 66 1.50% 192 124 103 66

Tolerable Deviation Rate

Sample Size at 95% Desired Confidence Level

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.



The auditor examines each selected contract for credit approval and determines the following:

Number of deviations 2 Sample size 78 Sample deviation rate 2.6%Computed upper deviation rate 8.2%Tolerable deviation rate 6.0%

Let’s see how we get the computed Let’s see how we get the computed upper deviation rate.upper deviation rate.

Let’s see how we get the computed Let’s see how we get the computed upper deviation rate.upper deviation rate.



Part of the table used to determine the computed upper deviation rate at 95% desired confidence level:

SampleSize 0 1 2 3

25 11.3 17.6 - - 30 9.5 14.9 19.6 - 35 8.3 12.9 17.0 - 40 7.3 11.4 15.0 18.3 45 6.5 10.2 13.4 16.4 50 5.9 9.2 12.1 14.8 55 5.4 8.4 11.1 13.5 60 4.9 7.7 10.2 12.5 65 4.6 7.1 9.4 11.5 70 4.2 6.6 8.8 10.8 75 4.0 6.2 8.2 10.1 80 3.7 5.8 7.7 9.5

Actual Number of Deviations Found



TolerableDeviationRate (6%)

ComputedUpper DeviationRate (8.2%)

<

Auditor’s Decision:Auditor’s Decision:Does not support reliance on the control.Does not support reliance on the control.

Auditor’s Decision:Auditor’s Decision:Does not support reliance on the control.Does not support reliance on the control.


Non-Statistical Sampling for Tests of Control

Determining the Sample Size

An auditing firm may establish a non-statistical sampling policy like the one below:

Such a policy will promote consistency in sampling applications.

DesiredLevel ofControls SampleReliance SizeLow 15–20Moderate 25–35High 40–60



Selecting the Sample Items

Non-statistical sampling allows the use of random or systematic selection, but also permits the use of

other methods such as haphazard sampling.

When haphazard sample selection is used, sampling

units are selected without any bias, that is to say, without a

special reason for including or omitting the item in the sample..

When haphazard sample selection is used, sampling

units are selected without any bias, that is to say, without a

special reason for including or omitting the item in the sample..



Calculating the Upper Deviation Rate

With a non-statistical sample, the auditor can calculate the sample deviation rate, but cannot mathematically

quantify the computed upper deviation rate and sampling risk associated with the test.


Considering the Effect of Population Size

The sample size tables in the chapter assume a large population. Sample size can be adjusted using the

‘finite correction factor’ in the Advanced Module or by using the table below for very small populations:

Control Frequency and Population Size Sample Size

Quarterly (4)Quarterly (4) 22

Monthly (12)Monthly (12) 2-42-4

Semimonthly (24)Semimonthly (24) 3-83-8

Weekly (52)Weekly (52) 5-95-9


End of Chapter 8

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Documents

sampling risk sampling

complement of sampling

types of sampling risk

mcgrawhill companies

sampling units

sampling techniques

audit evidence

expected error slide