Chapter 9

Audit Sampling: An Application to Substantive Tests

of Account Balances

McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 13

Auditing the Inventory

Management Process

McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Substantive Tests of Details of

Account Balances The statistical concepts we discussed in the last

chapter apply to this chapter as well. Three important

determinants of sample size are

1. Desired confidence level.

2. Tolerable misstatement.

3. Estimated misstatement.

Population plays a bigger role in some of the sampling

techniques used for substantive testing.

Misstatements discovered in the audit sample must be

projected to the population, and there must be an

allowance for sampling risk.

LO# 1

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Monetary-Unit Sampling (MUS)

MUS uses attribute-sampling theory to express a

conclusion in dollar amounts rather than as a rate of

occurrence. It is commonly used by auditors to test

accounts such as accounts receivable, loans receivable,

investment securities, and inventory.

LO# 2

MUS uses attribute-sampling theory (used primarily to

test controls) to estimate the percentage of monetary

units in a population that might be misstated and then

multiplies this percentage by an estimate of how much

the dollars are misstated.

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Monetary-Unit Sampling (MUS)

Advantages 1. When the auditor expects no

misstatement, MUS usually

results in a smaller sample

size than classical variables

sampling.

2. When applied using the

probability-proportional-to-size

procedure, MUS automatically

results in a stratified sample.

3. MUS does not require the

user to make assumptions

about the distribution of

misstatements.

LO# 2

Disadvantages 1. The selection of zero or

negative balances generally

requires special design

consideration.

2. The general approach to MUS

assumes that the audited

amount of the sample item is

not in error by more than

100%.

3. When more than one or two

misstatements are detected,

the sample results calculations

may overstate the allowance

for sampling risk.

9-4

Steps in MUS Steps in MUS Application

Planning

1. Determine the test objectives.

2. Define the population characteristics:

• Define the population.

• Define the sampling unit.

• Define a misstatement.

3. Determine the sample size, using the following inputs:

• The desired confidence level or risk of incorrect acceptance.

• The tolerable misstatement.

• The expected population misstatement.

• Population size.

Performance

4. Select sample items.

5. Perform the auditing procedures.

• Understand and analyze any misstatements observed.

Evaluation

6. Calculate the projected misstatement and the upper limit on misstatement.

7. Draw final conclusions.

LO# 2

9-5

Steps in MUS

If the upper misstatement limit is greater than the

tolerable misstatement, the auditor concludes that the

account balance is materially misstated.

When faced with this situation, the auditor may:

1. Increase the sample size.

2. Perform other substantive procedures.

3. Request the client adjust the accounts receivable balance.

4. If the client refuses to adjust the account balance, the

auditor would consider issuing a qualified or an adverse

opinion.

LO# 3

9-6

Risk When Evaluating Account

Balances

Auditor's Decision Based

on Sample Evidence Not Materially Misstated Materially Misstated

Supports the fairness of

the account balance Correct decision

Risk of incorrect

acceptance (Type II)

Does not support the

fairness of the account

balance

Risk of incorrect

rejection (Type I)

Correct Decision

True State of Financial Statement Account

LO# 3

9-7

Nonstatistical Sampling for Tests

of Account Balances The sampling unit for nonstatistical sampling is normally a

customer account, an individual transaction, or a line item

on a transaction. When using nonstatistical sampling, the

following items must be considered:

o Identifying individually significant items.

o Determining the sample size.

o Selecting sample items.

o Calculating the sample results.

LO# 4

9-8

Why Did Statistical Sampling

Fall Out Of Favor?

1.Firms found that some auditors were

over relying on statistical sampling

techniques to the exclusion of good

judgment.

2.There appears to be poor

linkage between the applied audit

setting and traditional statistical

sampling applications.

LO# 4

9-9

Classical Variable Sampling

Classical variables sampling uses normal distribution

theory to evaluate the characteristics of a population

based on sample data. Auditors most commonly use

classical variables sampling to estimate the size of

misstatement.

Sampling distributions are formed by plotting the

projected misstatements yielded by an infinite

number of audit samples of the same size taken

from the same underlying population.

LO# 5

9-10

Classical Variables Sampling A sampling

distribution is useful

because it allows us

to estimate the

probability of

observing any single

sample result.

LO# 5

In classical variables

sampling, the sample

mean is the best

estimate of the

population mean.

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Classical Variables Sampling

1. When the auditor expects a

relatively large number of

differences between book and

audited values, this method will

normally result in smaller

sample size than MUS.

2. The techniques are effective for

both overstatements and

understatements.

3. The selection of zero balances

generally does not require

special sample design

considerations.

LO# 5

Advantages Disadvantages 1. Does not work well when little or no

misstatement is expected in the

population.

2. To determine sample size, the

auditor must estimate the standard

deviation of the audit differences.

3. If few misstatements are detected

in the sample data, the true

variance tends to be

underestimated, and the resulting

projection of the misstatements and

the related confidence limits are not

likely to be reliable.

9-12

Applying Classical Variables

Sampling

Defining the Sampling Unit

The sampling unit can be a customer account,

an individual transaction, or a line item. In

auditing accounts receivable, the auditor can

define the sampling unit to be a customer’s

account balance or an individual sales invoice

included in the account balance.

LO# 6

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Applying Classical Variables

Sampling

Determining the Sample Size

where

CC = Confidence coefficient

SD = Estimated standard deviation

Sample

Size =

Population size (in sampling units) × CC × SD

Tolerable misstatement – Estimated misstatement

2

LO# 6

9-14

Applying Classical Variables

Sampling Mean

misstatement

per sampling

item

= Total audit difference

Sample size

LO# 6

Population size × Mean misstatement

per sampling item

Projected

population

misstatement

= (in sampling units)

Total audit

differences squared –

Mean difference

per sampling item2

Sample

Size ×

Sample size – 1

SD =

Project the error

and the SD:

9-15

Applying Classical Variables

Sampling

Confidence

bound

Population

size CC SD

Sample size × × =

Confidence

interval

Projected

misstatement

Confidence

bound ± =

LO# 6

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Applying Classical Variables

Sampling

Lower

limit ($1,653)

Projected

misstatement $14,575

Upper

limit $30,803

If both limits are within the bounds of tolerable

misstatement, the evidence supports the conclusion

that the account is not materially misstated.

LO# 6

($50,000) $50,000 $0

Tolerable Misstatement

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End of Chapter 9

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