BA 427 – Assurance and
Attestation Services
Lecture 23
Audit Sampling
Audit Sampling
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Definition: Audit sampling is the application
of an audit procedure to less than 100% of the
items in an account balance or class of
transactions, for the purpose of evaluating
some characteristics of the balance or class.
There are two general approaches to
sampling:
 Non-statistical sampling (a.k.a. judgment
sampling)
 Statistical sampling
Statistical Sampling

Statistical sampling has two essential
features:
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The items in the sample have a known
probability of selection.
The sample results are evaluated
mathematically, in accordance with
probability theory.
The advantage of statistical sampling is
that it allows the auditor to objectively
state audit risk associated with testing
less than 100% of the population.
Statistical Sampling
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Essential terminology:

Risk is the complement of reliability:
 One minus reliability is risk
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95% reliability equates to 5% risk.
Auditors talk about risk, statisticians talk
about reliability.
Reliability and confidence levels are
synonymous.

A confidence level of 95% is equivalent to
95% reliability.
Statistical Sampling

Essential terminology:

Precision defines the maximum degree of
sampling error that is acceptable.
 Precision can be a percentage or a
dollar amount.
 The precision of an estimate describes the
range of values around the point estimate
within which the true value is expected to
fall. The lower and upper bounds are the
precision limits.
Statistical Sampling

Essential terminology:

Precision defines the maximum degree of
sampling error that is acceptable.
 When we talk about error rates, the lower
bound is usually zero, and the upper
precision limit is sometimes referred to as
the allowable exception rate or the
tolerable exception rate.
Statistical Sampling

Essential terminology:


Precision and reliability have no meaning
unless they are paired together.
Reliability expresses the probability that
the precision interval contains the true
value.
Statistical Sampling

Statistical sampling can result in two
types of errors:


Sampling Error
 The sample is not representative of the
population.
 Sampling error is eliminated if the auditor
examines the entire population.
Nonsampling Error
 All other errors
Statistical Sampling

Two possible types of sampling error:
 Incorrect acceptance (type II error):
The risk that the auditor will incorrectly
conclude that the error rate does not exceed
the allowable rate. This can result in an
audit failure.
 Incorrect rejection (type I error): The
risk that the auditor will incorrectly conclude
that the error rate does exceed the
allowable rate. This can cause the auditor to
over-audit.
Statistical Sampling

Nonsampling Error

Examples of nonsampling errors include
 Inappropriate test design.
 Failure to adequately define exceptions in
the sample population.
 Failure to recognize that an exception
satisfies the definition of one.
 Failure to draw a random or
representative sample.
 Failure to evaluate the findings properly.
Statistical Sampling
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Nonsampling Error

Nonsampling errors are human errors, and
can be reduced or eliminated.
Statistical Sampling
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Steps in a statistical sampling plan:
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Determine the objective of the test.
Define the population.
Determine the acceptable level of sampling
risk.
Calculate the sample size.
Choose a sampling approach.
Identify and examine the sample.
Evaluate and document the test results.
Statistical Sampling
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Sampling with or without replacement:
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Statistical sampling auditing techniques
usually rely on statistical properties that
assume sampling with replacement.
In fact, auditors usually sample without
replacement.
For large populations and relatively small
samples, the difference is not important.
Statistical Sampling
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Statistical sampling has three broad
categories:
 Attribute
 Variable
 Probability-proportional-to-size
Attribute Sampling
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Attribute sampling examines qualitative
characteristics of the population.
Attribute sampling is used primarily for
tests of controls.
Three types of attribute sampling plans:
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Fixed sample-size
Sequential sampling (a.k.a. stop-or-go)
Discovery sampling
Attribute Sampling

Fixed sample-size
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Used to estimate the percentage rate of
occurrence of a specific quality (or
attribute) in a population.
Example: How often are the wrong goods
shipped?
Attribute Sampling

Fixed sample-size
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The auditor chooses
 The reliability desired from the test (e.g.,
95%).
 The anticipated exception rate.
 The upper limit on the allowable
exception rate.
Based on these choices, and on the
population size, a sample size is generated
(from an audit software package, a
statistical package, or a table).
Attribute Sampling
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Fixed sample-size
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Example:
 Auditor wants to achieve 95% reliability.
 Auditor anticipates a 1% exception rate.
 Auditor can accept an exception rate of
5%.
 For a relatively large population, the
sample size is 93.
 If no more than 1 exception is identified
in the sample, the desired result is
achieved.
Attribute Sampling
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Fixed sample-size
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Even if the desired result is not achieved,
the sampling technique allows the auditor
to quantify the exception rate.
For example, using the previous data:
 2 exceptions allows the auditor to be
95% certain that the exception rate
does not exceed 6.9%.
 3 exceptions allows the auditor to be
95% certain that the exception rate
does not exceed 8.4%.
Attribute Sampling
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Sequential sampling
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This is a sampling plan that also tests for
attributes, but it is designed to minimize
the likelihood of over-sampling.
It is an efficient sampling plan when the
auditor believes that the occurrence rate is
very low.
The sample is selected in several steps;
each step relies on the results of the
previous step.
Attribute Sampling

Sequential sampling

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The auditor chooses
 The reliability desired from the test (e.g.,
95%)
 The upper limit on the allowable
exception rate (e.g., 5%)
Based on these choices, and on the
population size, an initial sample size is
generated (from an audit software package,
a statistical package, or a table).
Attribute Sampling
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Sequential sampling
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A typical initial sample size in this setting is
60 items.
If no exceptions are found in this sample,
the auditor is done.
If one exception is found, the auditor is
95% certain that the exception rate does
not exceed 8%, but 8% is greater than the
desired allowable exception rate of 5%.
Attribute Sampling
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Sequential sampling
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The auditor can extend the sample. In this
situation, if the auditor examines another
36 items and finds no exceptions, the 5%
allowable exception rate is achieved.
Following is an example of a decision table
that might be used for sequential sampling:
Attribute Sampling
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Step
Sequential sampling decision table
Cumulative
sample size
to use
Stop if
Sample Go to Step 5
cumulative
more if
if deviations
deviations deviations are at least
are equal to
are
0
1–3
4
1
30
2
48
1
2–3
4
3
63
2
3
4
4
78
3
5
4
Consider increasing assessed level of control risk
Attribute Sampling
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Discovery sampling
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This sampling plan is appropriate when the
following conditions are met:
 the auditor believes that the attribute
occurrence rate is extremely low (or even
zero).
 the identification of a single exception is
likely to cause the auditor to significantly
alter scope.
Example: How many checks were signed by
individuals without check-signing authority?
Attribute Sampling

Discovery sampling

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The auditor chooses
 The reliability desired from the test (e.g.,
90%)
 The upper limit on the allowable
exception rate (e.g., 1%)
Based on these choices, and on the
population size, a sample size is generated
(from an audit software package, a
statistical package, or a table).
Attribute Sampling
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Discovery sampling
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The auditor pulls and examines a sample of
the appropriate size.
 Such a sample could be 240 items
If no exceptions are found, the auditor is
90% certain that the maximum exception
rate is 1%.
The auditor might choose to stop examining
the sample as soon as the first exception is
found.
Variable Sampling
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Variable sampling is also called
quantitative sampling.
Variable sampling is frequently used
when performing substantive tests of
account balances.
Three types of variable sampling plans:
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Unstratified mean-per-unit
Stratified mean-per-unit
Difference estimation
Variable Sampling
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Unstratified mean-per-unit
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Stratified mean-per-unit
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A sample mean is calculated and projected
as an estimated total.
A more efficient sampling technique that
divides the population into subgroups, and
samples from each group.
Difference estimation

A statistical plan used to estimate the
difference between two populations (e.g.,
audited values vs. book values)
Variable Sampling
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Unstratified mean-per-unit
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Sampling for substantive testing provides
evidence about whether an account balance
is materially misstated.
Management provides an assertion about an
account balance.
The amount is expected to represent the
true value, but the true value is not known.
The auditor collects evidence as to whether
management’s assertion is a fair
representation of the true value.
Variable Sampling
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Unstratified mean-per-unit
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By taking a sample and drawing an
inference about the population, the auditor
either supports or rejects the conclusion
that management’s reported number is a
fair representation.
Variable Sampling
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Unstratified mean-per-unit
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The auditor chooses
 The reliability desired (e.g., 90%)
 The precision interval (based on
materiality)
Based on these choices, and on both the
population size and the estimated standard
deviation of the population, a sample size is
generated (from an audit software package,
a statistical package, or a table).
Variable Sampling
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Unstratified mean-per-unit
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The sample is pulled, and the sample mean
is extrapolated to estimate the population
mean.
If the standard deviation of the sample
differs significantly from the estimate used
to determine the sample size, the precision
interval will have to be updated (i.e., it will
not be as planned).
Variable Sampling
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Stratified mean-per-unit
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Appropriate when the population has a large
standard deviation. (The size of the items in
the population is highly variable.)
Reduces the required sample size, relative
to unstratified mean-per-unit.
In order to apply stratified mean-per-unit,
every item in the population must belong to
one and only one stratum, and the exact
number of elements of each stratum must
be known.
Probability-Proportional-to-Size
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Also called Dollar-Unit Sampling
PPS uses a dollar as the sampling unit.
PPS sampling gives each individual dollar in
the population an equal chance of selection.
However, individual dollars do not constitute
the sample, but rather, the items that contain
those dollars.
Consequently, large dollar-value items have a
greater chance of being selected.
Probability-Proportional-to-Size
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PPS is appropriate for identifying
overstatement of assets (e.g., inventory or
accounts receivable).
PPS allows the auditor to draw a conclusion
about the likelihood that an account is
overstated by more than a specified amount.