AUDIT SAMPLING

The professional standards require the Auditor to obtain sufficient appropriate

evidence to be able to draw reasonable conclusions on which to base the audit
opinion. Auditors usually draw conclusions about the account balance or
transaction class by examining only a SAMPLE of EVIDENCE.

 PSA 530 defines audit sampling as,

The application of audit procedures to less than 100% of the items within an
account balance or class of transactions such that all sampling units have a
chance of selection.

Audit Sampling is performed on the assumption that the sample selected for
testing is the representative of the population. The auditor may decide that it
would be appropriate to examine the entire population (100% examination)
of items that make up an account balance since the population constitutes
a small number of large value items. Likewise, the auditor may decide to
apply audit procedures only to those items which have particular
significance (selective testing). The auditor needs to be satisfied that
sufficient appropriate evidence is obtained to meet the objectives of the test.

 Risks in Sampling
 Uncertainty of not detecting material errors in an account balance or
class of transactions may arise because of sampling and non-sampling
risks.

 Sampling Risk
 Refers to possibility that the auditor’s conclusion, based on a sample
may be different from the conclusion reached if the entire population
were subjected to the same audit procedures. This exist because the
sample selected for testing may not be truly representative of a
population.

a. Alpha Risk is the risk that the auditor will conclude,

 In the case of test of control, that internal control is not reliable
when in fact it is effective and can be relied upon (risk of under
reliance);
 In the case of substantive test, the material misstatement exists
in an account balance or transaction class when in fact such
misstatement does not exist (risk of incorrect rejection).

This type of audit risk affects audit efficiency.

 b. Beta Risk is the risk the auditor will conclude,
 In the case of test of control, that internal control is reliable
when in fact it is not effective and cannot be relied upon (risk
of overreliance); or
 In the case of substantive test, the material misstatement does
not exists in an account balance or transaction class when in
fact such misstatement does exist (risk of incorrect
acceptance).

This type of audit risk affects audit effectiveness.

 Non-sampling Risk
 Refers to the risk that the auditor may draw incorrect conclusions
about the account balance or class of transactions because of
human errors. This includes all aspects of audit risk that are not due to
sampling.

 Controlling the Risks

 The only way to eliminate sampling risk is to examine the entire
population. Accordingly, auditors do not normally attempt to eliminate
sampling risk. Instead, auditors control sampling risk by:
 Increasing the sample size; and
 Using an appropriate sample selection method.

 Non-sampling risk, on the other hand, is something that cannot be

eliminated even if the auditor examines the entire population. This risk,
however, can be minimize by:
 Proper planning; and
 Adequate direction, review, and supervision of the audit team.

 General Approaches to Audit Sampling

 There are two sampling approaches that can be used; the statistical
and non-statistical sampling.
 Statistical Sampling is a sampling approach that
 Uses random based selection of sample; and
 Uses the law of probability to measure sampling risk and
evaluate sample results.

 Non-statistical Sampling in contrast, is a sampling approach that

purely uses auditor’s judgement in estimating sampling risks,
determining sample size, and evaluating sample results.
 The only difference between the two methods is that statistical sampling
allows auditors to measure or quantify the sampling risks by using
mathematical formula. Thus, statistical sampling helps the auditor to:
 Design an efficient sample;
 Measure the sufficiency of evidence obtained; and
 Objectively evaluate the sample results.
However, these benefits cannot be obtained without additional cost.

 Audit Sampling Plus

 Audit sampling may be used when performing test of controls or
substantive test. When statistical sampling is used, the auditor may use
either attribute or variable sampling plan.
 Attribute Sampling
 This is a sampling plan used to estimate the frequency of
occurrence of a certain characteristic in a population
(occurrence rate).
 It is generally used when performing test of controls to estimate
the amount of misstatements in the financial statements.
 Variable Sampling
 This is a sampling plan used to estimate a numerical
measurement of a population such as peso value.
 It is generally used in performing substantive test to estimate the
amount of misstatement in the financial statements.

 Basic Steps in Audit Sampling

 Basic steps on audit procedures:

Determine
Determine
Define the the Select the Apply the Evaluate
the
Objective Sample Sample Procedure the Results
Procedure
Size

1. Define the objective of the test

The audit objective largely determines the audit procedures to be
applied. Hence, before deciding on the nature of the audit
procedures to be performed, the auditor must define the specific
objective of the test.

2. Determine the audit procedures to be performed.

 After defining the audit objective, the next step is to determine the
specific audit procedure that will be performed to satisfy the
objective. This step also involve defining the population and the
characteristics to be tested.

3. Determine the sample size

Once the auditor has decided to apply a certain audit procedure to a
sample of items in a population, the auditor must decide how many
sampling units to include in the sample.

4. Select the sample

A sample selection technique must be designed in such a way that all
items in the population will have an opportunity to be selected.
Statistical sampling requires the sample items be selected at random
so that each sampling unit has a known chance of being selected.

5. Apply procedures
After the sample items have been selected, the auditor applies the
planned audit procedure to the sample.

6. Evaluate the sample results

Once audit procedures have been performed on all sample items, the
results must be evaluated to determine whether sufficient evidence
has been obtained to satisfy the objective.

It is to be emphasized that steps (1), (2), (5), and (6) will be performed
whether the auditor uses audit sampling or not. Hence, the only
difference between audit sampling and 100% examination is that audit
sampling involves steps (3), (4), and (6)

 Sampling for Test of Control

Audit sampling for test of control is generally appropriate when application of
the control leaves evidence of performance. For those controls that leave no
documentary evidence of performance, non-sampling procedures would be
more appropriate.

 Determination of Sample Size

Three factors affecting the determination of sample size for test of control:
a) Acceptable sampling risk;
b) Tolerable deviation rate; and
c) Expected deviation rate

 Acceptable sampling risk

 Sample risk is inherent in an audit sampling application. The size of the
sample is affected by the level of sampling risk the auditor is willing to
accept.

There is an inverse relationship between the acceptable sampling risk

and sample size. The smaller the sampling risk the auditor is willing to
accept, the larger the sample size to be (and vice versa).

 Tolerable deviation rate

Tolerable deviation rate is the maximum rate of deviation the auditor is
willing to accept, without modifying the planned degree of reliance
on the internal control.

The tolerable deviation rate is inversely related to the sample size.

Therefore, a decrease in the tolerable deviation rate will cause the
sample size to increase.

Establishing tolerable deviation rate and the acceptable sampling risks

requires professional judgment and involves consideration of:
 The importance of the control; and
 The degree of reliance to be placed on such control.

If the control is important in providing reliable financial statements, the

auditor would most likely decrease the acceptable level of sampling
risk and tolerable deviation rate to obtain more evidence that such
control is working effectively.

 Expected deviation rate

The rate of deviation the auditor expects to find in the population

before testing begins. The expected deviation rate has a direct effect
on the sample size.

The expected population deviation rate should not exceed the

tolerable deviation rate. If it is exceeded, the auditor generally omits
testing of that control procedures and either seeks to obtain assurance
by testing other relevant internal control policies and procedures, or
asses control risk at a higher level.

Sample Acceptable Tolerable Expected

Size Sampling Risk Deviation Rate Deviation Rate
Small High High Low
 Larger Low Low High

 Sample Selection Method

PSA 530 has identified three principal methods of selecting samples namely,
(a) random number selection, (b) systematic selection, and (c) haphazard
selection.

 Random number selection

Under this method, the auditor selects the sample by matching

random numbers with the population numbering system. An
advantage of this selection technique is that it gives each item in the
population an equal opportunity to be selected.

 Systematic selection

This method involves determining a constant sampling interval and

then selects the sample based on the size of that interval. When using
systematic selection, the auditor should determine that the population
is not structured in such manner that the sampling interval corresponds
with a particular pattern In the population.

An advantage of this type of selection is that it is easy to use.

Furthermore, the population do not have to be pre-numbered in order
for the auditor to use this technique.

 Haphazard selection

When using this method, the sample is selected without following an

organized or structured technique. This selection is useful for non-
statistical sampling but it is not used for statistical sampling.

In selecting the sample and applying the appropriate audit procedures,

the auditor may encounter the following situations:

a) Voided documents

If the document that has been selected is properly voided, such

document should be replaced by another sample item.

b) Missing documents
 If the auditor encounters missing documents and he is unable to
determine whether the control has been properly performed such
item should be treated as a deviation for the purpose of evaluating
sample results.

 Evaluation of Results

When evaluating sample results, both the qualitative and the quantitative
factors of deviations should be considered. Here are some general
guidelines:

1. Determining the sample deviation rate

The sample deviation rate is computed by dividing the number of

deviations found in the sample by the sample size.

2. Compare the sample deviation rate with the tolerable deviation rate
and draw an overall conclusion about the population.

This comparison may result to the following situations:

 The sample deviation rate exceeds the tolerable deviation rate.

This means that the sample results do not support the auditor’s
planned degree of reliance on internal control. Hence, control
risk will be assessed at a high level and more extensive
substantive tests should be performed.

 The sample deviation rate is less than the tolerable deviation

rate.

If the sample deviation rate is less than the tolerable rate, the
auditor should consider the allowance for sampling risk- that is,
the possibility that these sample results could have occurred
even if the actual population deviation rate is higher than the
tolerable rate. As the sample deviation rate approaches the
tolerable deviation rate the allowance for sampling risk
decreases.

a) If the sample deviation rate is considerably lower than

the tolerable deviation rate, there is a low risk that the
actual population deviation rate will exceed the
tolerable deviation rate.
 b) If the sample deviation rate is barely lower than the
tolerable deviation rate, there is a high possibility that
the actual deviation rate will exceed the tolerable rate.

OTHER SAMPLING APPLICATIONS FOR TEST OF CONTROLS

 Sequential Sampling
- can be used as an alternative form of testing controls when an
auditor expects every few deviations within the population.

Under this method:

 the auditor does not use fixed sample size
 it is sometimes called stop-or-go sampling; after testing the sample
the auditor makes a decision whether to stop or go on with the
sampling plan.
 Thus, if no deviations are found in the sample, the auditor may
conclude that the internal control procedure is reliable and
therefore may stop the sampling plan. Also if the auditor observes
many deviations, the auditor may also terminate the sampling plan
and conclude that the planned degree of reliance on internal
control is not justified.

On the other hand, if one or few deviations are found, the auditor
may decide to go on with the examination of another set of sample
in attempt to obtain more evidence to support the planned
assessed level of control risk.

 Discovery Sampling
- this form of attribute sampling is most appropriate when no
deviations are expected in the population and therefore even
deviation would cause concern.
- it is normally used when the auditor suspects that an irregularity
might have been committed.
- under this method, the auditor determines the sample size efficient
to discover at least one deviation to confirm whether an irregularity
has occurred.

 Sampling for Substantive Tests

 Analytical procedures that involve comparison of the financial
statements with the auditor’s expectation do not involve sampling.
 Audit sampling is appropriate when performing Test of details to
estimate the amount of misstatements in the financial statements.
 Determination of Sample Size
When determining sample size for substantive tests, the following factors
must be considered.

 Acceptable Sampling Risk

When determining the acceptable level of sampling risk for substantive
tests, the auditor should consider the components of audit risk- inherent,
control, and detection risks.
 For practical purposes, the auditor uses the acceptable level of
detection risk as the acceptable sampling after giving adequate
consideration to the risk that analytical procedures may fail to detect
material misstatement in account balance.
 There is an inverse relationship between the acceptable sampling risk
and the sample size: the lower the risk the auditor accepts, the larger
the sample size must be.

 Tolerable Misstatement
Tolerable misstatement is the maximum amount of misstatement the
auditor will permit in the population to and still be willing to conclude that
the balance is fairly stated. This is determined in the planning stage of the
audit and it is related to the auditor’s preliminary estimate of materiality.
 There is an inverse relationship between the tolerable misstatement
and the sample size. A smaller measure of tolerable misstatement will
cause the sample size to increase.

 Expected Misstatement
Expected misstatement is the amount of misstatements that the auditor
believes exists in the population.
 Like the expected deviation rate in test of controls, the expected
amount of misstatements may be determined based on the results of
prior year’s substantive tests or pilot sample. As the expected
misstatement draws near the tolerable misstatements, the auditor
needs more precise information from the sample.
 There is a direct relationship between the expected misstatement
and the sample size. An increase in the amount of the misstatement
that the auditor expects to be present in the population will cause
the sample size to increase.

 Variation in the Population
 The peso amount included in the population tends to vary significantly.
When using statistical sampling, this variability is measured by the standard
deviation.

When a population consists of highly variable recorded amounts, it is

difficult to select a representative sample. Consequently, a larger sample
size is required as the degree of variability within the population increases.
The auditor can estimate the variation based on the prior year’s test results
or a pilot sample.

 Sample Selection Method

When selecting a sample for substantive tests, the auditor may use any one
of the sample selection methods mentioned earlier.

 Stratified Sampling
The auditor may divide or stratify the population into meaningful groups in
order to decrease the effect of variance within the population. When
selecting a stratified sample, the sample size should be determined for
each stratum and selected from that stratum.
 It is useful to the auditor when performing substantive tests because
a) It decreases the effect of variance in the population and as a
result, decreases the sample size, and
b) It allows the auditor to give more emphasis to those items with
higher monetary value.

 Value Weighted Selection

It also gives each item in the population an opportunity to be selected.
However, the probability of an item to be selected is directly proportional
to the monetary value of such item. This is the reason why this type of
sampling is sometimes called probability proportional to size sampling.
 Each peso is treated as one sampling unit. That is why, it is also called
monetary unit sampling.
 This method is similar to stratified sampling in that large monetary
values are given greater representation in the sample and it is
appropriate when the auditor anticipates overstatements in an
account, the greater the probability that the account will be
selected.
EVALUATING THE RESULTS

1. Project the misstatements to the population.

 Projecting misstatements can be accomplished using:
a. Ratio estimation
b. Difference estimation
 The only difference between the two methods is that ratio estimation
uses the book values of the population size and sample size to
project the misstatements, while difference estimation uses the
number of customers to project the misstatements to the population.
Hence, the use of ratio estimation is appropriate when the amount
of misstatements found is approximately proportional to the client's
book amount.
2. Compare the projected misstatements together with the tolerable
misstatements and draw an overall conclusion.

If the projected misstatements is greater than the tolerable misstatement,

the auditor will conclude that the account balance is materially misstated.

If the projected misstatement is less than the tolerable misstatement, the

auditor should consider the allowance for sampling risk. The auditor should
recognize that sampling risk increases as the projected misstatement
approaches the tolerable misstatement.

A summary of the essential audit sampling steps is presented on the next page

Test of Controls Substantive tests

1. Define the Specify the control Specify the purpose of
objective of the procedures to be tested the test and its
test relationship to the
financial statements
assertions
2. Determines the Determine the Determine the
procedures to be appropriate audit appropriate audit
performed procedures to be procedures to be
performed to satisfy the performed to satisfy the
objective objective
Define the population Define the population
and the conditions that and its characteristics
constitute a deviation
3. Determine the Consider the effects of Consider the effects of
sample size the following factors in the following factors in
determining the sample determining the sample
size size
  Acceptable  Acceptable
sampling sampling
risk(Inverse) risk(Inverse)
 Tolerable  Tolerable
Deviation Deviation
rate(inverse) rate(inverse)
 Expected  Expected
Population Misstatement and
Deviation Population
Rate(Direct) Variation
Rate(Direct)
4. Select the sample Use any of the following Use any of the following
techniques: techniques and stratify
 Random Number the population when
Selection appropriate:
 Systematic  Random Number
Selection Selection
 Haphazard  Systematic
Selection Selection
 Haphazard
Selection
 Valuated
Selection
5. Apply the audit Apply the audit Apply the audit
procedures procedures to the procedures to the
sample items sample items
6. Evaluate the Decide whether the Decide whether to
sample results results supported the accept the account
planned degree of balance as fairly stated
reliance on internal or to require further
control actions