General

Introduction to audit sampling

Othuke Andrew Akpeli9 years ago6 years ago047 mins

Clearly it is impossible, in all but the very
smallest organizations, for auditors to check every transaction. In the case of
the largest companies there may be millions of items of data which the auditor
would have to consider. Oddly the general public often has the perception that
auditors check everything, which is why, when some

form of financial scandal
surfaces, uninformed speculation often tries to attach blame to the auditors
because they are supposed to have checked everything.

The sheer impossibility of this, not to mention the
prohibitive cost if it were to be even attempted, is why auditors adopt a
either a systems-based approach to auditing or a risk based approach, which we
look at in chapters 13 and 14, both of which require the auditors to select
samples of transactions for testing.

Note, however, that the auditors expect to gain
audit evidence about a population from sampling it but wise auditors will use
sampling tests only in conjunction with other available evidence, in addition
to the evidence from the sample.

Sampling is only one method of gathering evidence
by audit testing and students should be familiar with other methods of evidence
gathering

Basis of sampling

Central to any form of systems-based auditing is
the concept of audit sampling.

The objective in all sampling is to draw
conclusions about a large volume of data, know as the population, based on
examination of a sample taken from that population. The population for this
purpose is a category of transaction e.g. all the sales invoices or all the
PAYE calculations or all the goods received notes.

Note that for sampling purposes every item in the
population must be of the same type. There is an auditing standard ISA 530
audit sampling and other means of testing. ISA 530 states:

When
designing audit procedures the auditor should determine appropriate means for
selecting items for testing so as to gather sufficient appropriate audit
evidence to meet the objectives of the audit procedures.

What this means is the application of audit
procedures to less than 100 per cent of items within a class or type of
transaction such that each individual item within that class has an equal
chance of selection. This enables the auditors to draw conclusions, based on
the results of those tests, about the population as a whole.

Sampling is most often used in compliance testing
of client’s internal controls, but can also be applied to tests of balance
sheet items such as stocks, debtor and creditor ledger balances, or fixed
assets.

There are two key issues fundamental to all
sampling techniques.

1 The population has to be homogeneous-
i.e. each item in the population has to be the same as the next one.

For
example, sampling test on sales invoices cannot include credit notes; a
sampling test on finished goods stock items cannot include raw material stocks.
Each class of transaction has to be sampled separately- which may mean lots of
tests!

2 Every item in the population must have an
equal chance of selection.

This
means that, for example, block sampling-where auditors pick a block of
transactions to test, e.g. all goods returned notes in may – is not actually a
very good basis for testing as, in this case, the goods returned notes for
January to April and June to December have no chance of being selected.

When sampling is not appropriate

Note that sampling may not be appropriate in
certain circumstances. They are primarily:

·
When the
auditor has already been advised of a high level of errors or systems failures
or in connection with a possible fraud.

·
Where
populations are too small far a valid conclusion – it may be quicker to check
them all!

·
Where all
the transactions in a population are material, e.g. a manufacturer of aero
planes – they may only sell 20 in a year but each contract is worth several
hundred million pounds.

·
Where
data is required to be fully disclosed in the financial statements, e.g.
directors’ emoluments.

·
Where the
population is not homogenous.

Points to consider before sampling

Auditors should consider:

Objective of the test

Why is this test being carried out? What
contribution does it make to the overall assessment of a true and fair view?

What is the population from which the sample will
be taken?

The population has to be defined precisely. This
may be, for example, all sales credit notes.

The sampling unit

Note that in
compliance testing it is the operation of the control on a transaction which is
being tested, not the transaction. It is the transaction which is the sampling
unit used to test the control.

The definition of error

The auditors have to define what constitutes an
error. Some ‘error’ may not be material or not considered to be significant –
auditors have to decide what it is they are looking for.

Sampling risk

Because they do not check the entire population
there is a risk that the sample, however well chosen, will not be
representative of the population as a whole. This is called ‘sampling risk’.

If the basis for choosing the sample is a rational
one and planning, testing and evaluation procedures is properly carried out
then sampling risk can be minimized to an acceptable level.

Note that auditors have to deal with sampling risk
both in compliance and substantive testing. For example, in compliance testing,
there is a risk that the auditor will place a higher estimate of the
effectiveness of a control, and therefore a lower estimate of control risk,
during compliance testing because the error in the sample used in testing the
control is less than the error in the population as a whole.

In substantive testing the sampling risk relates to
the relationship between the sample and the population described above.

Bases of sampling

There are two approaches to selecting samples:

·
Non-statistical
or ‘judgments’ sampling.

·
Statistical
sampling.

Non-statistical sampling

This means selecting a sample of appropriate size
on the basis of the auditors’ judgment of what is desirables

This approach has some advantages:

·
The
approach has been used for many years. It is well understood and refined by
experience.

·
The
auditors can bring their judgments and expertise into play.

·
No
special knowledge of statistics is required.

·
No time
is spent on struggling with mathematics.

There are, however, some serious disadvantages:

·
It is
unscientific.

·
Often
sample sizes are too large, which can be wasteful, or too small, which renders
the test invalid.

·
There is
no consistency of results – two different auditors will produce two different
samples.

·
No
quantitative results are obtained.

·
Personal
bias in the selection of the sample or its size.

·
The
sample selection can be slanted to the auditor’s needs, e.g. selection of items
near the year end to help with cut-off evaluation, but it may invalidate the
test.

Overall, judgments sampling is considered difficult
to defend in court and far too subjective to have any real validity so is
rarely used.

Statistical sampling

Drawing inferences about a large volume of data by
an examination of a sample is a highly developed part of the discipline of
statistics. It seems only common sense for the auditors to draw upon this body
of knowledge in their own work. In practice, a certain level of mathematical
competence is required if valid conclusions are to be drawn from sample
evidence.

The advantages of using statistical sampling are:

·
It is
scientific

·
It is
defensible

·
It
provides precise mathematical statements about probabilities of being correct.

·
Can be
used by all levels of staff.

·
It is
efficient – overlarge sample sizes are not taken.

·
It tends
to result in a uniform standard of testing.

Its primary disadvantages are:

·
That it
is a mathematical process, which needs to be understood; and

·
The
principles of testing have to be applied properly in order for the tests to be
valid.

Designing the sample

Auditors need to consider:

Population

As already stated the population is the data set
from which the sample will be chosen. The essential feature of the population
is that it be homogenous. Care has to be taken to ensure this is the case. For
example – suppose the population to be tested is all credit sales invoices, but
that, part way through the year, the company replaced its old invoice recording
system with a new one. In this case there are, in fact, two populations, the
old system and the new system and both have to be tested.

Note also that testing the sample of a population
does not test that population for completeness – it only tests what is actually
there. To test for completeness tests have to be performed from source
documents (sometimes called the reciprocal population) into the population.

Level of confidence

Auditors work to levels of confidence which can be
expressed precisely. For example, a 5 per cent confidence level means that
there are 19 chances out of 20 that the sample is repetitive of the population
as a whole. The converse view is that there is one chance in 20 that the
sample, on which the auditor draws conclusions, is non-representative of the
population as a whole.

Precision

From a sample it is not possible to say that the
auditors are 95 per cent certain that, for example, the error rate in a
population of stock calculations is x%, but only that the error rate is x% ± y%
is the precision interval. Clearly the level of confidence and the precision
interval are related, in that for a given sample size higher confidence can be
expressed in a wider precision interval and vice versa.

Tolerable error

Tolerable error is the maximum error in the population
that auditors are willing to accept and still conclude that audit objectives
have been achieved. The tolerable error in a population is usually determined
in the planning stage. It is related to and affected by:

·
Materiality
considerations;

·
Assessment
of control risk;

·
Results
of other audit procedures.

The essential procedure is to set a tolerable error
rate then to project the error rate in the population implied by the sampling
results and to compare the two. It the projected error is larger than the
tolerable error then further auditing procedures will be necessary in the area.

Expected error

This is level of error the auditors might expect to
find in the population. Sample sizes need to be larger in populations where a
high level of error is expected than if the population is expected to be error
free. This is because it is necessary to prove that the actual level of error
is greater than the expected error.

Materiality

This is really a subset of risk. Materiality is
fundamental to auditing and with all populations being sampled; materiality
should be considered in fixing the sample size because populations that are
material to the overall audit opinion (e.g. stock) must be sampled with smaller
precision intervals and higher confidence levels.

Sampling methods

In auditing, a sample should be:

·
Random –
a random sample is one where each item of the item of the population has an
equal (or specified) chance of being selected. Statistical inferences may not
be valid unless the sample is truly random.

·
Representative
– the sample should be representative of the items in the whole population. For
example, it should contain a similar proportion of high – and low – value items
to the populations.

·
Protective
– protection, that is, of the auditor. More intensive auditing should occur on high
– value items known to be high risk.

·
Unpredictable
– client should not be able to know or guess which items will be examined.

There are several methods available to an auditor
for selecting items. These include:

Random sampling ,

All items in the population have (or are given) a
number. Numbers are selected by a main which gives every number an equal chance
of being selected.

This is done using random number tables or
computer-or calculator-generated random numbers,

Simple random

All items in the population have (or are given) a
number. Numbers are selected by a means which gives every number an equal
chance of being selected.

This is done using random number tables or
computer-or calculator-generated random numbers.

Stratified sampling

This means dividing the population into
subpopulations (strata = layers) and is useful when parts of the population
have higher than normal risk (e.g. high-value items, overseas debtors).
Frequency high-value items form a small part of the population and are 100 per
cent checked and the remainder are sampled.

The information can be produced by a report
generator form the management information system and used by the auditor to
design the test,

As can be seen, the sample chosen is weighted
towards the high-value transactions because they are the most material. If one
of the transactions in excess of 1m is in error it may be material to the
accounts, an error in a transaction totaling £50 000 may not be.

Systematic selection

This method involves making a random start and then
taking every nth item thereafter. The sampling interval is decided by dividing
the population size, i.e. if the population is 1000 and the number to be
sampled is 10 the sampling interval will be every tenth transaction. The
starting point can be determined randomly.

This method is useful when sampling non-monetary
items, e.g. dispatch notes.

However, the sample may not be representative as
the population may have some serial properties, for example, there may be a
pattern in the way documents are filled so that say, every tenth dispatch note
is for Hull. If this is the case the sample will be distorted.

Multi-stage sampling

This method is appropriate when data is stored in
two or more levels. For example, stock in a retail chain of shops. The first
stage is to randomly select a sample of shops and the second stage is to
randomly select stock items from the chosen shops.

Block sampling

Choosing at random one block of items, e.g. all June
invoices.

This common sampling method has note of the desired
characteristics and is not recommended. Analogous to this is cluster sampling
where data is maintained in clusters (=groups or bunches), as wage records are
kept in weeks or sales invoices in months. The problem with this method is that
the sample may not be representative as the month or cluster chosen may have
unique characteristics.

Value weighted selection

This method uses the currency unit value rather
than the items as the sampling population and is sometimes called monetary unit
sampling (MUS).

·
Its
application is appropriate with large variance populations. Large variance
populations are those like debtors or stocks where the individual members of
the population are of widely different sizes.

·
The
method is suited to populations where errors are not expected.

·
It
implicitly takes into account the auditor’s concept of materiality.

Procedures are:

1 Determines
sample size. This will take into account:

·
The size
of the population;

·
The
minimum unaccepted error rate (related to materiality);

·
The
assurance level required.

2 List the items in the population (we will use
debtors)e.g., here is a list of debtors:

Debtor
name Balance Cumulative Selected

£ £

Jones 6201 6201 yes

Brown & co 474 6675 no

XY co ltd 1320 7995 yes

JB 1220 9215 no

RS Acne 4197 13412 yes

And so on… … … …

384
200 384 200

If the sample size were 100 items the sampling
interval will be every 382nd pound (£384 200/100) thereafter.

If we start
from £0, the first balance, Jones, has within it the first sampling interval of
£842, this next arrives in the balance belonging to XY & Co and finally (in
our list) in the balance belonging to RS Acne.

Note that, using this method, the larger balances
have a greater chance of being selected which is protective for the auditor.

MUS have some disadvantages:

·
It does
not cope easily with errors of understatement. A debtors balance which is
underestimated will have a smaller chance of being selected than if it was
correctly valued. Hence there is a reduced chance of selecting that balance and
discovering the error.

·
It can be
difficult to select samples if a computer cannot be used as manual selection
will involve adding cumulatively through the population.

·
It is not
possible to extent a sample if the error rate turns out to be higher than
expected. In such cases an entirely new sample must be selected and evaluated.

MUS are
especially useful in testing for overstatement where significant
understatements are not expected. Examples of applications include debtors,
fixed assets and stock. It may not be suitable for testing creditor’s balances
where understatement is a primary characteristic to be tested.

At the end of the process, auditors should evaluate the result, which
might be a conclusion that the auditor is 95 per cent confident that the
debtors are not overstated by more than £x is the materiality factor chosen.

If the conclusion is that the auditors find that the debtors appear to
be overstated by more than £x then they may take a larger sample and/or
investigate the debtors more fully.

Additional aspects of sampling

These include the following

Estimation sampling for variables

This method seeks to estimate (with a chosen level
of confidence and precision interval) the total value of some population. For
example, the auditor might be 95 per cent confident that the total value of debtors,
stock or loose tools, might lie between £58.3m and £59.4m and the best estimate
is £59m.

The
procedure is to extrapolate from a sample to an estimate of the total value.
However, the calculations involved in carrying this out scientifically are
complex and can only be performed easily using a computer application.

Attribute sampling

This provides results based on two possible
attributes, i.e. correct/not correct and is used primarily in connection with
the testing of internal controls, i.e. non-monetary testing.

It
is generally used in compliance testing where the extent of application of a
control is to be determined, i.e. the test is ‘complies/does not comply’. Each
deviation from a control from a control procedure is given an equal weight in
the final evaluation of results.

MUS
is an attribute sampling techniques as it measures monetary deviations.

Projecting the error into the population

Once error nave been identified they should be
projected into population.

This is relatively straight forwarded.

Suppose out of population of £100 000 errors of
£450 are discovered, the error in the population would then be expected to be
(within the confidence levels).

£100 000 = £1
800

The auditor would have to take a view as to whether
this was material if it exceeds the level of tolerable error. If it does the
auditors may well perform additional test to ensure that the level of error
they have discovered is constant.

This
may, of course, only serve to demonstrate that the population is materially
incorrect, which would result in a degree of substantive testing if the figures
were material to the financial statements.

Working papers

As in all audit work, the work done in audit
sampling situations should be fully documented in the working papers. In
particular the documentation in the working papers should show:

Planning the sample;

·
Stating
the auditor objectives

·
Definition
of error or deviation

·
The means
of determining the sample size

·
The
tolerable error rate

Selecting the items to be tested;

·
The
selection method used

·
Details
of the items selected

Testing the items;

·
The tests
carried out

·
The
errors or deviation noted

Evaluating the result of tests;