

Fundamentals
of Auditing ACC 311
VU
Lesson
39
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 auditor to draw
upon this body
of
knowledge in his own work.
In practice, a high level of
mathematical competence is required
if
valid
conclusions are to be drawn
from sample evidence.
However most firms that use
statistical
sampling
have drawn complex plans
which can be operated by staff
without statistical training.
These
involve
the use of tables, graphs or
computer methods.
The
advantages of using statistical
sampling are:
a. It is
scientific.
b. It is
defensible / justifiable.
c. It
provides precise mathematical
statements about probabilities of being
correct.
d. It is
efficient  overlarge sample
sizes are not
taken.
e. It
tends to cause uniform
standards among different audit
firms.
f. It
can be used by lower grade
staff; that would be unable to
apply the judgment needed
by
judgmental
sampling.
There
are some
disadvantages:
a. As a
technique it is not always
fully understood so that false
conclusions may be drawn
from the
results.
b. Time is
spent playing with
mathematics which might better be
spent on auditing
c.
Audit judgment takes second
place to precise
mathematics.
d. It is
inflexible.
e.
Often several attributes of
transactions or documents are
tested at the same tir
Statistics does not
easily
incorporate this.
Characteristics
of audit sample:
In auditing, a
sample should be:
a. Random

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

the sample should be
representative of the differing items in
the whole
population.
For example, it should contain a
similar proportion of high
and low value items
to
the
population (e.g. all the
debtors).
c. Protective

protective, that is, of the auditor. More
intensive auditing should occur on
high value
items
known to be high
risk.
d. Unpredictable

client should not be able to
know or guess which items
will be examined.
Sample
Selection Methods:
There
are several methods
available to an auditor for
selecting items. These
include:
a. Haphazard
Simply
choosing items subjectively
but avoiding bias. Bias
might come in by
tendency
to favor items in a particular location
or in an accessible file or conversely in
picking
items
because they appear unusual.
This method is acceptable for
nonstatistical sampling but
is
insufficiently
accurate for statistical
sampling.
b. 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.
c. Stratified

This means dividing the population
into sub populations (strata =
layers) and is
useful
when parts of the population
have higher than normal risk (e.g.
high value items,
overseas
debtors).
Frequently high value items
form a small part of the
population and are 100%
checked
and
the remainders are
sampled.
d. Cluster
sampling  This is
useful when data is
maintained in clusters (= groups or
bunches) as
wage
records are kept in weeks or
sales invoices in months. The
idea is to select a
cluster
randomly
and then to examine all the
items in the cluster chosen.
The problem with this method
is that
this sample may not be
representative.
125
Fundamentals
of Auditing ACC 311
VU
e.
Random
systematic  This method
involves making a random start
and then taking every
nth
item
thereafter. This is a commonly use method
which saves the work of computing
random
numbers.
However the sample may
not be representative as the
population may have some
serial
properties.
f. 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.
g. Block
sampling  simply
choosing at random one block
of items e.g. all June
invoices. This
common
sampling method has none of the
desired characteristics and is
not recommended.
h. Value
weighted selection  This method
uses the currency unit
value rather than the items
as
the
sampling population. It is now
very popular and it is also
known as "Monetary
Unit
Sampling".
This in relatively new variant of discovery
sampling which is thought to have
wide
application in
auditing. This is because:
a.
Its application is appropriate with
large variance populations. Large
variance populations
are
those like debtors or stocks
where the members of the populations
are of widely
different
sizes.
b. The method is
suited to populations where errors
are not expected.
c. It
implicitly takes into
account the auditor's
concept of materiality.
Procedures
are:
a. Determine
sample size. This will
cover:
i. The
size of the population
ii.
The minimum unacceptable error rate
(materiality)
iii.
The Beta risk desired
b.
List the items in the
population (e.g. 1,250
debtors)
Debtors
Name
Balance
Rs.
Cumulative
Rs.
Jameel
600
600
Ibrahim
100
700
Razi
1,200
1,900
Faiz
500
2,400
Saif
4,000
6,400
Etc.
***
***
Etc.
***
***
1,250.
***
***
_______
_______
300,000
300,000
======
======
c. If
the sample size were
100 items then take a random
start say 1,000 and
every 3,000th (Rs.
300,000/100
sample size) item
thereafter, i.e. using
systematic sampling with a
random start.
The
idea is that:
i. The
population of debtors is not
the 1,250 number of debtors
but Rs. 300,000.
ii. If
the particular Rupee is chosen then the
whole balance of which that Re. 1 is
a
part
will be investigated and any
error quantified.
In our
example, Razi would be
selected since 1,000 lies in
his balance and then Saif
would also be
chosen
as 1,000 + 3000 = 4,000 lies
in his balance.
Note
that the larger balances
have a greater chance of
being selected. This is protective for
the auditor
but it
has been pointed out that
balances that contain errors of
understatement will have
reduced
chance
of detection.
d. At
the end of the process,
evaluate the result which
might be a conclusion that the
auditor is
95%
confident that the debtors are
not overstated by more than
Rs. ***. Where Rs.
*** is the
materiality
factor (tolerable error) chosen. If the
conclusion is that the auditor finds that the
debtors
appear to be overstated by more than
Rs. *** then he may take a
larger sample
and/or
investigate the debtors more
fully.
Monetary
unit sampling is especially
useful in testing for
overstatement where
significant
understatements
are not expected. Examples
of applications include debtors,
fixed assets
126
Fundamentals
of Auditing ACC 311
VU
and
stocks. It is clearly not
suitable for testing
creditors where understatement is
the primary
characteristic
to be tested.
127
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