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Lesson#39
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STATISTICAL SAMPLING
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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
non-statistical 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.
page
126
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
and stocks. It is clearly not suitable for testing creditors
where understatement is the primary
characteristic to be tested.
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