STATISTICAL SAMPLING

<< AUDIT SAMPLING

CONSIDERING THE WORK OF INTERNAL AUDITING >>

Fundamentals of Auditing ACC 311

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 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.

125

Fundamentals of Auditing ACC 311

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

Ibrahim

100

700

Razi

1,200

1,900

Faiz

500

2,400

Saif

4,000

6,400

Etc.

***

Etc.

***

1,250.

***

_______

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

and stocks. It is clearly not suitable for testing creditors where understatement is the primary

characteristic to be tested.

127

Table of Contents: