## Audit Sampling

According to ISA 530 audit sampling refer to the application of audit procedures to less than 100% of the items within a class of transactions or account balance such that all sampling units have an equal chance of selection, in order to assist in forming a conclusion concerning the population from which the sample is drawn.

**Importance of Audit Sampling in Procurement Audits**

Audit efficiency relies on obtaining the minimum audit evidence, sufficient to form the audit opinion. The use of audit sampling in audit assignments, offers numerous benefits to auditors. These include:

a) Providing a framework within which sufficient audit evidence is obtained;

b) Forcing clarification of audit thinking in determining how the audit objectives will be met;

c) Minimizing the risk of over-auditing;

d) Facilitating more expeditious review of working papers;

e) Increasing the acceptability of audit conclusions by the auditee as they are seen to be unbiased.

**Situations when a sampling approach is appropriate**

- Where large populations exist, for example for organizations with numerous transactions or where there are many account balances within a class of transactions.
- Where the client has adequate internal controls. Where there are no controls it is impossible to use a sampling approach because of increased expected error.
- Population being tested must be homogenous in materiality. Where the population is not homogenous it is not possible to select a representative sample;
- Items must be separately identifiable therefore sequential numbering is essential. This will facilitate the sample selection process;
- Expectation of error must be low, i.e. that the internal control system must be reliable. Where the expected error is high it is not appropriate to use a sampling approach

**Sample Size**

In determining the sample size, the auditor should consider whether sampling risk is reduced to an acceptably low level. Sampling risk arises from the possibility that the auditor’s conclusion, based on a sample, may be different from the conclusion that would be reached if the entire population were subjected to the same audit procedure.

**Considerations When Determining the Sample Size**

**Required confidence level –**The greater the degree of confidence the auditor requires, the larger the sample size needs to be.**Risk of material misstatement –**The higher the auditor’s assessment of inherent risk and control risk the larger the sample size needs to be.**Tolerable error –**maximum error in the population that the auditor would be willing to accept and still conclude that the result from the sample has achieved his audit objective**Expected error –**to the rate of deviation from the prescribed control procedure that the auditor expects to find in the population. The greater the amount of error the auditor expects to find in the population, the larger the sample size needs to be in order to make a reasonable estimate of the actual amount of the error in the population.**Population size –**For large populations, little, if any, effect. For small populations, audit sampling is often not as efficient as alternative methods.**Stratification –**When a population can be appropriately stratified (by dividing it into discrete sub-populations which have an identifying characteristic), the aggregate of the sample sizes will generally be lower for the same sampling risk than if one sample had been drawn from the whole population.

### Sampling Selection Methods

Selection of items for the sample should be done in such a way that each sampling unit in the population has a chance of selection. When statistical sampling is used, each sampling unit has a known probability of being selected. When non-statistical sampling is used, judgement is applied. However, it is important that the auditor selects a representative sample, free from bias, by choosing sample items that have characteristics typical of the population. The main methods of selecting samples are random selection, systematic selection and haphazard selection.

**Random Sampling:** it implies that all selected elements are taken at random from any pre-determined data array. The random nature of the sample suggests the equality of the choice of any element. Such approach works well in situations where documents or operations with a unique registration number are subjected to audit (for instance, uniform public contracts, invoices, delivery documents, payment orders, etc.). To ensure the randomness of selection, a table of random numbers or computer random number generator may be used.

After the formation of the sample, pre-determined audit tests are applied thereto. It should be noted that a random sampling can also be used in audit procedure on the merit, for instance, when assessing the quality of delivery in the frame of performance of a public contract for the delivery of a large homogeneous nomenclature with pre-determined quality and quantity.

**Advantages**

- There is no bias in the sample selection. Judgement is not applied in sample selection;
- The sample selected is representative of the population because each unit in the population has an equal chance of being selected.

**Disadvantage**

- The approach does not give the auditor an opportunity to apply judgment in sample selection. Exercise of judgment is an important part of the audit process that gives the auditor an opportunity to select items that will enable him to meet his audit objectives.

**Systematic Sampling:** which involves selecting items using a constant interval between selections, the first interval having a random start. When using systematic selection, the auditors need to ensure that sampling interval corresponds with a particular pattern in the population.

Systematic selection, in which the number of sampling units in the population is divided by the sample size, to give a sampling interval, e.g. 50, and having determined a starting point within the first 50 (preferably randomly), each 50th sampling unit thereafter is selected. When using systematic selection, the auditor needs to ensure that the population is not structured in such a manner that the sampling interval corresponds with a particular pattern in the population;

**Advantage**

• The approach eliminates bias in sample selection.

**Disadvantage**

• The sample selected may not be representative of the population in circumstances where items within the population conform to a certain pattern. The selection of the nth item could therefore result in a sample consisting of similar items and therefore not representative of the entire population.

**Haphazard Sampling:** which may be an acceptable alternative to random selection provided the auditors are satisfied that the sample is not unrepresentative of the entire population. When auditors use this method, care needs to be taken to guard against making a selection which is biased, for example, towards items which are easily located, as they may not be representatives.

**Value weighted selection:** where items are selected for testing by weighting the items in proportion to their value. It can often be efficient in substantive testing, particularly when testing for overstatement. It is also known as ‘monetary unit sampling’ (MUS). This is a technique which, when applied correctly ensures that every Ksh.100 in a population will have an equal likelihood of being selected for testing. Under MUS, material balances will be automatically selected.

**Stratified Sampling:** is carried out with respect to an examined population, the constituent elements of which can be grouped (stratified) on certain, generally quantitative grounds. The established level of materiality is very important for the choice of a group (strata). Thus, in the frame of the entire population of procurement all public contracts may be grouped, for instance, on the cost basis:

Minimum – up to Shs 100,000

Medium – from Shs 100,001 to Shs 1,000,000;

Upper-medium level – from Shs 1,000,001 to Shs 10,000,000; Large – above Shs. 10,000,000.

**Statistical sampling** is built upon the use of various statistical criteria, where there is a large amount of heterogeneous procurement operations or procurement operations with special characteristics. Well-known heuristic methods, for instance, Pareto rule 80/20, could also be used for taking decisions on the amount and nature of the chosen population. In the latter case, the sampling is based on operations or contracts constituting 80% of expenses. The Pareto principle in this case suggests that about 20% of procurement contracts will form 80% of expenses of the audited entity on public procurement.

**Block selection:** may be used to check whether certain items have particular characteristics. For example, an auditor may use a sample of 50 consecutive cheques to test whether cheques are signed by authorised signatories rather than picking 50 single cheques throughout the year. Block sampling may however produce samples that are not representative of the population as a whole, particularly if errors only occurred during a certain part of the period, and hence the errors found cannot be projected onto the rest of the population.

**Cluster Sampling:** This is suitable when data to be examined are stored in such a manner that the selection of group, or cluster, would be appropriate test. In these circumstances, each cluster cloud be allocated a number, the particular cluster to be tested being selected by the use of random table. The contents of the cluster selected could in turn be tested completely, or by random number, or by interval sampling. The most precise results with this method will be obtained when each cluster contains a varied mixture as possible and any one cluster is as nearly like any other cluster as possible. Cluster sampling is helpful when the population is so dispersed as to make other forms of selection either burdensome or excessively time consuming.

Judgmental sampling also known as non-statistical sampling

Involves using experience and knowledge of client’s business and circumstances to select and test the sample without any mathematical or statistical tools. The auditor does not rely on probability theory and requires the use of judgment in making sampling decisions.

**Advantages of judgmental sampling**

- It’s well understood and refined by experience;
- Opportunity to bring expertise and knowledge into play in selecting and testing sample units.
- No special statistics knowledge required. The auditor uses his judgment in making sampling decisions.
- No time wasted on the mechanics of statistical tools. More time is spent on auditing the sample units and less on the mechanics of constructing the sample and computing the mathematical implications of the results obtained.

**Disadvantages**

- Unscientific, it does not form a strong basis for defence, i.e., it is difficult to justify why one selected some items and left out others.
- Wasteful and large samples are selected. This is because in an effort to reduce the sampling risk the auditor attempts to select as many items as possible as opposed to statistical sampling where the size of the sample is precisely determined using probability theory.
- Samples may not be representative of the population and the results cannot be extrapolated to the population.
- Danger of personal bias in sample selection

**Difference between Sampling Risk and Non-Sampling Risk**

Sampling risk is the risk that the auditor’s conclusion, based on a given sample may be different from the conclusion reached if the entire population were subjected to the same audit procedure i.e. either the auditor wrongly concludes

that control risk is higher than it actually is or that a material error exists when in fact it does not.

Non-sampling risk refers to risks arising from factors that cause the auditor to reach an erroneous conclusion for any reason not related to the sample size e.g. use of inappropriate procedures on the miss-interpretation of audit evidence.

**Reasons why an auditor should consider materiality when selecting a sample size**

– An auditor is not required to have confidence that all items in a set of accounts are 100% correct. His duty is to give an opinion on the truth and fairness of the accounts. Errors can exist to accounts and yet accounts still give a true and fair view. The maximum error that any particular magnitude can obtain without marring true and fair view is tolerable error. Tolerable error is auditing materiality.

– In his audit planning, the auditor needs to determine the amount of tolerable error in any given population and to carry out tests to provide evidence that the actual errors in the population are less that tolerable error.