AUDIT SAMPLING Questions and Answers

What is Audit Sampling?

Application audit procedures to less than 100% of the items within an account balance or class of transactions to enable the auditor obtain and evaluate audit evidence about some characteristics of the items selected in order to form or amidst in forming a confusion concerning the population.

INDUSTRY CONTEXT OF AUDIT SAMPLING

Audit sampling is a key aspect of obtaining sufficient appropriate evidence. A sample must be chosen which enables the auditor to get the evidence he needs. This is done on a day to day basis by the auditors during their work.

TERMS AND DEFINITIONS

Population

The population is the entire set of data from which the auditor wishes to sample in order to reach a conclusion e.g. all items in an account balance or class of transactions .The individual items that make up a population are called sampling units. The essential feature of population is that it must be homogenous i.e. must be composed of similar or uniform sampling units.

What is Sampling risk?

because auditors do not examine all the items in the population when applying audit sampling, there is a risk that is that the conclusion they draw may be different from which they would have drawn had they examined the entire population. This risk is called sampling risk. The auditor should use rational basis for planning, selecting and testing samples to ensure that he has reasonable assurance that sample used is to representative of the population.

Define Non sampling risk

This risk arises from factors that because the auditor to reach an erroneous conclusion for any reason not related to sample size e.g. use of inappropriate audit procedures leading to failure to identify an error. This risk can be minimized by improving training and review procedures.

DefineTolerable error

This refers to the maximum error in the population that the auditor is willing to accept and still to conclude that the results from the sample have achieved the audit objective. Tolerable error is considered during planning stage and for substantive procedures, is related to auditor’s judgment on materiality. The smaller the tolerable error expected in a balance, the larger sample size must be.

Define Confidence level

This refers to the degree of confidence the auditor requires that shows the results of the sample to be indicative of actual error in the population.

What is Stratification

This is the process of dividing population into sub populations so that items within each subpopulation are expected to have similar characteristics in certain aspects e.g.  high value items should be grouped separately from low value items.

in cases where auditors are concerned with discoveries of overstatement errors and consider that the largest monetary errors are likely to occur in the larges items, they will stratify the population by value and then direct their audit procedures on items with largest individual values. Expected errors

if the auditor expects errors in the population, a larger sample size than when no error is expected ordinary needs to be examined to conclude that the actual error in the population is not greater than the planned tolerable error. Smaller sample sizes are justified when the population is expected to be error free.

Reasons for Sampling

1. a complete check for all transactions and balances a business is no longer possible owing to the numerous numbers of transactions.
2. Time factor. Examining all the transactions will take a lot of time. The cost of doing this will be prohibitive because audit fees are largely based on amount of time spent on assignment. also a complete check will take so long that the accounts will be ancient history before users saw them.
3. The objective of an audit is to express an opinion as to whether the financial statements show a true and a fair view. it is possible for the auditor to obtain the assurance without examining all transactions. The use of sampling with properly set out objectives and properly constructed tests allows more valid conclusions to be reached than when many transactions as possible are tested. This is because detailed testing is done on a sample.
4. a complete check would bore the audit staff so much that their work would become ineffective and errors would remain unidentified.

Cases where sampling is inappropriate

1. When population is small, statistical sampling will create an unacceptable margin of error. If the population is not sufficiently large, then statistical methods are invalid. Instances where transactions or balances are small in number but material in relation to financial statements e.g. directors fees should never be sampled and any transactions involving a large capital expenditures.
2. Any situation where the auditor is put on high alert a result of earlier tests or information is received indicating material fraud in a certain accounting areas. iii. For statutory disclosure items such as director’s salaries, a full audit check is desirable because materiality consideration does not apply in this case.
3. Where population is not homogenous and requires stratification, it is not possible to select a representative sample.
4. When the population has not been maintained in a manner suitable for audit sampling

e.g. if sales invoices are filed according to customer name as opposed to a numerical order.

Stages in Audit Sampling

1. Planning the sample

When planning how to carry out sampling, the auditor considers the following:

1. objectives of tests and combinations of audit procedures which are likely to achieve the objectives e.g. objective to verify compliance of the debtors balances.
   1. The population and sampling units should be appropriate to the objectives of sampling e.g. if auditors objective is to test overstatement of debtors, an appropriate population would be a list of total debtors.
   1. Definition of errors is substantive testing and deviation in compliance testing. Before performing testing on a chosen sample, the auditor should define clearly test results and conditions that will be considered errors or deviations by reference to audit objective. For substantive testing, the auditor should project errors found in the sample to population and consider the effect of projected errors on a particular test objective.
2. Determination of sample size.

The auditor needs to determine the appropriate size of the sample on which audit procedures will be applied. Sample size is determined by;

1. The tolerable error. The larger the tolerable error, the smaller the sample size required for a given test.
   1. Auditor’s assessment of the inherent risk. The higher the assessment of inherent risk, the larger the sample size is required. Higher inherent risk implies that there is a greater risk of an account balance being misstated and this may be reduced by testing a larger sample.
   1. Auditor’s assessment of control risk. A higher control risk implies that little reliance can be placed on effectiveness of operations of internal controls and the sample size needs to be increased.
   1. Auditor’s required confidence level.  The greater the degree of confidence level the auditor requires, the larger the sample size needs to be so that the results of the sample are in fact representative of the actual amount of error in the population.
2. Selecting items to be tested.

The sample selected should be a true representative of the population so that the auditor can draw conclusions about the entire population. All sampling units should have an equal chance of being selected. Common sampling methods are;

1. Random sampling. This is done by use of random number tables or use computers to select sampling units
   1. Systematic selection. In this type of sampling, units in the population are divided by the sample size to give sampling intervals e.g. if the population to be sample has 600 items and sample size is 50, the sampling interval will be 12. One of the first 12 items will be selected as the starting point and thereafter, every twelfth item will be selected i.e. if the first item selected is third item, every 15^th, 27^th, 39^th and so on items will be picked. However, the auditor needs to determine that sampling units within the population are not structured in a way that sampling intervals corresponds to a particular pattern in the population.
   1. Haphazard selection. The auditor selects a sample without following structured techniques. The auditor should avoid conscious bias and predictability in selecting items in attempt to ensure that all items in the population have a chance of being selected. This technique is not suitable for statistical sampling.
   1. Block selection. This involves selecting a group of continuous items within the population e.g. all sales transactions for august. block sampling cannot be ordinarily used in audit sampling because most populations are structured such that items in a sequence can be expected to have similar characteristics therefore the sample selected may not be representative of the population.
2. Testing. After selecting the sample items the auditor should carry out the predetermined test on each item.
3. Evaluating results of the test.

The following procedures should be followed.

1. The auditor should estimate the expected error or deviation rate in the whole population by projecting the results of the sample to the population. This is then compared with the tolerable error.
   1. The auditor should assess the risk of an incorrect conclusion. in general, expected error is rarely a precise measure of the actual error in the population. actual error may be greater or smaller than projected error. The auditor most therefore consider on the basis of his sample results and relevant evidence from other sources, the possible levels which actual error or deviation might take.

Main approaches to audit  sampling

1. judgmental sampling

This is also called non-statistical sampling. it involves using experience and knowledge of client’s business and circumstances to select and taste a sample without using any mathematical of or statistical tools. The auditor does not rely on probability theory and uses judgment in making sampling decisions.

Advantages of judgmental sampling

1. It is well understood and refined by experience
   1. ii. opportunity to use expertise and knowledge in selecting sample units i.e. no special knowledge and statistics is required. The auditor simply uses his judgment in making sampling deacons
   1. no time is wasted on the mechanics of statistical tools. The time which could have been spent on constructing sample and computing mathematical implications of results obtained is spent on auditing sample units.

Disadvantages of judgmental sampling

1. Unscientific. The approach does not form a strong basis of defense. It is difficult to justify why the auditor selected some items and left out others.
   1. Wasteful as large simples need to be selected. This is because in effort to reduce the sampling risk, the auditor attempts to select as many items as possible as opposed to statistical sampling where sample size is determined using probability theory.
   1. Samples may not be representative of the population and thus results cannot be projected to the population.
   1. There is danger of personal bias in selecting samples.

2. Statistical Sampling.

This involves two steps;

1. Use of random selection to pick a sample.
   1. Use of probability theory to determine the sample size, evaluate quantitatively the sample results and measure sampling risk. Statistical sampling differs from non statistical sampling in that the auditor uses probability theory to measure the sampling risk and evaluate the sample results.

Advantages of statistical sampling

i. It is scientific and defensible. The auditor can justify the items selected because these are selected randomly. ii. Elimination of personal bias. The sample selected is unbiased which increases reliability of audit evidence.

1. Small samples are selected which improve the efficiency of the exercise. This is because probability theory helps determine a precise sample size.

Disadvantages of statistical sampling

1. It is difficult to extract samples especially if documents are not sequentially numbered.
   1. The need to follow a predetermined statistical report may reduce initiative and the need to apply judgment by the auditor.
   1. The result may be misunderstood if audit staff are not properly trained on use of the techniques.
   1. It may not be suitable for all applications. Probability theory works best for large populations and therefore cannot be applied for small populations.
   1. it is expensive because extensive staff training is required and the use of information technology.

Factors considered before adopting statistical sampling

1. The number of clients to whom a technique as appropriate. This is because the set up and training costs are high.
   1. Whether large population exists. Statistics is the science of large numbers. Where organizations are small with few transactions, a statistical approach is inappropriate.
   1. Adequate controls must exist where they are no controls it is impossible to use statistical techniques because of increased statistical errors iv. The population being tested must be homogenous.
   1. Sampling units must be separately identifiable and therefore sequential numbering is essential.
   1. The expectation of the error must be low i.e. the internal control system of organization must be reliable.
   1. The risk factors. The level of risk allowable and the degree of risk attached to an item being tested must be considered.

Qualities of a good sample

1. it should be representative of the population.  The sample should be representative of the differing items in the whole population.
   1. The size of the sample should be appropriate given the various risk considerations i.e. where the expected error is high, a large sample is chosen.

Unpredictable. The client should not be able to know in advance which items will be examined.

Sampling methods

1. Estimation sampling for variables.
2. Estimation sampling for attributes.
3. Acceptance sampling.
4. Discovery sampling
6. Estimation sampling for variables

Estimation sampling for variables

This method seeks the estimate the total value of some population e.g. total value of debtors, stock or loose tools. The procedure is to extrapolate estimate or form an opinion using the facts that are valid for one situation (sample) supposing that they will be valid in the new situation. This estimate can be compared with the book value and if any difference is within the materiality limits pre-established, the auditor has evidence for the book value of the item.

Estimation sampling for attributes

This method seeks to estimate the proportion of a population having particular characteristic e.g. overdue debts or damaged inventory.

Acceptance sampling

This method seeks to discover the error rate in a population to determine a maximum error rate.

Its uses include;

1. Whether a control can be relied upon. If non compliance is greater than the acceptable rate, the control will not be relied upon and other audit tests will have to be applied.
2. ii. Used to test whether stock calculation can be relied upon. if the error rate is greater than some acceptable proportion, the auditor will have to request the client to redo the calculations.
3. Discovery sampling

This method extends acceptance sampling to an acceptance level of zero. E.g. a system with controls exists in an investment trust company to ensure that all bonus issues are recorded. Even if one bonus has not been recorded, the auditor will be unable to accept the controls and will have to seek other evidence. This method requires a large sample. a form of discovery sampling is monetary unit sampling.

Monetary Unit Sampling

monetary unit sampling is appropriate for use with large variance population e.g. debtors or stock where individual units have widely different sizes or values. This method is suited to a population where errors are not expected  and it implicitly takes into account the auditor’s concept of materiality.

Procedure of monetary unit sampling

1. Determine the sample size taking into account the size of the population and the minimum acceptable error rate.
2. list the items of population e.g. list of debtors could be as

Debtor              amount (Sh)       Cumulative amount

TmK& Co.  500  500 aQ & Sons  20  520

T ltd  1,450     1,970

W Co.                4,420      6,390

            :               :

                           240,000

 Total                 240,000

1. assume that the total numbers of debtors is 1500. if sample size chosen is 100 items, then a random start of say Shs 1000 can be chosen and every Shs 2100^th item thereafter i.e. using systematic sampling with random start. The idea is that the population of debtors is not 1500 but Shs 240000 with single units of Shs 1. Therefore, we chose to sample to be picked from the cumulative shillings amount.
2. at the end of the process, evaluate the result which might be a conclusion that the auditor is 95% confident that the debtors are overstated by more than Shs. X where X is the materiality factor chosen.
3. If the conclusion is that the auditor finds that the debtors are overstated by more than Shs X, then he may take a large sample or investigate the debtors fully.

Disadvantages of monetary unit sampling

1. Does not cope easily with errors of understatement. a debtors balance which is understated 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.
2. It can be difficult to select samples where a computer cannot be used e.g. where the accounting system of an organization is manual. manual selection will involve adding items cumulatively through the entire population which is very tiring.
3. it is not possible to extend a sample if the error rate turns out to be higher than the expected error. in such cases an entirely new sample must be selected and evaluated.
4. Monetary unit sampling is useful especially in testing for overstatements where significant understatements are not expected i.e. when dealing with debtors, fixed assets and stock it is clearly not suitable for testing creditors where understatement is the primary

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