In which of the following circumstances would it be appropriate to apply a statistical sampling approach using Mus?

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Definition

Audit sampling is the application of audit procedures to less than 100 % of items in a population, so that all individual items in the population ("sampling units") should have a chance of selection. In order to be able to form conclusions about certain defined characteristics of the population (e.g. eligibility, measurement) without testing the whole population, the sample drawn should be representative of the population and free from bias.

Principles

When deciding which items to test, there are three main approaches available to the auditor:

• selecting all items (100 % examination);
• selecting specific items; and
• statistical sampling.

The choice of method is a matter for the auditor's professional judgement, based on risk assessment, materiality, audit efficiency and cost, but the method chosen should be effective in meeting the purpose of the audit procedure. When designing the sample, the auditor should consider the objectives of the audit procedure and the characteristics of the population.

Selecting all items

Selecting all items is appropriate when the number of items is small but of high value, when the risk is high, or when computer-assisted audit techniques allow all items to be tested effectively. It is more common for substantive testing (tests of details) rather than tests of controls.

Statistical sampling

While the results of statistical samples can be projected to the population, the results of judgemental sampling can only be used as an indication, but cannot be

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Selecting specific items (judgemental sampling)

Selecting items from a population in accordance with pre-determined and documented criteria based on the auditor's judgement (judgemental sampling). These are typically high-value or high-risk items (e.g. relatively high or low amounts, negative value items, etc.) or items that represent a large proportion of the area under review. Selecting specific items is useful for tests of controls and substantive testing, and also to gain an understanding of the entity or to confirm the auditor's risk assessment. This selection method cannot be used if the objective of the sample is to extrapolate the results, i.e. not relevant for the Statement of Assurance. When reporting results, auditors should take care to ensure that readers are not misled into thinking that the results are representative of the population.

Instructions

Designing the sample

Having established the audit objectives to be achieved and the audit procedures which are most likely to achieve them, the auditor should

• define what constitutes an error;
• determine the population from which items will be selected;
• explore the nature of the population;
• select the sample method and decide on stratification;
• determine the sample size.

Define deviations ("errors")

Auditors establish criteria as to what constitutes an error, depending on the type of audit and audit objective. For example, for the sample on the reliability of accounts the auditor should establish criteria as to what constitutes an error, depending on the type of audit objective for the specific balance sheet item under audit (See

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Determine the sampling population

The population is the entire data set from which the sample will be drawn and about which the auditor wishes to draw conclusions. The items in the population (sampling units) need to be defined, e.g. transaction, account balance or monetary unit. The population needs to be appropriate, complete and accurate for the specific audit objectives; auditors may need to obtain further evidence to ensure completeness and accuracy. As sampling does not provide evidence of completeness, audit work to satisfy this assertion should always be supplemented by analytical review and/or evidence of the operation of controls vis-à-vis completeness. In financial audit the populations to be tested include the following accounts or groups of accounts:

• from the financial statements: pre-financing, cut-off of accrued charges, invoices to be paid, guarantees, etc.;
• from the reports on budgetary implementation: the appropriations, commitments, payments, recoveries, RAL ("reste à liquider"), etc.

Any heading in the balance sheet in particular (e.g. "short-term pre-financings"), and the annual accounts in general, often comprises not just one single general ledger account, but several. For example, there are more than 20 general ledger accounts constituting the balance-sheet heading "Short-term pre-financing". The population from which the sample will be drawn therefore often constitutes a number of accounts. The population can be the number of final individual amounts which constitute the year-end balance of those several accounts at 31/12/N (e.g. final balance of individual pre-financings per contract), or some specific movements (e.g. debit movements or credit movements of individual pre-financings during the year).

Explore the nature of the population

In order to choose the appropriate sample selection method and the optimal sample size, auditors should gain as much information as possible about the population. Auditors investigate the degree of variation in population items, what is known of errors in the population (their nature, frequency, and distribution throughout the population), the existence of patterns (e.g. more errors at year-end due to increased effort to spend commitments) and the location of items (e.g. multiple member states). Auditors should ascertain the appropriateness of the population for sampling. For instance that:

• all items pertain to the year under audit;
• there is no exceptional amount which should be withdrawn, such as individual items exceeding the materiality threshold which are to be tested outside the sample;
• all items pertain to the entity under audit.

Select the sampling method and decide on stratification

The sampling method to be used should match the characteristics of the population. The following flowchart represents the process of arriving at the most suitable sampling method.

• dividing the population into sub-populations, or strata, using predefined and documented audit criteria (e.g. monetary value, age of receivables, etc.) so that a sampling unit can belong to one and only one sub-population, and
• applying audit procedures to a sample of items from each sub-population (e.g. stratification by value: testing all high-value items and a representative sample of low-value items);focus the audit on interim and final payments which are more prone to risk and put less emphasize on advance payments.

Determine the sample size

If a statistical sampling method is selected, the minimum sample size should be determined using ECA's Assurance model (based on the hypothesis that the samples are randomly selected). It is clear that the larger the sample size, the greater the accuracy and the likelihood that the sample is representative of the population; the

[a-glossary term="Sampling%20risk"]sampling risk[/a-glossary] 

• for tests of controls, the total rate of deviation does not exceed the tolerable rate of deviation (the rate of deviation the auditor will accept) ;
• for substantive tests of details, the monetary amount of the deviation does not exceed that which the auditor is willing to accept.

A reduction in the confidence level when drawing a representative sample for substantive testing may be envisaged if it is offset by using other substantive procedures (e.g. key and high-value item testing, analytical procedures, third party confirmation). The Assurance model is also used for

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Statistical sampling methods frequently used in the ECA audits

Monetary unit sampling method (MUS)

The monetary unit sampling method (MUS) is a method of statistical sampling in which every euro has an equal chance of selection. The practical implementation of the MUS method uses a random starting point and then an average sampling interval (ASI) for progression through the expenditure. MUS is a form of 'probability proportional to size' (PPS) sampling. Larger transactions involve the payment of a larger number of euros, represent a larger share of potential 'hit euros' and are thus more likely to be tested in the sample. The ASI is determined by dividing the population total by the planned number n of transactions to be audited. The resulting ASI is then used to select n evenly spread euros in the population. (ASI = total budget / planned sample size n). The population is thus cut into ‘slices' of equal size in euro and for each slice one euro is selected which determines the item to be tested. In most cases ordering the population randomly results in good statistical properties of the estimates. However, it can be cumbersome to implement and difficult to document. Normally keeping the population in the original order is good enough. These n euros selected by MUS are called “hit euros". The transactions to which they belong are called “hit transactions" and collectively they form the sample to be audited. The individual error rate of an audited “hit transaction" expressed as a percentage is called “tainting t". After the audit of all transactions is finished and when all individual error rates are available, the Most Likely Error (MLE), which is the estimated result for the whole population, should be calculated as follows: MLE = 1/n * sum of t (in %) or MLE = sum of t * ASI (in €) For purposes of the Statement of Assurance, this sampling method is applied.

Stratified MUS

Stratified MUS divides the population into several sub-groups (strata). The strata have to be pre-defined according to different characteristics within the population e.g. according to risk. The auditor should use professional judgement when determining these characteristics including his/her knowledge of the population subject to audit. In each stratum, a number of items is selected with MUS. The number of items to be selected can be different in every stratum. However, stratification does not allow to conclude per stratum.

Simple random sampling

Simple random sampling selects items from across the whole population so that each item has an equal chance of selection. It results in many small amounts to be tested and is likely to produce high standard deviations or a higher sample size. This method is suited to populations where individual items bear a similar level of audit risk. As compared to MUS it is therefore often less efficient.

Multi-stage sampling

One form of multi-stage sampling is Cluster sampling. This method can be useful when transactions are processed or records held at a number of locations, so that a sample cannot be extracted from across the whole population. In most cases, the locations are too numerous for them all to be visited. Therefore, the auditor first determines the number of locations to be visited, and secondly the number of items to test at those locations. Statistical qualities of this method are not optimal, but it represents a practical solution where other statistical methods are not feasible. The quality of the sample can be improved by increasing the number of clusters (rather than number of second stage hits). This method can be used together with all sample selection methods.

Resources

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Brexit considerations

Following Brexit payments to UK-based beneficiaries and revenue received from UK continue to be part of the population of underlying transactions for

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When should you use monetary unit sampling?

Why is it difficult to determine the appropriate sample size for MUS?

How does MUS use attribute sampling theory?