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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, with the monetary value as a sampling unit. 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. For each slice one euro is selected which determines the item to be tested.
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 the i-th audited “hit transaction" is called ti. After the audit of all transactions is finished and when all individual error rates ti are available, the Estimated Level of Error (ELE), which is the estimated result for the whole population, is calculated as follows:
- As a percentage for a single stratum:
- Or, if there are different sampling intervals ASIi,
At the lowest level of testing, we check a subsample of at least 10 cost items. This allows efficiency savings to be made and ensures that the audit results provide a reasonably good view of the expenditure checked. These 10 cost items do not constitute an error rate for the project, but contribute to the audit conclusion of the [link title="specific%20assessment" link="%2Faware%2FCA%2FPages%2FReporting%2FSpecific-assessments.aspx" /]
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In simple random sampling (SRS), each item from the whole population has an equal chance of selection. This often results in many small amounts to be tested and is likely to produce high standard deviations or a higher sample size. SRS is suited to populations where the constituent individual items bear a similar level of audit risk. As compared to MUS it is therefore often less efficient.
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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, monetary value, age of receivables. 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 us to conclude for an individual stratum where the sample size is too small. Stratification can be also used with simple random sampling method.
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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 the number of second stage hits). This method can be used together with all other sample selection methods.
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