Formal approach to non-statistical sampling
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1 EUROPEAN COMMISSION Formal approach to non-statistical sampling Commission européenne, B-1049 Bruxelles / Europese Commissie, B-1049 Brussel - Belgium. Telephone: (32-2)
2 1. SITUATION The population, from which to sample, shows that for 393 operations, expenditure has been declared. There is no possibility of increasing this number by e.g. sampling on expenditure claims since beneficiaries send in one claim per reference year. All data used originates from real declarations of expenditure and actual audit results. The auditors want to assess the validity of the expenditure declared. They consider that the systems work but that improvements are necessary. They wish to be 70% confident about their assessment of the legality and regularity of the expenditure declared. However, caution and due consideration needs to be applied when evaluating this, given that their assessment will be based on a non-statistical approach. The total value of the population is Materiality is set at 2% = STEP 1: DETERMINE THE INDIVIDUALLY SIGNIFICANT AMOUNTS The first step the auditors will apply is to identify the operations which, individually, represent a significant amount or are significant because of their nature. For the benefit of this example, the individually significant amounts are determined as equal to materiality (2% of ). The auditors can choose to use a lower level of materiality. The selection gives the following results: Project number Amount declared These projects will be excluded from sampling and will be treated separately. The total value of these projects is STEP 2: DETERMINE THE SAMPLE SIZE TO AUDIT From the remaining population (389 projects), a sample will have to be drawn with 70% confidence. The Confidence Factor to use is that of Monetary Unit Sampling which is, for the confidence level required: 1,21. The sample size (monetary hits) is: Remaining population value * Confidence factor 2
3 Planning materiality This results in a sample size of: * 1, = 60 hits The planning materiality used in this example is 1, 7 % 1 4. STEP 3: SELECT THE SAMPLE The sample should be selected in accordance with the principles of systematic sampling. If other methods are used, the sample size should be increased by, at least, 20%. The sample selection results in the following operations to audit: Project number Amount declared In this example, the planning materiality has been reduced. 3
4 STEP 4: AUDIT THE SAMPLE The results of the audit are as follows: Project number Error rate Error Amount declared 11 0,00% ,00% ,00% ,14% ,35% ,00% ,00% ,42% ,00% ,00% ,00% ,38% ,33% ,00%
5 97 0,00% ,00% ,87% ,59% ,00% ,00% ,60% ,48% ,00% ,00% ,00% ,00% ,84% ,00% ,54% ,76% ,86% ,26% ,00% ,90% ,00% ,00% ,00% ,00% ,61% ,87% ,00% ,46% ,00% ,98% ,56% ,00% ,14% ,00% ,00% ,03% ,87% ,02% ,00% ,56% ,00% ,47% ,00% ,00% ,28% ,00% The value of the sample is equal to The total amount of errors in the sample is (2,7%). The sum of the misstatement proportions amounts to 242,15%. 5
6 6. STEP 5: EVALUATING SAMPLE RESULTS When the auditor detects misstatements in selected items, two separate evaluations should be made: qualitative and quantitative Qualitative evaluation The qualitative evaluation involves investigating the cause of misstatements. This can lead the auditor to apply additional procedures, to revise the judgement on the quality of the management and control systems or to take actions as circumstances dictates Quantitative evaluation This involves projection of the misstatements in order to determine how much misstatement the remaining population is likely to contain. The methodology is based on MUS and recognises that larger items are selected rather than smaller items. The formula to apply is the following: Sum of misstatement proportions * remaining population value Sample size In the example given, the quantitative evaluation (the projection of error to the remaining population) leads to the following result: 2,42 * = (4,03% of remaining population value). The amount of projected errors has to be added to the results of the audit of the 100% strata in order to determine the maximum amount of error in the population. In this example, no errors were found in the 100 % strata 7. CONCLUSION The conclusion that can be derived from this example is that the auditor can reasonably conclude that the population contains a material error. The difficulty with the non-statistical approach is that the achieved precision cannot be determined. The auditor will therefore have to decide whether or not to apply additional audit procedures or alternative strategies to evaluate the declared expenditure. For illustration purposes, the 100% audit of 393 operations in the population showed an error amount of
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