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Sample size calculator

Monetary unit sampling for tests of details and attribute sampling for tests of controls, with the evaluation step.

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Sampling risk

Sampling risk (NV COS 530.5): the risk that your conclusion from the sample differs from the one you would reach testing the whole population.

Non-sampling risk (NV COS 530.5): the risk of a wrong conclusion for any other reason, such as an unsuitable procedure or a misread result. A bigger sample does not reduce it.

Select the sample so every sampling unit has a chance of selection (NV COS 530.8). In MUS each euro is a sampling unit, so larger items are more likely to be picked.

Monetary unit sampling (tests of details)

NV COS 530 bijlage 3, number of sampling units: in MUS every euro is a unit, so a larger population at the same tolerable misstatement → larger sample.

NV COS 530 bijlage 3, tolerable misstatement: higher tolerable misstatement → smaller sample.

NV COS 530 bijlage 3, expected misstatement: higher expected misstatement → larger sample.

NV COS 530 bijlage 3, desired assurance that tolerable misstatement is not exceeded: higher confidence → larger sample. Lower confidence can fit a lower assessed risk of material misstatement or other substantive procedures on the same assertion.

NV COS 530 bijlage 3, stratification: MUS stratifies by value on its own, because selection is per euro.

Sample size
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Sampling interval
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Evaluate the results (NV COS 530.14–15)

After testing, enter each misstatement found: book value and audited value of the item. Leave empty if you found none.

Basic precision
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Projected overstatement
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Upper misstatement limit, overstatements
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Projected understatement
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Upper misstatement limit, understatements
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Formula: n = (population value × reliability factor) / (tolerable misstatement − expected misstatement × expansion factor), rounded up. Sampling interval = population value / n. Evaluation: misstatement ÷ book value = tainting; projected misstatement = tainting × interval (items at or above the interval count at their actual misstatement). Upper misstatement limit = basic precision (reliability factor × interval) + projected misstatements ranked from largest, each multiplied by its incremental factor.

Attribute sampling (tests of controls)

NV COS 530 bijlage 2, tolerable rate of deviation: higher tolerable rate → smaller sample.

NV COS 530 bijlage 2, expected rate of deviation: higher expected rate → larger sample.

NV COS 530 bijlage 2, desired assurance that the tolerable rate is not exceeded: higher confidence → larger sample. The more your risk assessment relies on the control, the more assurance you need.

NV COS 530 bijlage 2, number of sampling units: for large populations size has little effect, so it is not an input here.

Sample size
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Deviations allowed
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Formula: Smallest n for which, allowing k = n × expected rate (rounded up) deviations, the binomial probability of finding k or fewer deviations at the tolerable rate is at most 1 − confidence. This reproduces the AICPA Audit Sampling Guide Tables A-1 (95%) and A-2 (90%).

Structured according to NV COS 320, 450 and 530. Indicative only: your firm's audit methodology takes precedence and professional judgement remains with the auditor.

Sources

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