Audit sampling (planning & evaluation)

What is Audit sampling (planning & evaluation)?

Planning finds the smallest sample size n such that, if the population misstatement rate equalled the tolerable rate (performance materiality), a sample containing no more than the expected number of errors would occur with probability at most 1 − confidence. Computed under a binomial, Poisson, or hypergeometric (finite-population) likelihood, this reproduces the published attribute sample-size tables — e.g. 95% confidence, tolerable 5%, expected 0% gives n = 59 (binomial) or n = 60 (Poisson factor 3.0).

Attribute evaluation inverts the same test: given k observed errors in n items, the upper confidence bound is the largest population error rate not rejected by the sample (exact Clopper-Pearson bound for the binomial; gamma percentile for the Poisson; exact inversion over population error counts for the hypergeometric).

Monetary-unit evaluation applies the Stringer bound: each misstated item contributes a taint (misstatement ÷ book value); taints are ranked largest-first and the upper limit is basic precision (the zero-error factor × the sampling interval) plus each taint weighted by the increment in the upper-bound factor. Understatements are reported separately, not netted — netting would sacrifice the bound's conservatism.

When should I use Audit sampling (planning & evaluation)?

• Designing a test of controls or of details: how many items must be examined to support a conclusion at a given confidence and materiality.
• Concluding on a completed attribute sample: is the population misstatement rate below materiality at the stated confidence?
• Evaluating a monetary-unit (dollar-unit) sample of recorded amounts with partial misstatements.

What data does it need?

Planning: confidence, tolerable rate, expected rate, optional population size, likelihood. Attribute evaluation: n, observed errors, confidence, tolerable rate. Monetary-unit evaluation: n, taints, population book value, confidence, materiality amount. Runs on parameters alone — no data columns needed.

What does it report?

Planning: minimum n, errors tolerated, attained risk, sensitivity table of n vs expected rate. Evaluation: observed (MLE) rate, upper confidence bound, conclusion vs materiality. MUS: projected misstatement, basic precision, incremental allowance, Stringer upper limit, conclusion.

What does it assume?

• Random (for MUS: probability-proportional-to-size) selection from the population.
• Attribute modes treat each item as simply right or wrong; taints assume the misstatement of a sampled monetary unit is representative of its item.
• The Stringer bound is conservative — its true coverage meets or exceeds the stated confidence, often comfortably.

How do I interpret the result?

The audit conclusion rests on the upper bound, not the observed rate: a clean sample of 59 still only demonstrates 'below 5% at 95% confidence'.

In planning, expected rates close to the tolerable rate inflate n without limit; if errors are genuinely expected near materiality, sampling cannot support acceptance.

See also

• Benford's law (first-digit audit)
• Acceptance sampling plan (OC curve)
• Binomial test

References

• AICPA (2017). Audit Guide: Audit Sampling.
• Stringer, K. W. (1963). Practical aspects of statistical sampling in auditing. Proc. ASA, Business & Economic Statistics Section.
• Clopper, C. & Pearson, E. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26.
• Leslie, Teitlebaum & Anderson (1979). Dollar-Unit Sampling: A Practical Guide for Auditors.