Statistical sampling lets auditors draw conclusions about a population from a defensible sample. Calculate sample sizes for tests of controls with attribute sampling, or for account balances with monetary unit sampling.
How it works
Determine statistical sample sizes for tests of controls with attribute sampling, or for substantive testing with monetary unit sampling (MUS), including the sampling interval.
Attribute: smallest n where P(deviations ≤ k | n, tolerable rate) ≤ 1 − confidence,
k = expected deviations = ⌈n × expected rate⌉ (binomial)
Finite population: n′ = n ÷ (1 + n ÷ N)
MUS: n = Book value × Reliability factor ÷ (Tolerable − Expected misstatement × Expansion factor)
Sampling interval = Book value ÷ nCommon uses
- External and internal audit testing
- SOX and internal control testing
- Compliance and quality reviews
Worked example
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| Sampling approach | Attribute sampling (tests of controls) |
| Confidence level | 95% |
| Tolerable deviation rate | 5% |
| Expected deviation rate | 1% |
| Sample size | 93 |
| Deviations allowed | 1 |
| Risk of overreliance | 5.0% |
| Tolerable deviation rate | 5.0% |
If more than 1 deviation is found, the upper deviation limit will exceed the tolerable rate and the control cannot be relied on as planned. Sample sizes use the binomial distribution, the basis of the AICPA attribute sampling tables.
Interpreting the results
- A wider gap between tolerable and expected rates reduces the sample size; a narrow gap increases it sharply.
- MUS is efficient for detecting overstatement but poor for understatement and for populations with many zero balances.
- Sample size is only half the work: select items randomly or systematically and evaluate every deviation’s cause.
Frequently asked questions
What determines an attribute sample size?
Attribute sample size depends on the confidence level, the tolerable deviation rate and the expected deviation rate. The closer the expected rate is to the tolerable rate, the larger the sample needed. Population size matters only for small populations.
What is monetary unit sampling?
Monetary unit sampling treats each dollar in a population as a sampling unit, so larger balances are more likely to be selected. It is efficient for testing overstatement of account balances such as receivables and inventory.
Why is the sample size 59 for zero expected deviations?
At 95% confidence and a 5% tolerable deviation rate, 59 items with no deviations give at least 95% confidence that the true deviation rate is below 5%, because 0.95 raised to the 59th power is just under 5%.
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- Sample Size Calculator: Required sample size for surveys, means and A/B tests with power.
- Bank Reconciliation Worksheet: Adjusted bank and book balances with the journal entries the reconciliation requires.
- Allowance for Doubtful Accounts (Aging Method): Required allowance from an A/R aging, bad-debt expense and net realizable value.