What is sample size determination?
Sample size determination is the process of calculating how many items an auditor must test from a population to draw a reliable conclusion about that population. It is governed by the factors in ISA 530 and the auditor's acceptable level of sampling risk.
ISA 530.A10 lists the factors that drive sample size for tests of details. The four that matter most on a real engagement are the acceptable level of sampling risk, the tolerable misstatement, the expected misstatement in the population, and the characteristics of the population itself. Reduce the acceptable risk and the sample grows. Narrow the tolerable misstatement and the sample grows again.
The standard does not prescribe a formula. ISA 530.A11 notes that the auditor may use statistical or non-statistical methods, provided the sample is sufficient to reduce sampling risk to an acceptably low level. In practice, most non-Big 4 firms use either a statistical formula (the AICPA-style or MUS approach) or a table-based method from their methodology provider. What matters is that the inputs are documented and the relationship between risk assessment, materiality, expected error, and sample size is visible in the file.
One point that gets missed: ISA 530.A10(e) requires you to consider the stratification of the population. If you stratify well, the required sample size for each stratum drops because variability within each stratum is lower.
Key Points
- A larger sample does not automatically mean a better test. The design of the sample matters more than the count.
- Reducing the acceptable level of sampling risk forces the sample size up, not down.
- If you cannot justify your sample size with reference to the population and your risk assessment, an inspector will challenge it.
- Most sample size disputes trace back to tolerable misstatement being set without reference to performance materiality.
Why it matters in practice
Getting sample size wrong has direct consequences for audit quality and efficiency. Set it too low and the auditor accepts too much sampling risk, potentially missing material misstatements. Set it too high and the team over-audits, wasting time on immaterial items without improving the conclusion.
Worked example: Lindberg Precision AB
Client: Swedish engineering group, FY2024, revenue SEK 380M (approx. EUR 33M), IFRS reporter.
Population: 1,247 trade receivable balances totalling SEK 89M.
Step 1 — Set tolerable misstatement: Performance materiality is SEK 2.7M. The engagement team sets tolerable misstatement for this test at SEK 2.7M (equal to performance materiality, since no other substantive procedures address the same assertion).
Step 2 — Estimate expected misstatement: Prior year testing found SEK 180K of projected misstatement. The team estimates expected misstatement at SEK 200K to allow for growth.
Step 3 — Determine confidence factor: The team uses a 95% confidence level (risk factor 3.0) because the risk of material misstatement for receivables existence is assessed as significant.
Step 4 — Calculate sample size: Using MUS: sample size = (population book value x confidence factor) / tolerable misstatement = (89,000,000 x 3.0) / 2,700,000 = 99 items. Rounded to 100.
Conclusion: A sample of 100 items from 1,247 balances is defensible. The four inputs (risk assessment, confidence factor, tolerable misstatement, expected misstatement) are documented and traceable. If the team had set tolerable misstatement at half PM (SEK 1.35M), the sample would have doubled to 198.
Key standard references
- ISA 530.A10: Factors affecting sample size for tests of details — acceptable sampling risk, tolerable misstatement, expected misstatement, and population characteristics.
- ISA 530.A11: The auditor may use statistical or non-statistical methods, provided the sample is sufficient to reduce sampling risk to an acceptably low level.
- ISA 530.A8–A9: Factors affecting sample size for tests of controls — tolerable deviation rate, expected deviation rate, and assessed risk of material misstatement.
- ISA 530.A10(e): Stratification of the population as a factor the auditor must consider when determining sample size.
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Frequently asked questions
What are the main factors that determine sample size?
ISA 530.A10 lists four key factors: acceptable sampling risk, tolerable misstatement, expected misstatement, and population characteristics.
Does a larger sample always mean a better test?
No. The design of the sample matters more than the count. A large sample using the wrong procedure produces no useful evidence.
Why do inspection findings often challenge sample sizes?
Most disputes trace back to tolerable misstatement being set without reference to performance materiality, or sample sizes documented without the inputs that produced them.