Audit Sampling Size Calculator
Calculate the statistically required sample size for audit procedures using classical variables or attribute sampling methods.
Formulas Used
Attribute Sampling (infinite population):
n = Z² × p × (1 − p) / (te − p)²
Where: Z = z-score for confidence level, p = expected error rate, te = tolerable error rate
Attribute Sampling (finite population correction):
n_adj = n / (1 + n / N)
Variables Sampling — Mean-Per-Unit (with population count N):
n = Z² × σ² / ē² where ē = (TM − EM) / N
With finite correction: n_adj = n / (1 + n / N)
Variables Sampling — Ratio Estimation (without population count):
n = Z² × σ² × BV / (TM − EM)²
Where: σ = standard deviation per item, BV = population book value, TM = tolerable misstatement, EM = expected misstatement
Assumptions & References
- Attribute sampling assumes a binomial distribution of errors in the population.
- Variables sampling assumes a normal distribution of misstatements (Central Limit Theorem applies for n ≥ 30).
- The finite population correction (FPC) is applied when population size N is provided and reduces required sample size for smaller populations.
- Expected misstatement must be strictly less than tolerable misstatement to ensure a positive precision allowance.
- Z-scores used: 90% → 1.645, 95% → 1.960, 98% → 2.326, 99% → 2.576 (two-tailed for variables; one-tailed for attribute).
- If the computed sample size equals or exceeds the population, a 100% examination (census) is recommended.
- References: AICPA Audit Sampling Guide (2014); ISA 530 — Audit Sampling; PCAOB AS 2315; Arens, Elder & Beasley, Auditing and Assurance Services.
- This calculator provides a statistical starting point. Professional judgment, risk assessments, and audit objectives should guide final sample size decisions.