Audit Sample Size Calculator

Choose the Sampling Model

These models assume you expect zero deviations.

This audit sample size calculator supports zero-acceptance detection sampling. You define a failed test, expect zero deviations and choose the population deviation rate you want the sample to detect.

The exact model assumes simple random selection without replacement from a complete population. Each record has the same chance of selection. A record can appear in the sample only once.

The binomial model assumes independent trials with a constant deviation probability. Its size is conservative for random selection without replacement. The result is capped at the population size for full examination.

AUASB’s ASA 530 audit sampling standard permits statistical formulas or professional judgement when sizing a sample. It requires the auditor to address sampling risk. These results are model outputs, not an ASA-required minimum.

Judgemental selection chooses records for particular reasons. A search for suspicious transactions targets known risk indicators. Neither selection method inherits the probability calculation shown here.

Calculate and Round the Sample

The finite threshold is 5 deviating records. At 45 draws, the probability of missing all 5 is 4.62%. At 44 draws it is 5.07%.

For the binomial model, the probability of zero deviations in n independent trials is (1 − p)^n. Here p is the tolerable rate as a decimal.

Set that probability at or below 1 − C, where C is confidence as a decimal. The unrounded size is log(1 − C) / log(1 − p). Round up to a whole record.

At 95% confidence and a 5% tolerable rate, the unrounded binomial size is about 58.4. Rounding up gives 59 records before any population cap.

For the exact finite model, set D = ceiling(N × p), where N is population size. D is the smallest whole count at or above the tolerable rate.

The probability of zero deviations is choose(N − D, n) / choose(N, n). The function choose(a, b) counts ways to select b items from a items.

The tool finds the smallest integer n whose miss probability is at most 1 − C. If n exceeds N − D, missing every deviation is impossible. This is an exact finite-population calculation, without a survey margin-of-error correction.

With 100 records, a 5% tolerable rate means D = 5. At 95% confidence, 45 draws meet the threshold. The adjustment from the binomial size is 59 − 45 = 14 fewer records.

The formula follows the hypergeometric distribution documented by R. The independent-trial alternative follows NIST’s binomial distribution. Calculations retain precision before display rounding, with a 1e-12 numerical tolerance at integer boundaries.

Interpret the Sample Size

At 95% detection confidence, a population at or above the tolerable deviation rate has at most a 5% chance of producing zero observed deviations. The statement depends on the selected model and random sampling assumptions.

This confidence is not the probability that a particular audit conclusion is correct. The tolerable rate measures failed records, not their monetary value. A small number of high-value errors can still matter.

Expected deviation is fixed at zero because both models use an acceptance count of zero. If you expect deviations or find one in the sample, reassess the plan and evaluate the finding. Do not treat this size as sufficient for a plan that accepts errors.

A calculated size alone cannot make a sample representative. Define the population and test first, confirm the population is complete and retain the random selection method with the selected record identifiers.

Incorrect testing or missing records can invalidate an inference even when the sample size is correct. A statistical sample also cannot prove the absence of fraud or replace an audit programme.

Use forensic data analytics to examine the wider transaction population and identify records that need targeted investigation. Keep those targeted selections separate from the random sample.