The formulas
- Infinite population: n = ln(1 - confidence) / ln(1 - critical rate), rounded up
- Finite population: smallest n where the hypergeometric chance of drawing no exception is at most 1 - confidence, with exceptions = critical rate x population rounded up
How it works
Discovery sampling is used when even one exception is significant, as in tests for fraud indicators or missing controls. If the population exception rate is at least the critical rate, a sample of this size will contain at least one exception with the confidence you chose.
If the sample shows no exception, you can conclude the exception rate is below the critical rate at that confidence. If it shows one, the sample cannot be projected as a rate and further procedures are needed. The finite version applies when the sample is a large share of the population.
Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
What if I find an exception?
Discovery sampling does not estimate a rate. Investigate the exception and expand work as needed.
Why is the finite answer smaller?
Sampling without replacement from a small population learns more per item.
Which confidence is typical?
Set it by your risk assessment and your firm methodology.
Formulas on this page are the standard definitions.
Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.