The formulas
- Upper limit p solves: sum for i = 0 to k of C(n, i) p^i (1 - p)^(n - i) = 1 - confidence
- Compare p to the tolerable deviation rate
How it works
After testing a sample of controls, the auditor needs an upper limit on the deviation rate in the whole population. This tool finds the exact binomial limit. It is the rate at which seeing k or fewer deviations in n items would have probability of only 1 minus your confidence.
If the upper limit is at or below the tolerable rate, the sample supports the planned reliance on the control. If it is higher, reduce reliance, expand the sample, or revise the risk assessment. Tables built on the Poisson approximation give a slightly higher limit than the exact binomial result.
Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
Why does it differ from a table?
A table built on the Poisson approximation gives a slightly higher limit than the exact binomial. Check which basis your table uses.
What if no deviations are found?
The limit is still above zero. With n of 60 at 95 percent it is about 4.9 percent.
Does it apply to a small population?
For a sample that is a large share of the population, the binomial limit is conservative.
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.