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About Rule of three
In statistical analysis, the rule of three states that if a certain event did not occur in a sample with n subjects, the interval from 0 to 3/n is a 95% confidence interval for the rate of occurrences in the population. When n is greater than 30, this is a good approximation of results from more sensitive tests. For example, a pain-relief drug is tested on 1500 human subjects, and no adverse event is recorded. From the rule of three, it can be concluded with 95% confidence that fewer than 1 person in 500 will experience an adverse event. By symmetry, for only successes, the 95% confidence interval is [1 − 3/n,1].
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