Rule of three (statistics)

For example, a pain-relief drug is tested on 1500 human subjects, and no adverse event is recorded.

Denoting the number of events by X, we therefore wish to find the values of the parameter p of a binomial distribution that give Pr(X = 0) ≤ 0.05.

Rounding the latter to −3 and using the approximation, for p close to 0, that ln(1−p) ≈ −p (Taylor's formula), we obtain the interval's boundary 3/n.

Chebyshev's inequality removes the assumption of unimodality at the price of a higher multiplier (about 4.5 for 95% confidence)[citation needed].

A century and a half ago Charles Darwin said he had "no Faith in anything short of actual measurement and the Rule of Three," by which he appeared to mean the peak of arithmetical accomplishment in a nineteenth-century gentleman, solving for x in "6 is to 3 as 9 is to x."