The EEE Formula. The formula we use was first introduced to us by Robert Elston (Personal communication, January, 1995) and we have taken to calling it “Elston’s Excellent Estimator” (EEE). The basic formula for EEE can be expressed as: (1)Power=1−β*=Φ((Φ−1(1−β)+Φ−1(1−α2))×n*n−Φ−1(1−α*2)), where Φ−1(•) denotes the inverse of the standard normal cumulative distribution function (cdf) evaluated at •, n is the initial sample size used for the available power estimate (often from a prior simulation study), n* is the new sample size an investigator is planning to use for his/her study, α is the two tailed significance level on which the initial power estimate was based, α* is the significance level for the two tailed test in planned study, 1−β denotes power given in the simulation study, and 1−β* denotes power to be estimated for the planned study. Derivations are in the Appendix.
