A new approach to sample size calculations for the power of testing and estimating population means of gaussian distributed variables.

Sample size calculations for demonstrating and estimating an effect are two distinct approaches that respectively concentrate on the power of the statistical test and on the precision of the confidence interval: however, they both have some unsatisfactory aspects. This paper describes a sample size calculation method that, starting from the precision given by the power-based sample size, is based on the probability (conditional on the coverage) of obtaining both a statistically significant result (the power of the statistical test) and sample half-width confidence intervals lower than a considered precision threshold (power of the confidence interval). This procedure, therefore combines the two powers of the inferential statistical procedures, fulfils the regulatory requirements and the needs of a scientific research that are mainly focused on the probability of demonstrating a clinically relevant difference, and demands a generally acceptable increase of the power-based sample size. The proposed method is pertinent to sample size calculation for controlled clinical trials planned to compare a new treatment against a reference one (or a placebo) on Gaussian distributed variables according to crossover or parallel group designs.