A practical approach to sample size calculation for fixed populations

Researchers routinely compute desired sample sizes of clinical trials to control type-i and type-ii errors. While for many experimental designs sample size calculations are well-known, it remains an active area of research. Work in this area focusses predominantly on controlling properties of the trial. In this paper we provide ready-to-use methods to compute sample sizes using an alternative objective, namely that of maximizing the outcome for a whole population. Considering the expected outcome of both the trial, and the resulting guideline, we formulate and numerically analyze the expected value of the entire allocation procedure. Our approach strongly relates to theoretical work presented in the 60's which demonstrated the effectiveness of allocation procedures that incorporate population sizes when planning experiments over designs that focus solely on error rates within the trial. We add to this work by a) extending to alternative designs (mean comparisons not assuming equal variances and comparisons of proportions), b) providing easy-to-use software to compute sample sizes for multiple experimental designs, and c) presenting numerical analysis that demonstrate the efficiency of the suggested approach.