Some thoughts on sample size: A Bayesian-frequentist hybrid approach August 3, 2012

Traditional calculations of sample size do not formally incorporate uncertainty about the likely effect size. Use of a normal prior to express that uncertainty, as recently recommended, can lead to power that does not approach 1 as the sample size approaches infinity.

Purpose To provide approaches for calculating sample size and power that formally incorporate uncertainty about effect size. The relevant formulas should ensure that power approaches one as sample size increases indefinitely and should be easy to calculate.

Methods We examine normal, truncated normal, and gamma priors for effect size computationally and demonstrate analytically an approach to approximating the power for a truncated normal prior. We also propose a simple compromise method that requires a moderately larger sample size than the one derived from the fixed effect method. Read more