An introduction to evidential sample size calculations

The evidential paradigm provides the likelihood ratio as an objective measure of the strength of evidence. It neither uses p values as a measure of evidence nor views inference as a decision making exercise. Most sample size methods are based on the Type I and Type II error probabilities of the Neyman-Pearson (NP) paradigm, regardless of the framework used to determine the evidence in the data. Sample size estimates using the evidential paradigm, illustrated with an example for Gaussian response data, are compared to those obtained using NP methodology. A relation between the error probabilities of the two paradigms is derived. The sample size estimates from the NP framework are found to be too small for the purposes of an evidential analysis.