Usefulness of Akaike information criterion for making decision in two-sample problems when sample sizes are too small

Abstract

There are studies in medical science that researchers want to show the equivalence, or non-equivalence, of two treatment effects, but an application of the routine statistical test is useless when sample size is small. Concentrating on a simple two-sample problem that assumes normality with unknown common variance, and comparing power functions and positive and negative predictive values, it is shown in this paper that the decision rule based on Akaike information criterion is superior to those rules based on Bayes information criterion and on statistical test when sample sizes are too small.