A short introduction into Bayesian evaluation of informative hypotheses as an alternative to exploratory comparisons of multiple group means

Abstract

This paper presents an introduction into Bayesian evaluation of informative hypotheses, that is, hypotheses representing explicit expectations about multiple group means The authors begin by discussing some limits of exploratory methods before presenting a non-technical overview of the Bayesian approach. References are provided for the technical details. A particular effort is made to illustrate the method with an example from psychology. References to software, more elaborate textbooks and tutorials enable researchers to apply this novel method to their own data. * Comparisons among multiple groups are frequent in the context of behavioral research. For example, a researcher can be interested to know if a difference exists between three groups of students or patients that have received different treatments. Classical hypothesis testing is based on the evaluation of a null hypothesis, H0, where all group means j (j = 1,, J groups) are stated to be equal: This hypothesis can be conceived as a highly constrained hypothesis because it provides a lot of information about the means under investigation: the j are all equal. On the other hand, the alternative hypothesis, Ha, can be written as The alternative Ha is an unconstrained hypothesis because we don't make any assumptions about the means j. This