Does Bayesian evaluation of informative hypothesis outperform analysis of variance?(Forum: Closed ANOVA and its beyond-The current state and future prospects of statistics in psychology-)

Abstract

The analysis of variance (ANOVA) has long held the status of being the most used (or I should say "abused") statistical technique in psychological research. Although there is no doubt about the usefulness of ANOVA, it is not free from disadvantages such as difficulty in accepting null hypothesis and multiplicity problem with multiple tests. In order to deal with these problems, the objective of this paper is to introduce Bayesian evaluation of informative hypothesis to psychonomic researchers. An informative hypothesis consists of inequality constraints between the parameters of interest. The relevance of informative hypothesis is evaluated thorough the Bayes factor against the unconstrained hypothesis. The calculation of Bayes factor is generally performed by means of Markov chain Monte Carlo techniques. This approach is illustrated by analysis of experimental data with mice having different nighttime light conditions.