ABSTRACT

Chapter 3 contained an introduction to Bayesian evaluation of informative hypotheses in the context of a two group ANOVA model. In this chapter the J group ANOVA model is used to illustrate the evaluation of informative hypotheses. Five situations are considered: hypotheses formulated using simple constraints, the situation where only one informative hypothesis is of interest, hypotheses formulated using constraints on combinations of means, hypotheses formulated using ordered means and effect sizes, and hypotheses formulated using about equality constraints. Three topics are discussed for each situation. First of all, what researchers themselves have to do: specify the hypotheses in which they are interested, and interpret the Bayes factors that result from executing software for the evaluation of

Informative and Social

TABLE 4.1: Data Concerning Reduction in the Level of Aggression

Group 1 Group 2 Group 3 Group 4 Nothing Physical Behavioral Both

1 1 4 7 0 0 7 2 0 0 1 3 1 2 4 1 −1 0 −1 6 −2 1 2 3

2 −1 5 7 −3 2 0 3

1 2 3 5 −1 1 6 4

Sample Mean −.20 .80 3.10 4.10 Standard Deviation 1.55 1.03 2.60 2.08

informative hypotheses. Second, it is illustrated how the software package BIEMS (Mulder, Hoijtink, and de Leeuw, In Press) can be used to obtain the Bayes factors. BIEMS is further discussed in Section 9.2.2. Third, the sensitivity of Bayes factors with respect to the prior distribution, and the performance of the Bayes factor are discussed.