# Interpretations of Bayesian ANOVAs: Interaction vs. main effects + interaction

I'm using JASP to analyze a data from a 3 by 2 factorial experimental design. This is the first time I am using JASP (and Bayesian statistics), and I am unsure of the exact meaning of the interaction model that appears in the Bayesian ANOVA table:

I understand that the table displays evidence for the models where there is a main effect of distraction level only, arousal level only, and independent main effects of both distraction and arousal. But the interaction model puzzles me. Does evidence for this model depend on there being an interaction between the two factors AND a main effect of both, as is implied by the "factor 1 + factor 2 + factor 1 * factor 2?

Is the JASP Bayesian repeated measures ANOVA ignoring the following models:

"factor 1 + factor 1*factor 2" (a main effect and an interaction)
"factor 2 + factor 1*factor2" (the other main effect and an interaction)

and

"factor 1*factor 2" (interaction only)

If this is the case, do you know if the BayesFactor R-package can provide a more detailed analysis of all types of interaction models.

Thanks

Árni

## Comments

Hi Arni,

In our modeling, the main effect is included whenever a specific factor appears in the interaction. This adheres tp the principle of marginality (https://en.wikipedia.org/wiki/Principle_of_marginality) and it is considered good modeling practice.

Cheers,

E.J.

Thanks EJ

I get your point, and realize my faulty thinking. It's hard to detach completely from the usual terms of an ANOVA. But I think you managed to push me over the edge.

Á