# Interpretation of Bayesian ANOVA Interaction for Negative Findings

I have a question about interpreting Bayesian ANOVA results that are in favour of the null hypothesis. My primary hypothesis was that I would see an interaction between a within-subjects factor (time) and a between-subjects factor (response). I did not see a significant interaction with frequentist statistics. I would like to use a Bayesian approach to clarify whether the negative interaction findings are inconclusive, or if there is evidence in support of the null hypothesis (no interaction).

I understand that if you want to quantify the evidence in favour of the alternative interaction hypothesis, you would compare the BF10 of [Time + Response + Time*Response] to the BF10 of [Time + Response]. However, does the same logic apply if you want to quantify the evidence in favour of the null model, as compared to an interaction model?

In the attached example, the null model is favoured to both a main effects model and a main effects + interaction model. Considering that a model is said to be complete if it contains all lower-order terms (Bernhardt & Jung 1979), I am unsure if the evidence in support of the null model compared to an interaction model should be:

A) Null model vs. Time + Response + Time*Response (BF01 = 13.17, therefore the null model is 13 times more likely than an interaction model)

Or

B) Time + Response + Time*Response vs. Time + Response (BF01 = 0.996, therefore the evidence is inconclusive)?

Thanks in advance for your help.

## Comments

Dear JenL,

Interesting question. You could argue either way I guess. Usually you would consider the two main effects model and judge whether you need the additional interaction term (this is your approach "B"). However, it appears as if there is evidence against the main effects as well, and including them means both models from approach "B" may overfit the data and should therefore not be used to draw strong conclusions. I think it is best to present the entire table and discuss all of the results, instead of picking just one.

Cheers,

E.J.