Reporting the results of my Bayesian RM ANOVA in my paper

Kindred

Hello, I'm trying to report my results, any tips are appreciated :)

Methods: I have a group composed of young adults (YA) and older adults (OA) who have a trained on a task. Their performance (DTc) is the dependent variable as measured pre- and post-training (variable of Session, with levels Pre- & post-)  

Reporting:

A Bayesian Repeated Measures ANOVA revealed that the data are 392.34 (BF01) times more likely under the model that includes the main effect of SESSION, the main effect of Age, and the interaction between Session and Age as predictors than under the null model. The analysis of effects revealed that the data is extremely likely (BFincl = 144.25) to occur under models that only include a main effect of Session, strongly likely (BFincl = 19.83) to occur under models that only include the Session x Age interaction, and moderately likely (BFincl = 7.97) to occur under models that only include the main effect of AGE. Furthermore, post-hoc analysis revealed strong evidence (i.e., posterior odds of 28.36) that DTc differs between Pre- & Post-training, but weak evidence (i.e., posterior odds of 1.5) that DTc between OA & YA differed. The model averaged posterior distributions reveal that DTc decreased from pre- to post-training.

Results:

EJ

Dear Kindred,

The links to the png's are broken, so I cannot see those. Without visual support, here is some comment on the text:

1. "A Bayesian Repeated Measures ANOVA revealed that the data are 392.34 (BF01) times more likely under the model that includes the main effect of SESSION, the main effect of Age, and the interaction between Session and Age as predictors than under the null model."

You could report this (would it not be "BF10", since you report evidence in favor of H1 over H0), but the null model without any predictors is rarely of interest. What I would want to know is "what is the best-supported model?"; what is the second-best supported model, and what conclusions do we draw?

2. "The analysis of effects revealed that the data is extremely likely (BFincl = 144.25) to occur under models that only include a main effect of Session, strongly likely (BFincl = 19.83) to occur under models that only include the Session x Age interaction, and moderately likely (BFincl = 7.97) to occur under models that only include the main effect of AGE."

This interpretation is not quite correct. In JASP, whenever an interaction is included so are the constituent main effects. So the analysis of effects does not consider "only" the interaction. The analysis of effects compares the models that include the term of interest against the models that exclude that term. But I think that with only a few models, you might be better off interpreting the main output table.

3. "Furthermore, post-hoc analysis revealed strong evidence (i.e., posterior odds of 28.36) that DTc differs between Pre- & Post-training, but weak evidence (i.e., posterior odds of 1.5) that DTc between OA & YA differed. The model averaged posterior distributions reveal that DTc decreased from pre- to post-training."

I find no fault with the wording, but keep in mind that I cannot see the pngs

Cheers!

E.J.

Kindred

Hello,

Thanks for the feedback!

1. So is the best way to report the results using the BF10 and compare it to the null model?
2. Does the analysis of effects table tell us what to look at in the post-hoc? Like if I had a bayefactor of 1 for the models that contain the interaction, does that mean that there is no point in interpreting the post hoc or the model averaged posterior distributions?

That's bizarre, the images disappeared. I re-attached them here.

pic 1.jpg

Kindred

Hello,

Thanks for the feedback!

1. Are you saying that the best way to report the results is using BF10, while having the "compare to null model" box checked? If we have the best supported model, what is the use in looking at the second best supported model? Other than the fact that the data are more likely under the model including the main effects and interactions, what other conclusions can we draw?

Here is my reworked output based on your feedback:

Using a Bayesian RM ANOVA, the Bayes factor indicates that the data best supports the model that includes the main effect of Session, the main effect of Age, and the interaction between Session and Age as predictors (BF10 = 378.61), indicating extreme evidence for H1. The second-best model includes the main effect of Session and Age (BF10 = 42.39), indicating very strong evidence for H1. Interestingly, given that the model that includes the main effect of Age provides no evidence (BF10 = 1.11) for H1 nor H0, we conclude that the data does not support the existence or lack thereof of age differences. Indeed, post-hoc comparisons of DTc between Young Adults and Older Adults revealed posterior odds of 1.5 against the null hypothesis, thereby indicating weak evidence for the age differences. Furthermore, post-hoc comparisons of DTc between pre- and post-training revealed posterior odds of 28.36 against the null hypothesis, which indicates strong evidence in favor of the alternative hypothesis. The model averaged posterior distributions reveal that DTc decreased from pre- to post-training. 

It's weird the pics have disappeared. Here they are again