Bayesian Independent Samples T-Test - priors to compare likelihood of 2 effect sizes
Hello,
I have a very basic question about the Bayesian Independent Samples T-Test - if it is not appropriate for this forum please let me know and/or delete. I am also sure that it was already widely discussed, however I am too big newbie to even google it correctly:
When comparing the two groups, I got the effect size of -0.3 (95% CI: -1.02 to 0.428). I would like to use Bayes Factors to show that based on the data I have obtained, it is more likely that the true effect size is small (e.g. 0.5 or lower) than large (e.g. greater than 0.5). I thought I could present the result as BF01 (with prior set around larger effects) / BF01 (with prior set around smaller effects). Interpreting - the higher the quotient, the greater the likelihood of a smaller effect. My questions:
a) Is this thinking correct?
b) How should I set my priors to be optimal?
I will be grateful for any help
Comments
a) Yes you can do this, especially when you use informed prior distributions. The null divides out so you are left with a direct comparison between two instantiations of H1.
b) This is a little tricky in this specific case. I suggest that your question can be addressed more directly by the "equivalence t-test" module! (Based on the work by Morey & Rouder, Psych Methods 2011)
Cheers,
E.J.