i used a bayesian t-test(adapted the code from a book) and i need help interpreting the results.
For my Bayesian approach i left mu,sigma and delta as Cauchy(0,1) prior.
The results based on the Savage-Dickey density ratio yield the folowing Bayes factors:
Bayes Factor for H0 d=0 over H1 d<>0: 1.858271
Bayes Factor for H0 d=0 over H1 d<0: 1.098369
Bayes Factor for H0 d=0 over H1 d>0: 8.016245
I need help interpreting the results. In the first case the Bayes factor tells me that the data are 1,85 times more likely under H0. Is that "strong evidence". Then i have the 3rd case where the data are 8 times more likely under H0 than H1 in that case.
1. Can i infer that the groups are similar? Do i even have a result that point to this direction?
2. Is my use of this priors valid? I have no previous information and nobody has tested the above hypothesis before. I suspect that procons were more powerful(this is is my subjective belief) but i feel that the Cauchy distribution offers an objective belief on the matter. (i know that bayesians have to choose between objectivists and subjectivists). What would be the best in my case?