Prior distribution on Bayesian T Test?

I have two subgroups of structure (bone structure) and I want to test if there is any difference of size (area) between them, and if there is, how important this difference is. The first set is a group non-heated, and the second was heated. I wanted to do a Bayesian T-test (Mann-Whitney because my data isn't normal and the variance of the two groups isn't equal).

I am just not sure about the prior distribution to set for the test. I understand what is a prior distribution but I am not sure if I have any ... My take is that if I had some information about my priors, I think it would be more clear than that and I would know. Is it better to keep the default prior in JASP (cauchy = 0,707) if I am not sure about the priors distribution (I've seen this in some publications)? Is it often that we can't add some priors knowledge to those tests?

• ". I wanted to do a Bayesian T-test (Mann-Whitney because my data isn't normal and the variance of the two groups isn't equal)." - what does this mean? – AdamO Apr 8 at 16:23

You have mixed a couple of ideas. A $$t$$-test is a parametric test (although the Bayesian $$t$$-test can relax the assumptions) while the Wilcoxon test treats Y as ordinal and uses only its rank ordering. To get a Wilcoxon test, use its generalization the proportional odds ordinal logistic regression model. The blrm function in the R rmsb package makes this easy and detailed case studies may be found here.

For the Bayesian $$t$$-test read this and see examples in BBR. BBR also has more background information about using the proportional odds model to get a Wilcoxon test.

• Thank you @FrankHarrell. I read the section about assumption being more flexible with bayesian model in the link BBR. I thought they were as important as in the ''classic'' t-test, and particularly after reading some publication. I have a LOT of tests to do,~600 groups to compare (300 non-heated and 300 of the heated counterpart) and for 10 variables. Not all the samples are normal, not all the variance are equal, but the majority are. I wanted to apply the same test to all for comparison purpose. I am not sure how a bayesian model can relaxe those assumptions and if it can apply to my data? – user317954 Apr 8 at 14:23
• Like this publication (researchgate.net/publication/…) – user317954 Apr 8 at 14:24
• The most important Bayesian contribution besides making a $t$-test much more robust is in handling the 600 groups and 10 variables by having a unified model, perhaps a hierarchical one that borrows information. Any time you rely on significance tests, and especially any time do you many of them, expect bad things to happen. – Frank Harrell Apr 8 at 14:58