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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?

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  • $\begingroup$ ". 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? $\endgroup$ – AdamO Apr 8 at 16:23
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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.

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  • $\begingroup$ 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? $\endgroup$ – user317954 Apr 8 at 14:23
  • $\begingroup$ Like this publication (researchgate.net/publication/…) $\endgroup$ – user317954 Apr 8 at 14:24
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    $\begingroup$ 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. $\endgroup$ – Frank Harrell Apr 8 at 14:58

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