Setting Cauchy prior scaling in Bayesian t-test - use related effect size?
I'm performing a Bayesian paired-samples t-test in JASP and am trying to choose a prior. I read a few papers (Rouder et al 2009 etc) and some blog posts, and my understanding is that using a Cauchy, the scale can be set to the expected effect size, and I can use the resulting computed JZS Bayes factor. I'm testing two variables, and have a robust effect on one at effect size 0.62. Is it then a principled approach to use that as a scaling factor for the prior of the other, or would it be preferable to use a standard one in the literature e.g. r=0.707 or 1?
I should add that with the second variable I'm interested in asserting the null hypothesis if this is supported, so I should be sufficiently conservative to avoid favouring the null unjustifiably (i.e. avoid too high a scaling factor).