Calculating Cauchy scale from Cohen d confidence interval?
I have been reading on previous posts and blogs on informed prior parameters but I could not find info on how to calculate the scale (or width) of the Cauchy distribution for informed priors.
Location is easy, I simply take the effect size (Cohen d for t-test).
However, for scale, it was less clear.
My reading of this blog (http://xeniaschmalz.blogspot.com/2019/09/justifying-bayesian-prior-parameters-in.html) led to understand that scale is here based on a confidence interval around the informed/expected effect size.
So, would it be correct to compute the 95% confidence interval of my previous study's Cohen d effect size and use it to calculate the Cauchy scale?
But then, if so, how should I translate it into the Cauchy scale?
Simply cut in half my half CI. Eg. if CI = 0.257 to 1.091 centered on 0.679 then I use 0.412 as scale?
I am guessing it is more complex that ! Could you tell me how?
Thanks a lot in advance!