R scale Cauchy prior
I am teaching a statistics class and while the examinable contents are based on the frequentist approach, I wish to briefly show my students an alternative way of analysing data using Bayesian statistics and I am using JASP to do this. Therefore, I would like to know a little bit more on the Cauchy prior width (r scale) for the Bayesian t-test. Is it correct for me to say that the default value of r = 0.707 translates to an expectation of an effect size of d = 0.707? In other words, probability mass corresponding to effect magnitude less than 0.707 will be 0.5 and more than 0.707 will be 0.5 as well?
Additionally, where does this default prior width come from?
Thank you for your time.