Probability of 80% vs 50% in default priors?
Hi EJ - I'm just reading some papers on prior specifications in t-tests.
And the author first seems to be suggesting the default prior means: "“The prior is described by a Cauchy distribution centred around zero and with a width parameter of 0.707. This corresponds to a probability of 80% that the effect size lies between -2 and 2. [Some literature to support that this is a reasonable expectation of the effect size.]”"
And then amends this to 50% certainty (based on recommendation by you).
My question is, if my prior belief is that the effect size is between 01.1 to 1.1, would I specify the Cauchy at 0.3 (see the table in that link above) - and does that correspond to 50% or 80% cetainty? (And if I want to specify more than 80% certainty, say, 95% certainty, how do I specify that in JASP? I can obtain the vlaues using the R code but not sure what to input in the model for JASP).
I have also read the van Doorm (2021) guidelines paper that yo ucontributed to but didn't find it as helpful regarding informed priors.
I also wondered about specifying the model vs parameter priors in JASP and whether we can do both? (i ask because I read Kruschke's paper https://www.nature.com/articles/s41562-021-01177-7 which was really damning of papers that don't specify both and explain in precise wording how they did this and what it means!)
Thank you, and sorry if this is really obvious!