This continues yesterday’s post: I checked out the the” xtranormal” http://www.xtranormal.com/ website. Turns out there are other figures aside from the bears that one may hire out, but they pronounce “Bayesian” as an unrecognizable, foreign-sounding word with around five syllables. Anyway, before taking the plunge, here is my first attempt, just off the top of my head. Please send corrections and additions.

*Bear #1:* Do you have the results of the study?

Bear #2:Yes. The good news is there is a .996 probability of a positive difference in the main comparison.

Bear #1: Great. So I can be well assured that there is just a .004 probability that such positive results would occur if they were merely due to chance.

*Bear #2:* Not really, that would be an incorrect interpretation.

*Bear #1:* Oh. I see. Then you must mean 99.6% of the time a smaller difference would have been observed if in fact the null hypothesis of “no effect” was true.

*Bear #2:* No, that would also be an incorrect interpretation.

*Bear #1:* Well then you must be saying it is rational to believe to degree .996 that there is a real difference?

*Bear #2:* It depends. That might be so if the prior probability distribution was a proper probabilistic distribution representing rational beliefs in the different possible parameter values independent of the data.

*Bear #1:* But I was assured that this would be a nonsubjective Bayesian analysis.

*Bear #2:* Yes, the prior would at most have had the more important parameters elicited from experts in the field, the remainder being a product of one of the default or conjugate priors.

*Bear #1:* Well which one was used in this study? Continue reading →