A conceptual question about prior contribution

Userxyz

I had a question about JASP Bayesian t-tests:

In the t-test problems, conceptually, how much weight the cauchy prior on the effect size carries compared to the observed data?

For example, if the scale of the cauchy prior is 1 vs. 1/2, how much prior contribution changes to the effect size posterior given some fixed amount of observed data?

Thank you,

sebastiaan

Hi,

how much weight the cauchy prior on the effect size carries compared to the observed data?

If I understand your question correctly, there seems to be a misunderstanding of what a prior is. There is no weighting, in the sense that your Bayes Factor depends on 10 ounces of cauchy prior and 20 ounces of observed data—no! Rather, the prior is like a prediction (for the alternative hypothesis): It specifies how big you expect your effect to be. So the Bayes Factor, in a sense, reflects how well your observed data matches your alternative hypothesis, which is indirectly specified through a prior. Does that make sense?

Cheers,
Sebastiaan