# medium effect size but very large Bayes factor ?

We got a (friendly) reviewer question - could someone help me phrase a correct answer or perhaps point me to a good reference?

"What I find difficult to understand is how you can have a medium effect size and a very strong Bayes Factor such as seen on page .., d = .60 & BF = 1,720,000."

## Comments

Hi HannaG,

What is relevant for the BF is the relative predictive performance of H0 vs H1. Unless d=0, the value of d actually tells you nothing at all about the BF; what you need is d

andn. Specifically, when you have a low d but high n, you can still be pretty darn sure that H1 outpredicts H0. Conversely, a high d but very low n may only yield inconclusive evidence.This is actually similar to NHST: you need both the sample effect size

andthe number of observations.The equations for the BF have "n" in there; also, a prior-posterior plot will show exactly why you have this much evidence: the posterior must be relatively peaked and located away from zero; consequently, the posterior density at delta=0 is much reduced compared to the prior density at delta=0. I could go on, but basically the reviewer ignores sample size.

Note that this can be easily explored using the "Summary Stats" module in JASP (which requires that you enter the t-value and the sample size).

Cheers,

E.J.