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medium effect size but very large Bayes factor ?

I just received reviews of my first manuscript including Bayesian statistics (just for paired t-tests).
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 and n. 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 and the 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.

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