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# Counterintuitive comparison BF?

Hi there. Following a previous discussion of ours, I am conducting BAIN ANOVAs with ordered competing hypothesis. This is my question:

Under a set of hypotheses, I received as output the attached file. Is it not weird that the BF32 is only 1.36 when the BF of H3 is 24757.71 and that of H2 8.11? I understand that BF32 is not a division of the two numbers, but still I find it weird that the ratio is so small.

• Your result is correct. Something like the following might be going on:

mean1 = 8, mean2 = 20, mean3 = 8.1, mean4 = 8.1

Than your H2 1 < 2,3,4 is in agreement with the data but only barely so.

Your H3 2 > 1,3,4 is, however, strongly in agreement with the data.

But, both in comparison to their own specific complement. A direct comparison of H3 with H2 is based on the fit (f) and complexity (c) of both hypotheses (see Hoijtink, H., Mulder, J., van Lissa, C., and Gu, X. (2019). A tutorial on testing hypotheses using the Bayes factor. \emph{Psychological Methods}. DOI: 10.1037/met0000201 also retrievable from the bain website).

BF32 = (f3/c3)/(f2/c2) which since I expect the complexity of both hypotheses to be the same reduces to f3/f2. Both are numbers between 0 and 1. In my hypothetical example above f3 is probably 1 (or close to 1), while f2 might be something like .5. This implies that BF32 = 1/.5 = 2.

I hope this helps. Otherwise let me know.

Herbert Hoijtink (h.Hoijtink@uu.nl)

• Thanks! It helped!