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# Why is the standard Bayes factor test for directional hypotheses against the point-null?

In the JASP software as well as in the BayesFactor R package with the ttestBF method, the standard Bayes factor test is testing an alternative against the point-null hypothesis.

Assume we want to test the directional hypothesis that d<0. It seems to me that a frequentist analogue (i.e. a one-sided paired samples t-test), would test the hypothesis d<0 against the the null hypothesis d>=0. However, the standard Bayes factor test would test the hypothesis d<0 against the the null hypothesis d=0. Why is this the case? In what cases would be interested in such point-null comparisons?

I am aware that the Bayes Factor test that d<0 versus d>0 can be obtained by dividing the Bayes factor of the defined null interval (-Inf<d<0) and the Bayes factor of the complement of the interval !(-Inf<d<0), so I would be glad to hear your thoughts on a conceptual level.

Thanks in advance!

## Comments

• Dear AnnalenaB,

Thanks for this interesting and very relevant question. I believe the Bayesian directional test makes complete sense. Suppose we start by testing the point H0 (the skeptics' position: d=0) against the two-sided alternative H1 (the proponents' position: d \neq 0). Then we learn that the proponents position is actually more specific, and involves a particular direction, for instance positive; this means that the proponents wish to test H+: d>0. Why in the world would this necessitate a change in the position of the skeptics? This is really weird (to me), and I suspect that the only reason that frequentists do things this way is because they have no other choice.

Of course, if one believes that the skeptics' position is not of any interest, one may also compare the "positive proponents" (H+ : d>0) to the "negative proponents" (H-: d<0). But this analysis departs substantially from the two-sided analysis, as it gives up the skeptics's position. It is generally much easier to decide whether something is negative or positive than if something is absent or present (and positive).

Cheers,
E.J.

Thanked by 1annalenaB
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