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# Can I say "H1 for red trials (BF = 15) is 5 times more likely than H1 for green trials (BF = 3)"?

edited April 2020

Hi,

First of all, thanks a lot for the great tool that is JASP and the great support that you created around it!

I've got a simple question:

In a 2 (red/green trials) x 2 (congruent/incongruent trials) within-subject design :

H0 = congruency has no effect on performance.

H1 = congruency has an effect on performance.

When computing BF separately for green and red trials I get a BF of 15 for red trials and a BF of 3 for green trials. With these results, am I correct to state that H1 is 5 times more likely in red trials than in green trials?

If I am incorrect to state that, would I be correct to state more simply that "H1 for red trials is more likely than H1 for green trials"? (assuming a large superiority of one BF over the other, e.g., more than 5 times)

Henryk

• Hi Henryk,

This is actually a difficult question. I'd be inclined to say "no", as the hypotheses are computed on different data. It seems to me that you need the BF for the interaction between congruency and red/green trials. So I'd model all the data at once, and not do separate analyses and then bring them together later.

Cheers,

E.J.

Unless I am wrong, the Congruency x Red/Green interaction term would inform me about whether considering red/green separately is better than not considering separately. (hypotheses: H0 = null model (or only main effects), H1 = model with interaction).

In my case, I expect the presence of a congruency effect for both green and red trials so it is rather unlikely that H1 will be favored over H0 in the interaction term.

What I am interested into specifically is to quantify to what extent the congruency effect is "stronger" in Bayesian terms in red trials than green trials (thus irrespective of whether this congruency difference is high enough to support H1 over H0).

So, since in my case red and green trials have:

• same hypotheses
• same participants
• same prior distribution and parameters
• same metric (BF)

Are you sure I cannot state "H1 for red trials is (X times) more likely than H1 for green trials" ?

Sorry to insist :-)

Henryk

• Hi EJ again,

I think you are right that then the best way is to directly test the difference between red and green trials.

However, do you have a way to directly test whether evidence for H1 is higher in red trials than green trials. You suggested to test the interaction term in the repeated ANOVA (color (red/green) x congruency (con/incongruent)) but then this doesn't really test the wanted comparison, is it?

My understanding is that testing the interaction term only tests whether separating red and green trials explains better the data than not separating them (null model), which is not equivalent to test whether evidence for H1 in red trials is higher than green trials. What do you think?

• Well, the evidence is the evidence. So if BF = 3 in condition X, and BF = 4 in condition Y, then the evidence is larger for Y than for X. So what you really want to know, it seems, it whether effect size is larger in one condition than in the other, and that brings me back to the interaction.

E.J.