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# ANCOVA interpretation help

I'm fairly new to Bayesian stats and am performing an ANCOVA for the first time (in JASP). I want to find out if there is a difference between two groups on a task, while controlling for IQ scores.

Therefore, the available models of interest are:

group
IQ
group +IQ

How do you interpret the relationship between the different BFs (or BF inclusion, analysis of effects) for each model? If the BF for group + IQ is more than 3x the group BF (or the BFinclusion > 3) what does this mean for how the group BF should be interpreted?

Many thanks in advance for any help!

• First and foremost, it is important to be aware that if IQ differs between the groups, adding it as a covariate does not "control" for it. ANCOVA was meant to be used when the covariate (IQ) is important, but does not differ between the groups. See Miller & Chapman, 2001.

Assuming the IQ variable is important but does not differ between the groups, I would add it as a nuisance (i.e., always include it in the null model).

If you look on this list for ANOVA / ANCOVA you will see several examples of how the results are interpreted. Also, see the part II paper at https://osf.io/m6bi8/
If you still have questions after consulting this material, let me know
Cheers,
E.J.

• edited January 2018

Many thanks for the reply EJ - I was not aware of this! Not quite sure where it leaves us as our groups do differ on IQ. I will do some more reading.

• I've just been reading the part II paper, and apologies if I've missed something obvious, but I can only find anova examples not ancovas. I'm familiar with how to interpret the former, but am having problems understanding whether the group BFs in the ancova output have been altered to take account of the covariate 'noise' ? i.e. as would be the case with the frequentist output of an ancova.

I understand that for my study ANCOVA is not an appropriate analysis, but I'm still interested for future reference and general education.

• I would add the nuisance parameter (covariate) to the null model, and then interpret the outcome as you would do for the ANOVA. If you are also interested in the covariate itself, you can keep it out of the null model. If you send a screenshot of the output table we can discuss more concrete questions.
Cheers,
E.J.