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# Interpreting Bayesian ANCOVA

Hi,

May I double check that I am interpreting the Bayesian ANCOVA correctly? Here are 2 versions of the analysis, where I modify only the BF setting, i.e. BF01 to BF10 but both versions are comparing to the null model. Are my intepretations in each version, correct?

Thanks very much,

Francesca

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VERSION 1

Comparing to the null model

BF01

Model 1: BF01 = 75

Model 2: BF01 = 0.666

Model 1 interpretation: this model is 75 times more likely than the null model.

Model 2 interpreation: the null model is 1/3 times more likely than model 2

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VERSION 2

Comparing to the null model

BF10

Model 1: BF10 = 87

Model 2: BF10 = 0.50

Model 1 interpretation: the null model is 87 times more likely than model 1.

Model 2 interpreation: model 2 is 1/2 times more likely than the null model

• Dear Francesca,

Good question! I think according to the guide published here (see p. 40), I think your interpretations are actually backwards:

I think BF10 is actually representative of the alternative in the numerator of the BF formula, so larger numbers here indicate strong evidence for the alternative. I think BF01 is the inverse, with the null in the numerator, so large numbers here would be indicative of strong evidence for the null.

• I would need to see a screenshot of the table, but I can already note that the BF measures relative predictive performance -- it is the evidence or the degree to which the data change our opinion. It is therefore *not* the probability or plausibility of the models, unless we assume that the models are equally likely a priori. See https://www.bayesianspectacles.org/the-single-most-prevalent-misinterpretation-of-bayes-rule/

So BF01 = .666 means the data are 3/2 times more likely under H1 than under H0. (NB. this is a statement about the predictive ability of the models, not their posterior plausibility)

E.J.