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# Bayesian ANOVA_fixed factor

Hi everyone,

I am trying to understand the results of a Bayesian ANOVA.

I am assessing the influence of two periods of competitions (congested and non-congested) on soccer players physical performance (e.g., distance covered, accelerations, sprints, etc.).

I considered physical performance variables as a "dependent variable", the competition period as a "fixed factor", and the players were considered a "random" factor.

Similar to previous studies where I performed a Bayesian ANOVA, the model comparison table present the null model in the first line, with a BF10 equal to 1.000 (please see picture below).

However, when I consider the distance covered variable, the model comparison table is quite different, showing the fixed factor in the first line with a BF10 equal to 1.000 (please see picture below).

Could you please explain to me why this happen? Do my data (table 2) provide no evidence that the competition period influence the players' distance covered?

Mateus

• Hi Mateus,

This happens because "compare to best model" is the default setting, and the first row gives the model of reference. The BF in the first row is always 1 because the model is compared to itself. In the first table there is a smidgen of evidence for H0 (you can also see this from the posterior model probabilities, P(M|data)). In the second table, there is evidence against H0 -- BF_10 = 0.106, meaning the data are 0.106 times more likely under whatever model is in the row (in this case H0) relative to the reference model (in this case the model with Congestion). The subscripts on the BF are confusing here and we intend to change those in the future. But you can see the direction of the evidence by looking at the P(M|data) column.

Cheers,

E.J.

• Hi E.J.,

First of all, thank you for your response. Second, sorry to bother you again with news questions.

Can I make the following assumptions:

Table 1 - Anecdotal evidence for the null hypothesis in the accelerations variable was observed.

Table 2 - The Bayes factor indicates moderate evidence that the distance covered is not influenced by the competition period, as the data was 0.106 times more likely to occur under the null model.

Thank you in advance,

Mateus

• Your conclusion for Table 2 should be the other way around. 0.106 under the null is 1/0.106 = 9.43 under the alternative. That this is support *against H0* and *in favor of H1* is also evident from the P(M|data) column.

E.J.

• Of course, my mistake.

Correction: the Bayes factor indicates moderate evidence that the distance covered is influenced by the competition period, as the data was 9.43 times more likely to occur under the competition period model (null model: BF10 = 0.106, BF01 = 1/0.106 = 9.43).

I have some trouble analysing the posterior model probability column. Can you tell me if a similar table to this one is available (please see picture below) to improve the description of my results?

Thank you in advance,

Mateus

• Hi Mateus,

There isn't, as far as I know. But most people find it relatively straightforward to interpret posterior probability. Actually, our "pizza plot" method works with posterior probabilities. See https://www.bayesianspectacles.org/lets-poke-a-pizza-a-new-cartoon-to-explain-the-strength-of-evidence-in-a-bayes-factor/

E.J.

• Hi E.J.,

Now I get it.

Thank you for your time,

Mateus

• Now I get it.

Thanks a lot

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