I think I have to clarify some more why I turned to pymc3 and I’m not just doing a Bayesian ANOVA in JASP or jamovi.
I’m especially interested in predictions from 2 hypotheses I haven’t mentioned before.
1: low variability for orthogonal in all blocks, high variability for parallel projection in block 1 & 3, but not in block 2.
sigma
^
| . . parallel
| \ /
| \ /
| \./
| .___.___. orthogonal
|------------> block
1 2 3
2: same as before except that orthogonal variability rises in block 2.
sigma
^
|. . parallel
| \ /
| \ /
| \./
| /*\
| ./ \. orthogonal
|------------> block
1 2 3
The ANOVA on the Synergy Index (a measure of the variability ratio) can’t discriminate these 2 predictions, only that there is some difference in block 2 vs 1 & 3, which doesn’t help much. Therefore, I hope to model these 2 predictions in pymc3, amongst other ones.
That’s why I think counting the samples where parallel > orthogonal would not be able to give me the answer I seek, because it would give me the same result for these 2 examples?