Hi - I'm new to R and Bayesian statistics and could use some help! Any advice would be greatly appreciated.
My first question is whether an F-value and/or p-value (which I know are inversely related to one another) are related to the Bayes Factor (BF). For example, if you have a significant p-value with a decent effect size, would you expect the BF to indicate evidence in favor of the alternative hypothesis? (This is a question for a different dataset than what I show below).
Second, why would one want to include Subject as a random factor for a within-subjects design? When I run anovaBF with Subject as the random factor:
bf = anovaBF(accuracy ~ orientation * validity + Subject, data= UnrSC_long2, whichRandom = "Subject")
I get the following output:
Bayes factor analysis
[1] orientation + Subject : 0.2443014 ±1.9%
[2] validity + Subject : 305.9225 ±1.11%
[3] orientation + validity + Subject : 74.90707 ±2.08%
[4] orientation + validity + orientation:validity + Subject : 539.979 ±6.95%
Against denominator:
accuracy ~ Subject
Bayes factor type: BFlinearModel, JZS
When I run it without Subject:
bf2 = anovaBF(accuracy ~ orientation * validity, data= UnrSC_long2)
I get the following output:
bf2 = anovaBF(accuracy ~ orientation * validity, data= UnrSC_long2)
|=====================================================================================| 100%
bf2
Bayes factor analysis
[1] orientation : 0.2296698 ±0.03%
[2] validity : 31.69291 ±0%
[3] orientation + validity : 7.140034 ±1.38%
[4] orientation + validity + orientation:validity : 16.22604 ±1.07%
Against denominator:
Intercept only
Bayes factor type: BFlinearModel, JZS
I know the comparison models are different (accuracy ~ Subject and Intercept only, respectively), but I am having a hard time interpreting the results. Why are the BFs so much larger when Subject is included? What is the intercept-only model? How does the intercept-only model differ when I use the anovaBF function versus the lmBF function? (I know anovaBF computes several model estimates at once whereas lmBF computes one comparison at a time, but how does that influence the intercept-only model?)
Thank you in advance for any help! 