I have a simple experiment in which ~30 people responded to 100 words, half of which were of Type A and half of which were of Type B. I am using a mixed effects linear regression to predict reaction time differences between words of Type A and Type B. I am also using a ME logistic regression to predict accuracy differences. These models are being fit using Bayesian parameter estimation.
Ultimately I am interested in determining the probability that the null hypothesis is true given the data. I am going to do this using Bayes Factors to compare models with and without the parameter of interest (i.e., word type).
Based on the literature, the largest possible mean difference I would expect between Type A and Type B is 100 ms. The effect size that I'd expect to be most likely is around 30 ms. I should be clear that these are both what I would expect if there is an effect. I think the most likely expectation is to find no effect at all.
I am curious how to now turn this into a prior. The various advice I have found so far is to:
- use a normal distribution centred at zero with a standard deviation equal half of the maximum expected effect size
- use a normal distribution centred at zero with a standard deviation equal to the expected effect size
- set a uniform distribution across all possible effect sizes
I'm wondering if there are other rules of thumb in setting up the prior based on a maximum possible effect size and/or expected effect size? Is it common practice to centre the prior at zero? Note that this is all for the purpose of computing a Bayes Factor for the effect of word type.