We could easily make a two-way anova to test whether there is an interaction between two independent variables, but it is advisable to do a bayesian inference when the p value is not so straightforward (such as a marginal p value). I refered to a book "Bayesian Modeling Using WinBUGS" to achieve this in WinBUGS software. The model is as following(2×2 within group design,30 samples):
model{
for (a in 1:LA){
for (b in 1:LB){
for (k in 1:K){
y[a,b,k] ~ dnorm( mu[a,b,k], tau)
mu[a,b,k]
Hi,
the most appropriate way is a direct modelling of the the interaction. The Bayes factor (Ratio posterior/Prior) then answers your question. The interpretation of the 'confidence interval' (better call it 'credibility interval') in hypothesis testing (p-value) is declined by many if not most Bayesians.
Thank you, Mr. Kleinjung. But how to get the Bayes factor from winBUGS? The Node statistics only shows me the estimated values of the nodes. @Frank Kleinjung
Dear Guochun,
I cannot give an exhaustive answer here. Maybe the keyword 'Savage-Dickey method' helps and I added a few links that also should help (especially the second one, which I saw the 1st time answering your question - thank you).
Best reagards,
Frank
https://static.jasp-stats.org/presentations/ICPS2015/ICPS15EJ.pdf
http://ejwagenmakers.com/2011/LodewyckxEtAl2011.pdf
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Applied Statistics