I am running an online survey experiment where participants are randomly assigned to different treatment groups. They are asked to make a three alternative forced choice (3AFC) decision, i.e., pick A, B, or C. I am interested in whether participants in one treatment group are more likely to choose A over B, than participants in another treatment group. Which test should I use? And how would I set it up? Also, any advice on how to analyze in R would be greatly appreciated. Thank you.
Edit 1: The 3AFC question is just one question in a longer survey. So it's single trial (i.e., one observation per participant).
Edit 2: We are also collecting data on age, gender, education, reaction time, and confidence in their choice (5-point Likert scale). How can I include this data as covariates in the analysis?