I have a question regarding a post hoc test following an Anova.
I ran an Anova (response variable~Factor1xFactor2xFactor3)and found that I have 2 significant main effects, but no significant interactions :
Factor1 *** Factor2 *** Factor3 n.s. Factor1:Factor2 n.s. Factor1:Factor3 n.s. Factor2:Factor3 n.s. Factor1:Factor2:Factor3 n.s.
Factor1, Factor2 and Factor 3 all have 2 levels
I wondered now how to proceed from here. Would I simply do a post hoc test on the two main effects without an interaction term (response variable~Factor1 + Factor2)? Eventually, I'd like to have a barplot where letters above each bar indicate statistical differences, but if I want to do that, I would have to do all possible comparisons in an e.g. Tukey HSD test, which I don't do if I only test the two significant main effects without the interaction. Is that correct? Is it appropriate to run the post hoc test on the full model despite not having significant interactions? Can I infer from the Anova that certain comparisons are not significant without doing comparisons via a post hoc test?
Sorry for asking a question that is probably very basic to many of you but it got me really confused. All helpful answers will be greatly appreciated.