I have an experimental design with 4 groups: (1) Controls, (2) Treatment A, (3) Treatment B, and (4) Both treatments A and B
The data looks like this:
In this experiment, I want to know what Treatment A does on its own, what Treatment B does on its own, and what they do together. It seems like a classic 2-way ANOVA situation.
When I just glance at the data, it obviously looks like A has some effect, B has some effect, and A+B does something opposite. When I run the actual 2-way ANOVA, however, it only comes up with an interaction effect. The main effects of A and B are both non-significant.
But the t-tests for all of these are extremely significant (p < 0.001). Is a 2-way ANOVA not the right way to go? Is it not right to interpret the main effects here? What's going on?