I have a relatively simple 2x2 design. I give a hypothetical example. I have a continuous variable Y (Plant Growth) and I have 2 factors with 2 levels; Temperature (warm/cold) and Condition (Fertilizer, no Fertilizer).
I did an Anova (Plant Growth~Temperature*Condition) and get the following p-values:
- Temperature: p = 0.01
- Condition: p = 0.002
- Temperature*Condition: p = 0.245
As the interaction is not significant, I do not want to do every single comparison in a post hoc test. Instead, I want to see if Condition has a significant effect on plant growth under warm temperatures, and I also want to know if Condition has a significant effect on plant growth under cold conditions.
Now I wondered what the correct way of doing this is? Would I do a simple t-test under Condition cold and another one under Condition warm? If that is possible, would I have to correct for multiple comparisons (I guess so)? It doesn't seem to make sense to do a post hoc test in that case.