# Post hoc test 2x2 design

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.

• Do the values 0.01, 0.002 and 0.245 refer to p values? Apr 5 '20 at 12:51
• Yes. Sorry. I should have mentioned that! Apr 5 '20 at 13:55