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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.

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  • $\begingroup$ Do the values 0.01, 0.002 and 0.245 refer to p values? $\endgroup$
    – Groovy_Worm
    Commented Apr 5, 2020 at 12:51
  • $\begingroup$ Yes. Sorry. I should have mentioned that! $\endgroup$
    – Deschain
    Commented Apr 5, 2020 at 13:55

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You do not need to do a post-hoc test.

Because the interaction term is not significant, we know that the main effect of Condition is significant at both Temperatures.

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  • $\begingroup$ Many thanks for that fast reply and the clarification. That does make a lot of sense. I must have misunderstood this. $\endgroup$
    – Deschain
    Commented Apr 6, 2020 at 6:48
  • $\begingroup$ If the answer was useful, please help others by accepting it. Thank you. $\endgroup$
    – Groovy_Worm
    Commented Apr 6, 2020 at 7:28
  • $\begingroup$ Sorry that I didn't answer that but I actually do not know how to accept an answer. $\endgroup$
    – Deschain
    Commented Apr 25, 2020 at 10:41
  • $\begingroup$ I have, however, a follow up question in terms of how to display the statistical results in a boxplot or barplot. A common thing after a post hoc test would be to add letters over the, in this case, 4 bars. But as I didn't do all the individual comparisons I guess I cannot do that. What is a common way to do that? $\endgroup$
    – Deschain
    Commented Apr 25, 2020 at 10:48
  • $\begingroup$ It should be obvious to the reader once you draw the barplot with confidence intervals. The figure legend can state the results of the significance tests. $\endgroup$
    – Groovy_Worm
    Commented Apr 26, 2020 at 8:20

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