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I think I have a rather simple question. I have a 2x2 ANOVA and I am both interested in the main effects and their interaction. Usually, I'd simply run the ANOVA (type 3) to see whether main effects or interaction is significant. However, I have directional hypotheses regarding the main effects (i.e., needing a one-sided test).

Is there a way to include this in my analyses? I thought about using contrasts but usually you only need such contrasts if you have more than two conditions per factor. Or do I need to run the ANOVA and use post-hoc t-tests to specifically test the hypotheses?

Thanks for any help!

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To convert a two sided test to a one-sided test, you can always divide the p-value by two and compare to the significance threshold. Verify first that the effect lies in the prespecified hypothesis direction, otherwise do not reject the null hypothesis.

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  • $\begingroup$ Adamo, thanks for your reply! So running the ANOVA with contrasts would not help at all, right? $\endgroup$ – Mathias Jan 11 at 22:23
  • $\begingroup$ @Mathias all ANOVAs involve contrasts of some form, if not implicitly, as part of the summarized output. When the software says, "Running ANOVA with contrasts..." it is saying: "I am summarizing the mean differences according to the model you gave me and I will show you some of those mean differences." You will need to inspect the contrasts to know whether the mean difference is in the expected direction per my answer. $\endgroup$ – AdamO Jan 14 at 17:05

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