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I have experiment leading to 4-way ANOVA:

  • 3 experimental groups.
  • participants in each group responded to 70 trials.
  • Reaction time as DV.
  • trials were divided into separate groups by full factorial design by three variables A,B and C.

I'm not sure what is the best way to analyze the data. I can run one 4-way ANOVA with (RT ~ group*A*B*C) or run three 3-way ANOVAs for each group separately (RT ~ A*B*C).

What is the best practice? Run one 4-way ANOVA, but harder to interpret, or run three 3-way ANOVAs and correct for multiple testing?

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  • $\begingroup$ Please consider: if each variable, A, B, and C, had just 2 levels, then there would be 2x2x2=8 groups. Does this design really have only 3? And if so, what splits the participants into these 3? I suspect that where you speak of "variables" you actually have 3 levels of a single variable. $\endgroup$ – rolando2 Jan 4 '16 at 23:47
  • $\begingroup$ Sorry for the confusion. Group is also a variable (with 3 levels), variables A,B and C have 2,2 and 3 levels respectively. $\endgroup$ – fidadoma Jan 7 '16 at 15:10
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If you are not really interested in the comparison between groups go for the 3-way definitely. The 4-way case will end up with A LOT of interactions for you to study. This is very complex and tiring...

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  • $\begingroup$ Thank you, unfornutaly, I'm interested in comparison between groups. Can I run three 3-way anovas and correct for type I error? I'm not sure, how to interpret significant coeficients for higher level interactions. $\endgroup$ – fidadoma Jan 7 '16 at 15:14
  • $\begingroup$ So one analysis for each group is not an option. You could remove one of the factors or run the analysis with all 4 of them, selecting what interactions and main effects you think are important to be interpreted. $\endgroup$ – Walter Jan 8 '16 at 0:58

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