# Several 3-way ANOVA vs one 4-way ANOVA

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?

• 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. Jan 4, 2016 at 23:47
• Sorry for the confusion. Group is also a variable (with 3 levels), variables A,B and C have 2,2 and 3 levels respectively. Jan 7, 2016 at 15:10