# $3^3$ factorial design

Suppose in a $3^3$ factorial design, factor A has three levels. We want to test the significance of A and after setting hypothesis $$H_0:\alpha_i=0 \quad\text{for}\quad i=1,2,3 \quad\text{Vs.}\quad H_1:\alpha_i\ne 0 \quad\text{(Is that correct H_1 setting?) }$$ performing an ANOVA test, we conclude that "there is significant effect of factor A."

What does it mean? is there variation among different levels of factor A?

Is that $2^3$ factorial design one way ANOVA (Because there is no blocking) or two way ANOVA (Because there is two treatment effects)?

• I don't think that factor A can have three levels in a $2^{3}$ design (unless one of its levels was omitted). See onlinecourses.science.psu.edu/stat503/node/34 – Andrew M Dec 12 '14 at 6:51
• Also, if this is a homework problem, please tag the question with [self-study]. – Andrew M Dec 12 '14 at 6:52
• @AndrewM oh, this would be $3^3$ factorial design. – user 31466 Dec 12 '14 at 9:54