I have data which appears to contain a 3 way interaction (the interaction of treatment with time differs across sex) when graphed. However, when I conduct the mixed factor ANOVA the 3 way interaction does not approach significance. Because my interest is whether the treatment X time interaction differs by sex I held sex constant and performed 2 ANOVA on the treatment X time relationships. In this case there was an interaction for females, but not for males.
My question is, why wouldn't the 3 way interaction be significant if the 2 way is significant at one level of the third variable, but not at the other level of the third variable?
More importantly, is the literature to justify these subsequent analyses despite the absence of a 3 way interaction?
Thanks for your insights!!!