Dear CrossValidated community,
I have run a 3 by 2 mixed ANOVA, in which my between-factor is group (treatment1, treatment2, and treatment3) and my within-factor is time (pre and post). Let's call my dependent variable X. Accordingly, I first tested for an interaction, which came out as non-significant, and then moved on to testing for the main effects of group and time.
Both the main effects of group and time came out significant. My question is related to the main effect of time, which the results of suggests there was an overall decrease in X across groups.
Now my question is, because this is a main effect of time, does it automatically mean that if I did a dependent t-test with each group independently, each group would exhibit a statistically significant reduction?
My hunch is no, which leads to my main question. If someone was to ask me how do I know that each group independently showed a statistically significant reduction in X, would it be okay for me to then run a dependent t-test analysis for each group separately, to show that in each group, X was significantly reduced?
Thank you in advance. P.