I'm trying to get my head around which effect size is most meaningful for a 2x2 mixed ANOVA for two intervention groups. I have pre and post assessement data (measured at the continuous level) for two different intervention groups (A and B).
For ease of asking this question I've made the image below as a reference and made the mean and standard deviation straight forward just for this example as I'm confused about whether an effect size calculation is needed for pre-to-post within groups analyses (analyses 1 and 2 below), pre/post between groups analyses (analyses 3 and 4 below) or an analysis of the mean difference in pre-to-post assessment scores between the groups (analysis 5 below).
I'm guessing that I should be doing a between groups t-test to demonstrate that the two groups did not differ at pre-assessment (analysis 3 below) and then a t-test on the mean difference in pre-to-post scores between groups (analysis 5 below)?
Edit: Participants were allowed to choose which intervention group they attended, so participants were not randomly assigned to groups.