I am conducting a quasi-experimental research in a school, where I have access to 100 students who are chosen as classrooms and who will be the participants of the study. I am interested in the effects of two separate treatments and want to conduct a pre-test/post-test study (with two post-tests). So I have two independent variables (the two treatments) and four dependent variables. I need to form three groups out of the 100 students: one for each experiment and a single control group. Participants will be assigned to these groups randomly.
My questions are:
What should I take into consideration when deciding the in what proportions I divide the students to the groups (i.e. how big each group should be). Surely the both treatment groups should have an equal amount of participants, but how about the control group? Would it be better to have 33 in each group, or rather to have for example 40 in each treatment group and only 20 in the control group?
What is the best way to calculate the statistical power in such a study that includes three groups?
What statistical methods would you consider for this kind of study? Since I have have multiple dependent variables, would it be better to use ANCOVA treating each dependent variable as a independent experiment or to rather use Two-way MANOVA? Or would you suggest something else?