I have a continuous outcome variable, Y, that is a daily consumption score and want to study the impact of a policy change on a control group and 4 test groups t1, t2, t3 and t4. The policy change took place on may 1st and the the number of observations in each group pre/post the change will be different.
I was thinking of doing 4 regressions, one for each test group t1,t2, t3 and t4
Y ~ prepost + testgroup + prepost*testgroup
where prepost is an indicator variable that is 1 if the observation is after may 1st and 0 if it before, testgroup is an indicator variable that takes 2 values (0 and either 1,2,3,4) that indicates the control group 0 and which test group is being tested. and prepost*testgroup inidcates the effect that the policy had on the test group.
For example, for test group 1 the regression has 25 observations for the control group pre may 1st and 40 observations post may first. the regression has 60 observations pre may first for test group1 and 40 observations post may first.
I'd run a similar regression above but replace test groups 2,3 and 4 for test group1
Is this the right set up to test for the impact of the policy on the test groups. I thought you would need to include the control group to control for other variables that may have changed pre and post may 1st.
Is this how the data should be analyzed if you want to find out if the policy impacted the test groups?
Are there any paper or lectures on how to design the analysis when the data is set up like this and you want to find out if the policy had and impact on test groups?
--I read the how to age page. What am I leaving out? I think i described the problem and asked the question. What is unclear? Let me know and I'll clarify.