I am trying to determine if the treatment effect on different groups are statistically different using a statistical test. More specifically, my data is divided into 6 strata. and in each stratum there is a treatment as well as a control group. For each group in each stratum, I then measure three outcome variables post-treatment. However, I do not know which statistical test is the most appropriate to use when I try to determine if the different in each outcomes between the two groups in each stratum differs significantly with respect to the chosen stratum. Also, if there is a suitable test, please also point out the corresponding function in R (if there is one).
I will give a more specific example. Say in stratum one group C1 has 1000 data points with an average outcome value of 0.06, while in group T1, the treated group in the same stratum, the outcome value has a mean of 0.11. We then have a difference of 0.05. Say in the 2nd stratum with 800 data points, C2's mean outcome value is measured to be 0.10, and T2 0.24. The difference is 0.14. We are then interested in finding out if the two differences 0.14 and 0.05 are statistically different.