I would like to propose an alternative explanation about the "Randomized Experiments", especially in "potential outcomes are independent of the treatment". The current explanation is still confusing, but the idea behind it is not very complicated.
In one possible world, if the treated group and control group both received the treatment, they would have the same expected outcome. E[Y1 | T=1] = E[Y1| T=0]
In a second possible world, if the treated group and control group did not receive the treatment, they would also have the same expected outcome. E[Y0 | T=1] = E[Y0| T=0]
Furthermore, the treatment consisted of two steps: 1) treatment assignment, 2 treatment realization. The experiments expect to observe that the outcome depend on the step 2, which is the true effect of treatment. Meanwhile, the experiments try to avoid the noise from the step 1, that means the outcome should independent from the treatment assignment.
Hi everyone
I would like to propose an alternative explanation about the "Randomized Experiments", especially in "potential outcomes are independent of the treatment". The current explanation is still confusing, but the idea behind it is not very complicated. In one possible world, if the treated group and control group both received the treatment, they would have the same expected outcome.
E[Y1 | T=1] = E[Y1| T=0]In a second possible world, if the treated group and control group did not receive the treatment, they would also have the same expected outcome.E[Y0 | T=1] = E[Y0| T=0]Furthermore, the treatment consisted of two steps: 1) treatment assignment, 2 treatment realization. The experiments expect to observe that the outcome depend on the step 2, which is the true effect of treatment. Meanwhile, the experiments try to avoid the noise from the step 1, that means the outcome should independent from the treatment assignment.