Suppose I have a group(X) of people receiving a treatment for high blood pressure. Suppose I match these people to controls(Y) who have high blood pressure but who are not receiving any treatment. I perform a 1:n match based on sex, age at study start, and date of birth. I would like to the blood pressure between these two groups. However, I am having a hard time justifying the use of either a paired or two sample t-test. Any insights would be appreciated.
If n=1: I have two options: Paired t-test: Compute Xi-Yi and test the mean of these differences. Difficulty: Hard to convince myself that these really are paired observations. I have really only made the two populations more comparable by matching. Two Sample t-test: test the difference of the means in the two populations Difficulty: I find it hard to convince myself that the two populations are independent.
If n>1: Paired t-test: For each case i compute Xi-Y1, Xi-Y2,....Xi-Yn (given that there are n controls) and then test the mean of the differences. Difficulty: It's hard to convince myself that these observations are independent of eachother given that Xi appears in the differences n times. Two Sample t-test: Test the difference in means between the two groups. Difficulty: I find it hard to convince myself that the two populations are independent.
My concern is mainly about violation of assumptions of these tests which might lead to incorrect inference. I am not really concerned about power, as both tests return significant results.