# Matched data: Paired t-test vs. indpendent

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.

A two-sample $t$-test seems more reasonable here, predominantly because of the following reason.
When doing a two samples $t$-test, you are assuming the two samples are not dependent on each other. This assumption will not be violated just because the participants had a similar demographics. If you went out and obtained the $Y$ randomly and the $X$ randomly, and assigned them treatment randomly, then there should be no problem with the independence assumption.