Is it correct to use paired t test after 1:2 matching? Is it correct to use paired t test after 1:2 propensity score matching? How we can do this in R? I found the following link in SPSS (https://www.researchgate.net/post/how_is_paired_t-test_performed_for_21_case_controlled_studies_on_SPSS).
 A: This question is still unsettled in the literature. Propensity score theory says no; propensity score pairing is not meant to induce dependence within pairs and simply is a tool to balance the covariate distributions in the groups. Empirical studies have shown that it doesn't matter too much, but that you can have less conservative standard errors if you perform a matched pairs T-test rather than an independent samples T-test. It has also been found that a paired analysis of matched data can improve the robustness to unobserved confounding. 
Note that including a regression of the outcome on treatment group and pair membership is equivalent to a matched pairs t-test. With a large sample size, you may find the same model but using random effects (i.e., in a multilevel model) can improve power further while accounting for the pairing. The simplest technique is simply to use an independent samples T-test, which is common in the literature. You can also perform regression of the outcome on treatment and any relevant covariates as well.
