Say I want to compare some measure before and after a treatment. To my understanding, I should use a paired t-test. But, if I manually normalise the data so that each before measurement is 1 and each after is something like 1.2 and do a paired t-test, should the result not be the same? I thought the paired t-test already dealt with only with the difference within a pair so whether it is normalised or not makes no difference.
Edit: by normalise I mean divide each value before treatment by itself to get 1, then divide each value after treatment by the same value, that is divide by the value for that individual before treatment.