The title is my question, here is a little more information. I was checking off on an analysis done by someone else and they used a paired t-test on data from the same subject; however the difference that was calculated for the paired t-test was from two different variables (the variables are not measurement 1 and 2 of the same thing, they represent measurements of the same idea, energy expenditure measured in two different ways. Variable A is expenditure measured using method A and variable B is expenditure measures using method B).
Each subject had a measurement taken on them using method A and a measurement using a different method method B (these methods theoretically measure they same thing, but one is the gold standard and the other is not) and then the difference was calculated as method B - method A and the paired t-test was done on the vector of the differences.
My question for this specific data set is, is this a valid pair? Typically, I see paired t-tests using the same variables, for instance pre-post measures on an individual variable for each experimental unit, or twin studies where the same variables are collected.
More generally my question is what constitutes a valid pair for a paired t-test? Is it valid to consider two different variables (for instance variable for method A and a variable for method B) a pair? And if so what if any issues can arise when a paired test is being performed on different variables.