I am doing a study in which I am measuring a set of lengths using two different methods. I want to test how close the measurements given by the two methods are for corresponding lengths. Is there a way to do this? I know that a matched pairs t-test can give a p-value for the means being different, but how can I test how close the differences are to 0?
In other words, since the two methods are measuring the same lengths, they should most ideally give the same measurement for any given length. I want to test how close this is to being true and quantify the amount of error that is present. So say I plotted the lengths given by one method against those given by the other. If they did give the same measurement for every length, it should form the line $Y=X$. Basically, I want to test the hypothesis that the data does form the line $Y=X$, calculate the mean error (maybe the average distance from $Y=X$), and perhaps produce a p-value for it.