I have the following velocity measurements, where the sign of defines opposing directions of movement in a completely symmetric experimental setting:
In this table,
Running a Student t-test on , we find that the mean does not significantly differ from zero, under a type I error of 5%. From this result, I conclude that is a random error.
The reviewer of my work (I'm an academic student) insists that my method does not account for the direction (i.e. the sign of ). That is indeed the case, since my test answers a precise question: Does the measurement method () systematically over/underestimates the true velocity ()?
Instead, the reviewer uses to show that the method significantly overestimates , especially when , using the same t-test. However, I am having trouble finding what specific question such a test answers, and the reviewer's statement is wrong in my opinion.
What is the correct way of defining and discern a systematic measurement error?