I have the following velocity measurements, where the sign of $V_e$ defines opposing directions of movement in a completely symmetric experimental setting:
\begin{array}{|l|l|r|} \hline V_e [cm/s] & V_m [cm/s] & \Delta V [cm/s]\\ \hline 9 & 9.38 & 0.38\\ 8 & 8.491 & 0.491\\ 7 & 7.482 & 0.482\\ 6 & 6.502 & 0.502\\ 5 & 5.726 & 0.726\\ 4 & 4.499 & 0.499\\ 3 & 2.021 & -0.979\\ 2 & 2.34 & 0.34\\ 1 & 2.018 & 1.018\\ 0 & 0 & 0\\ -1 & -0.501 & -0.499\\ -2 & -2.328 & 0.328\\ -3 & -2.988 & -0.012\\ -4 & -3.503 & -0.497\\ -5 & -4.506 & -0.494\\ -6 & -5.762 & -0.238\\ -7 & -7.479 & 0.479\\ -8 & -7.981 & -0.019\\ -9 & -8.496 & -0.504\\ \hline \end{array}
In this table, $\Delta V = \left| V_m \right| - \left| V_e \right|$
Running a Student t-test on $\Delta V$, we find that the mean does not significantly differ from zero, under a type I error of 5%. From this result, I conclude that $\Delta V$ 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 $V$). That is indeed the case, since my test answers a precise question: Does the measurement method ($V_m$) systematically over/underestimates the true velocity ($||V_e||$)?
Instead, the reviewer uses $\Delta V = V_m - V_e$ to show that the method significantly overestimates $Ve$, especially when $V_e<0$, 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 $\Delta V$ and discern a systematic measurement error?
If you google "velocity versus speed" you can get that velocity is a vector, with speed being the magnitude of that vector. In your case the velocity is a vector pointing only along one direction. You are asked in this problem to check the velocity, not the speed, so $\Delta V=V_m-V_e$, not $\Delta V=|V_m|-|V_e|$.