I have the following velocity measurements, where the sign of V e defines opposing directions of movement in a completely symmetric experimental setting: V e [ c m / s ] V m [ c m / s ] Δ V [ c m / s ] 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 In this table, Δ V = | V m | − | V e | Running a Student t-test on Δ 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 Δ 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 Δ V = V m − V e to show that the method significantly overestimates V e, especially when V e &lt; 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 Δ V and discern a systematic measurement error?

Question

I have the following velocity measurements, where the sign of       V    e   defines opposing directions of movement in a completely symmetric experimental setting:                              V          e                [        c        m                  /                s        ]                              V          m                [        c        m                  /                s        ]                    Δ        V        [        c        m                  /                s        ]                            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            In this table,   Δ  V  =      |          V      m        |    −      |          V      e        |  Running a Student t-test on   Δ  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   Δ  V is a random error.The reviewer of my work (I&#039;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   Δ  V  =      V    m    −      V    e   to show that the method significantly overestimates   V  e, especially when       V    e    &amp;lt;  0, using the same t-test. However, I am having trouble finding what specific question such a test answers, and the reviewer&#039;s statement is wrong in my opinion.What is the correct way of defining   Δ  V and discern a systematic measurement error?

Johnathan Morse · Accepted Answer

If you google &quot;velocity versus speed&quot; 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   Δ  V  =      V    m    −      V    e  , not   Δ  V  =      |        V    m        |    −      |        V    e        |  .

I have the following velocity measurements, where the sign of V e </msub> define

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