I have a device which obtains velocity based values over a period of 1 minute (average). I also have another device with which I am comparing that device. Now the velocity values can be quite random, but both devices should be similar in terms of increase or decrease within each minute: essentially they should have the same flow.

I saw online that some research has utilized the Pearson correlation to compare these values, but what I'm wondering is why? I read that this correlation only works for linear based values, and from what I read up, the velocities themselves were quite random (although similar in terms of devices). Or at least I don't think they are linear.


If you think your two devices are measuring the same quantity despite fluctuations then equality is a reference case for you, so you should be considering whether $y = x$ is a good approximation for their measurements $y$ and $x$. That certainly qualifies as a linear relationship as it is merely a special case of $y = a + bx$ for which $a = 0$ and $b = 1$.

Conversely, correlation measures linearity of relationship, not agreement. The correlation between any $x$ and any $bx$ is identically $1$ for positive $b$, whether $b$ is 2 or 2 billion or anything else positive. Concordance correlation is a specialised measure of agreement, not linearity, which has its uses. So, you need to be careful as correlation only measures agreement in special circumstances.

A complication here is that your devices are on an equal footing, so that there is no sense in which one is a response to the other rather than conversely. Opinion differs on what to do here, but better advice might follow a plot of your data so we can see how well or badly behaved they are.

It is not clear here exactly what you mean by "random".

  • $\begingroup$ I think I sort of understand, so say in one device I get velocity values 5,10,15,20,15,10,5 and the second device I get 8,13,18,23,18,13,8 (All 3 values higher) this would show a positive correlation as device 1=y and device 2 = x and the linearity is that y=x+3 assuming b=1. So even through the velocity values here increase then decrease (nonlinear) the correlation is still linear? $\endgroup$ – John McKenzie Nov 12 '14 at 12:12
  • $\begingroup$ Indeed. In that case the correlation is not just positive but identically $1$ even though agreement is clearly imperfect. But watch out: what you are calling "nonlinear" is a plot of velocity versus time, which whatever its interest has nothing to do with the correlation between values paired for the same times. What is linear and what is nonlinear depends entirely on what graph you are looking at. $\endgroup$ – Nick Cox Nov 12 '14 at 12:18
  • $\begingroup$ You're amazing mate, thanks heaps, I really appreciate it!! Unfortunately my rep is too low to vote up, but I marked it as answer accepted. It makes so much more sense now. Thank You!! $\endgroup$ – John McKenzie Nov 12 '14 at 12:26

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