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What I am trying to do?

Let's think, there are some diabetic patients and I am interested to find whether acceleration (when they will run to do physical exercise) correlates with amount of spent calories. I am counting spent calories and acceleration of different axes (x, y, z) via a device.

Then, what does create the problem?

I am calculating the magnitude of acceleration by using the formula: square_root(x^2+y^2+z^2). Then, I will correlate acceleration with spent calories. However, I do not know whether the accelerometer calculates acceleration including or excluding gravity. Therefore, there may have error in measuring magnitude of acceleration.

After that, what do I think?

If I would want to know each participant's magnitude of acceleration, then I must had to know whether the accelerometer calculates acceleration including or excluding gravity. If it would include gravity, I had to exclude it to find magnitude of acceleration. However, as I want to just calculate the correlation coefficient (using Spearman, Pearson, Kendall's Tau etc.), therefore, it may not need to be concerned whether acceleration includes gravity or not.

But, what is the motivation behind the thought?

Let's think, the accelerometer calculates acceleration including gravity. Then, each time, it measures acceleration, that gravity (there can be negligible variation of gravity, each time it measures) will be included. That is why I think, this will not create a problem in measuring correlation coefficient as correlation does not change when the units of measurement change (I am assuming one type of unit when gravity is included and another type of unit when gravity is excluded).

At the end, my question?

Will it be problematic if I want to correlate acceleration (by calculating magnitude of acceleration) with spent calorie without considering whether gravity is included or excluded from acceleration?

Any kind of suggestion or help will be greatly appreciated!

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  • $\begingroup$ In what sense does "including gravity" constitute a mere change of units of measurement?? $\endgroup$
    – whuber ♦
    Commented Apr 11, 2020 at 21:55
  • $\begingroup$ In Physics, acceleration is a strength while calories are energy. Spent calories will constantly increase while acceleration will alternate between increasing and decreasing. How would you correlate them? $\endgroup$
    – manu190466
    Commented Apr 11, 2020 at 22:04
  • $\begingroup$ @whuber Thanks for your response. I am not telling that "including gravity" constitute a mere change of units of measurement". Rather, I am thinking in the way that adding gravity will give you one value and exclusion of gravity will give you another value. Hence, it seems to be like converting from one unit to another unit. $\endgroup$
    – Md Sabbir Ahmed
    Commented Apr 12, 2020 at 4:08
  • $\begingroup$ @manu190466 Thanks for your comment. Is there any sentence like "If one variable increases and another variable alternate between increase and decrease, we will not be able to use any existing formula to find correlation"? I think, it may not be true. There are many ways to find correlation, even if we fail to find correlation using the general formula: Pearson, Spearman, Kendall's tau etc. On the other hand, here, I focused on acceleration and added calorie to make a complete problem. If you feel that calorie can not be correlated, then, you may set any variable along with acceleration. $\endgroup$
    – Md Sabbir Ahmed
    Commented Apr 12, 2020 at 4:26
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    $\begingroup$ It's unclear what you are trying to ask. One possibility is that you are unsure whether to use $\sqrt{x^2+y^2+z^2}$ as a variable in a model or $\sqrt{x^2+y^2+(z-g)^2},$ where the $z$-axis is up and $g$ is the gravitational contribution to acceleration. (If so, this should make it clear that the problem is not one of changing a unit of measurement.) The answer ultimately depends on your instrument, so why not consult its documentation? $\endgroup$
    – whuber ♦
    Commented Apr 12, 2020 at 13:40

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