Do I use instrument error or arithmetic mean error?

[MartinTheStudent]

Hi.
Let's say I have data which I have measured. For example I measured a length of an object and the measurment was repeated 5 times. An instrument which I used to measure has an error, value of which I know.

My options are to either to just go with the instrument error (probably not, right?) or to calculate the arithmetic mean error from my statistics and go with that. Or I could calculate both and add them together somehow.
Which one of these?
Thanks!

 

[jedishrfu]

Here's some guidance:

https://www2.southeastern.edu/Academics/Faculty/rallain/plab194/error.html

 

[MartinTheStudent]

Here's some guidance:

https://www2.southeastern.edu/Academics/Faculty/rallain/plab194/error.html

Thanks for a quick response, but it does not answer my question at all. I read all of it, but it is not what I would like to know.

I am asking whether I should use the arithmetic mean error (standard error) to determine the uncertainity in my measurement, or if I should take the instrument error into the calculation of the uncertainity. If so, how?
Thanks in advance!

 

[FactChecker]

The only defensible thing to do is to use the larger of the two.
You can not use a value that is less than the known instrument error. The instrument might have a constant error bias which would not show up in a sample variance. So you can not use a smaller sample variance. If the sample variance is larger than the known instrument error, then you know that the larger sample error is coming from something. You can't ignore it.

 

[MartinTheStudent]

That sounds reasonable, thank you.

The instrument might have a constant error bias which would not show up in a sample variance.

If i understand it right, the instrument's error could be a constant, not a different error each time we measure. Then the samples would be all in a smaller region. Which means the variance would be smaller, right?

 

[FactChecker]

That sounds reasonable, thank you.

If i understand it right, the instrument's error could be a constant, not a different error each time we measure. Then the samples would be all in a smaller region. Which means the variance would be smaller, right?

Right. I guess that if your goal is just to determine the sample variance, then you should use the sample variance. If your goal is to draw conclusions about the uncertainty of the length, then you need to use the larger of the sample variance or the known instrument uncertainty.

 

[mfb]

The only defensible thing to do is to use the larger of the two.
You can not use a value that is less than the known instrument error. The instrument might have a constant error bias which would not show up in a sample variance. So you can not use a smaller sample variance. If the sample variance is larger than the known instrument error, then you know that the larger sample error is coming from something. You can't ignore it.

Or add both in quadrature to be conservative. Your sampling error could be independent of a constant offset of the measurement device.

 

[FactChecker]

Or add both in quadrature to be conservative. Your sampling error could be independent of a constant offset of the measurement device.

Good point if you want a conservative number. I thought about that. But then I thought that the known uncertainty of the instrument might (should?) already include the errors of the typical use of it. So I left my comment as-is. You might be more correct.

 

[MartinTheStudent]

Thank you guys.