combination of uncertainties

#1
I try to measure a specific quantity in a target. I assume there are mainly 2 sources of uncertainties, let's call them sigma 1 and sigma 2. I want to know the contribution in the uncertainty due to sigma 2.
I already have a some knowledge about sigma 1 (sigma 1 is known) and since I made multiple measurements on the target, I have the experimental variance s².

Is it correct to say that, since s² = s1²+s2², then s2 = sqrt(s²-s1²) and is a good estimate of sigma 2?

If yes, what to do when the contribution from sigma 2 is very small, which leads me sometimes with a s2² being negative...

Kinda lost, would really appreciate any help
 

rogojel

TS Contributor
#2
hi,
this is a bit more complicated and the estimate will depend in the model you have. Do you have a simple additive midel (like Y=X1+X2)?
 
#3
Yes i have Y=X1+X2, and expected value of both X1 and X2 is 0.


Basically, the second contribution to the uncertainty is due to an specific effect I want to quantify. Since i know the first contribution to the uncertainty analytically, and since I can calculate the experimental variance, I'm trying to say : "See, the experimental variance is bigger than just s1², so it is reasonnable to think that it is because of that specific effect, and its contribution to the total uncertainty (at least its best estimate ) is s2 = sqrt(s²-s1²). "

Eventually, if i can estimate the risk of being wrong, that would be even better.

Does this seems okay?
 
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#4
This problem is very like that of estimating Variance Components from an anova table. In Variance Components, if a particular variance is estimated to be less than zero, it is simply put to zero.
You can probably get a bootstrap confidence interval for s2 if you have set of experimental data.