[email protected] wrote:
Hi All,
I am wondering why f/sigf is always about twice of i/sigi. Is there any mathematics behind this relation? Maybe it is not directly related to phenix, but i sincerely hope someone could help me with it.
I'm not sure if that is exactly the case, and it may depend on the the distribution of errors and the size of the error, but in the limit of small errors it should be a good approximatin. Start with some calculus: d/dx(x^2) = 2x or dx^2 = 2xdx (the change in x^2 is 2*x times the change in x but we like to express as a fraction, or percent error, so divide both sides by x^2 dx^2/x^2 = 2 dx/x the percentage change in x^2 is twice the percentage change in x (for small dx) Now say <F> is X, and dX is the distance from that to one of the measurements. each of the measurements will be twice as far from the mean values when expressed as I as when expressed as F. Then run that through the root-mean-square math for calculating sigma, and see if it doesn't come out twice as large for I as for F. Or take an example: F is 100, which was derived from I=10000 a second measure is F=101 (1% different), which was derived form I=101^2 = 10201 (2.01% different)
Thank you in advance! Fengyun
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