[phenixbb] question on f/sigf

Edward A. Berry BerryE at upstate.edu
Fri Jul 13 15:34:09 PDT 2012

fn1 at rice.edu 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
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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