[phenixbb] question on f/sigf
Edward A. Berry
BerryE at upstate.edu
Fri Jul 13 15:52:27 PDT 2012
Edward A. Berry wrote:
> 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
> 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.
Better, use chain rule for propagation of error- sigma(F(I)) = Sigma(I)*dF/dI
>
> 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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