Quantifying the statistical error in a counting experiment


by JoePhysicsNut
Tags: binomial, branching fraction, statistics
JoePhysicsNut
JoePhysicsNut is offline
#1
Jan22-13, 03:54 AM
P: 34
I need to find the statistical error in a counting experiment. Specifically, a decay can proceed via option A or option B and I need to find the branching ratio BR_a=(N_a)/(N_a+N_b). If I were to do this counting experiment multiple times my results for BR_a would follow the binomial distribution since there are two decay channels.

How do I quantify the statistical error in my result given that I conduct the experiment only once?
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mfb
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#2
Jan22-13, 10:25 AM
Mentor
P: 10,853
Do you have a fixed number of decays ("I take data until I have 100 decays in those two channels")?
No => you can treat N_a and N_b as the result of independent Poisson processes.
Yes => the denominator is fixed, and N_a comes from a binomial distribution.
Meir Achuz
Meir Achuz is offline
#3
Jan28-13, 09:33 PM
Sci Advisor
HW Helper
P: 1,937
The usual statistical error gives N_A+ - sqrt{N_A}.


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