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Statistical uncertainty of weighted mean 
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#1
Nov912, 11:56 AM

P: 7

Hello!
I am using physical data to do an analysis (~30k measurements). These measurements include energies, momenta, angles... of particles. I am calculating a value (call it v) at the end after a lengthy process, and if I introduce all the data into my program I did, the result is v±σ. If, however, I "bin" my events in energy and angle (say I made four bins in total), when I calculate "v", I get v1±σ1, v2±σ2, v3±σ3, v4±σ4. Then I combine these values into one using a weighted average (c stands for combined): [itex] v_c = \sum(v_i/\sigma^2_i)/\sum(1/\sigma^2_i)[/itex], and [itex]\sigma_c = 1/\sqrt{\sum(1/\sigma^2_i)}[/itex] (as can be seen here). When I do this, it turns out that [itex]\sigma_c \simeq \sigma/2[/itex]. How can this be? I am using the same amount of statistics! Any reply or idea will be very welcome!! Thank you! Brais. 


#2
Nov912, 05:52 PM

P: 4,579

Hey Brais.
The wiki article looks straightforward, but perhaps you could just outline your calculations in a little more detail step by step to show the simplifications and assumptions you used. 


#3
Nov1012, 04:49 AM

P: 7

Hi, thanks for your reply!
I am calculating a fit. If I put all my data together I get an error that is higher than that of fitting different sets of points separately and then combining them with a weighted mean. I didn't do any simplification, just applied the expression seen in wikipedia. Brais 


#4
Nov1012, 09:28 AM

Sci Advisor
P: 3,319

Statistical uncertainty of weighted mean



#5
Nov1012, 06:49 PM

P: 4,579

Following Stephen Tashi's post, you should probably just clarify exactly what attribute you are using.



#6
Feb113, 09:32 AM

P: 7

Hi again!
A long time ago I had to stop this analysis and so my doubt wasn't importantr for some time :) I use the errors that my minimization algorithm "MINUIT" gives. Unfortunatelly I cannot find anything except that it (obviously) calculates a covariance matrix and error matrix... Thanks, Brais 


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