[Sane-analysis] Statistical errors of the asymmetries

[O. A. Rondon]

Hi,

There have been some questions about calculating the statistical
uncertainties for our combined run data for each kinematic bin. The
procedure is given below

For raw counts N+, N- for each run, for each bin in W, the asymmetry will be
Ai(W) = (N+(W) - N-(W))/sum(N+,N-)
and the error
dAi(W) = 2*sqrt(N+(W) N-(W))/(N+ + N-)^(3/2)

For charge normalized, live time corrected counts N+/(LT+ Q+), etc., the
error is a little more complicated. I have posted the results on the
wiki (click on "Error calculation")

https://hallcweb.jlab.org/experiments/sane/wiki/index.php/Main_Page#Analysis

Keep in mind that the charge and live time are x or W independent, but
not run independent.

Then, one needs to combine runs for each W bin by calculating the sum

A(W) = Sum(i=1, number of runs) Ai(W)/dAi(W)^2/dA(W)

and the error

dA(W) = Sum(i=1, number of runs) [1/dAi(W)^2]

One cannot just add counts for all runs for each W, with charge
normalization and live time correction, because the charge and live time
are run dependent and the error for all runs cannot be calculated
correctly that way.

There is no need to keep track of the corrections run by run since all
the information is condensed in the corrected asymmetry and its error.

Cheers,

Oscar