[Halld-physics] Pull Definition

[Curtis A. Meyer]

Hi Everyone -

   The definition of a "pull" that was quoted in Will's talk raised some 
questions by
people in the audience. I have dug up some references on this and report 
them here.
The first is a hard-to-find collection, so I have scanned the relevant 
article and placed
it on the portal as document number 1775

     
http://argus.phys.uregina.ca/cgi-bin/private/DocDB/ShowDocument?docid=1775

Please see page 27 in this article which gives this pull at the end of a 
long derivation. I
also a reference on page 290 of "Probability and Statistics in Particle 
Physics" by Frodesen
et. al.

    The basic idea is that the pull is defined as the change in the 
measured quantity divided
by the error in the change. The error-squared in the change is the 
corresponding element of
the covariance matrix (Vii) for the measured (m) minus the fit (f) 
quantity. This covariance element
is
           Vii(m-f) = Vii(m) - 2*cov(f,m)ii + Vii(f)

The next step notes that f and m are 100% positively correlated, so 
cov(f,m)ii = Vii(f),
so we get

           Vii(m-f) = Vii(m) - Vii(f)

which leads to the formula that Will presented for the pull.

   Curtis



-- 
Prof. Curtis A. Meyer		Department of Physics
Phone:	(412) 268-2745		Carnegie Mellon University
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