Hi Zbyszek, thanks for your reply!
The scalepack log file gives the formula:
Chi**2 = SUM ( (I - <I>) ** 2) / (Error ** 2 * N / (N-1) ) )
which equivalent to the Jay Ponder's formula, with the important
addition, that sigma_avg and Iavg represent the average of all
_other_ measurements with the same reduced hkl index.
All sigmas are calculated from the error model described in the
publications.
So sigma_avg and I_avg in Ponder's formula are values that exclude
the I_meas(hkl). That makes sense since we want the distributions of
I_avg and I_meas to be independent.
I'm still confused about how the "Error" value is calculated.
What we want is the sigma that corresponds to the distribution of
I_avg - I_meas values. As Ponder says this is sigma_avg^2 +
sigma_meas^2. So I assume that sigma_avg is simply the calculated
sigma of ALL the measured I's with the same reduced hkl index (no
error model used for this term). The error model comes in with the
sigma_meas term. That is calculated by scaling the measured sigma's
from the integration with a factor derived from the error model.
The error model as given in the International Tables F Eqs.
(11.4.8.5-7) is
W = 1/[(sig*E1)^2+( <I_corr>*E2)^2] (5)
<I_corr> = SUM (I_corr*W)/ SUM W (6)
sig(I) = I/sqrt[SUM W] (7)
So, to get sigma_meas above, presumably would use (7) for some I
value (which one?).
How does one compute the values of I_corr and W ?
-----
Thanks
Richard Gillilan
MacCHESS
Some of the error model parameters are defined at the moment by
user, they can be refined iteratively by experimenter by adjusting
parameters in subsequent runs of scalepack, but most of the time it
is not required. New version will adjust all these parameters
automatically.
Zbyszek Otwinowski
Richard Gillilan wrote:
chi-2 = 1/N sum (I_avg - I_meas)^2/(sigma_avg^2 + sigma_meas^2)
