The scalepack log file gives the formula:
Summary of reflections intensities and R-factors by intensity bins
R linear = SUM ( ABS(I - <I>)) / SUM (I)
R square = SUM ( (I - <I>) ** 2) / SUM (I ** 2)
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.
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:
Thanks Joe and others.
Bits and pieces of this story appear in 11.4.8 of International Tables
volume F, Borek et. al. Acta Cryst D59 (2003) and the Scalepack manual,
but none are complete or have enough detail to follow easily. None of
them give the expression for Chi-square for this problem.
I found a presentation by Jay Ponder online (for his Bio5325 course)
that gives:
chi-2 = 1/N sum (I_avg - I_meas)^2/(sigma_avg^2 + sigma_meas^2)
where the sum probably runs over all reflections and the I_avg is the
average of the appropriate group of symmetry-related reflections.
Sigma_avg^2 should be the sigma computed from the error model below (not
given in the presentation) I think and sigma_meas is the sigma^2 from
the actual symmetry-related reflections.
One would then adjust the error parameters below to give chi-square
approx unity and this leads to the proper scaling factors for
intensities and sigmas.
One confusing hitch seems to be that (according to the International
Tables F Eqs.(11.4.8.5) and (11.4.8.6)), the error model is also
implicitly defined and must be solved iteratively ... though it's hard
to see that from the text.
Does this sound right?
Richard
--
Zbyszek Otwinowski
UT Southwestern Medical Center
5323 Harry Hines Blvd., Dallas, TX 75390-8816
(214) 645 6385 (phone) (214) 645 6353 (fax)
zbys...@work.swmed.edu
