From: H. Olin Spivey <ospivey@bmb-fs1.biochem.okstate.edu>
  To  : Chandra Boon , rasmb@alpha.bbri.org
  Date: Thu, 26 Apr 2001 17:21:35 -0500

Re: Weighted vs nonweighted fits

   Chandra, Weighted fits are better in principle.  The best-fit parameters
are rigorously the most probable parameters when the squared residuals of
the fitting function y are weighted by the inverse square of the standard
deviations in y(i) where i is the i-th data point.  Often there won't be a
noticeable differences between weighted and "non-weighted" (assuming the
same standard deviations for all points) fits, but this should not be
trusted.  The Beckman program uses standard deviations in y(i) based on the
"Replicates" you specify in the Equilibrium Detail panel.  A global fit to
these standard deviations as a function of absorbance A is generally linear
(y = a + b*A) with a = ca. 0.003 and b = ca. 0.005 using 280 nm light and
absorbances limited to about 1.0.  This is common to many XL-A instruments.
Thus you can see that the weighting of the points varies over a scale of
1/9 to 1/64 under these conditions - an appreciable variation.  I advise
collecting 16 replicates per point to give reliable estimates of std. dev's
in y, if you use the Beckman Software.

   I don't have interference optics, so I don't know what the variation in
fringe displacements is for this mode, but I think this variation is
negligible in most experiments with these optics.

   Olin
________________________________________________________


At 2:50 PM -0400 4/26/01, Chandra Boon wrote:
>Hello.  I am using the Beckman software (Origin) to analyse some
>sedimentation equilibrium data.  I obtained fairly different results (for
>Ka and the variance) when using the weighted vs the nonweighted fit for
>the same model.  What is the difference between the two fits and which
>one is more reliable?  Thanks.
>
>Chandra Boon
>Dept. of Medical Biophysics
>University of Toronto


H. Olin Spivey                       Phone: (405) 744-6192
Dept. Biochem. & Molec. Biology      Fax:   (405) 744-7799
246 NRC                              Email: OSpivey@Biochem.Okstate.Edu
Oklahoma State University
Stillwater, OK 74078-3035