[Ifeffit] R-factor uncertainty

Kelly, Shelly D. SKelly at anl.gov
Mon Jan 8 13:43:40 CST 2007

Hi Lisa,

In general the R-factor is good if it is less than a few percent.  The
value reported is 0.01 or 1% then the fit is satisfactory.  Just as a
note the R-factor is calculated over the entire data range given by rmin
and rmax of the fit, so make sure that they are reasonable values.  

To compare two different models, use the reduced-chi-square (RCS) value.
One standard deviation in the RCS value is SQRT(2/nu), where SQRT is
square-root and nu is the number of independent points.  If the first
model has RCS1 and nu1 and the second model has RCS2 and nu2 then the
second model is better than the first model if  their difference
(RCS1-RCS2) is greater than 2*SQRT((2*RCS1*RCS1)/nu1 +
(2*RCS2*RCS2)/nu2)) which is twice the fluctuation of the difference.

The number of independent points is equal to the number of data points
minus the number of variables in the model.

I do this kind of comparison in this paper:  S.D. Kelly, K.M. Kemner,
G.E. Fryxell, J. Liu, S.V. Mattigod, K.F. Ferris, "X-ray Absorption
Fine-Structure Spectroscopy Study of the Interactions Between
Contaminant Tetrahedral Anions and Self-Assembled Monolayers on
Mesoporous Supports," The Journal of Physical Chemistry B 105 (27)
6337-6346, Aug 2001.
The paper can be found here:  http://www.mesg.anl.gov/sdkpublist.html. 


Shelly Kelly
Argonne National Laboratory
Bldg 203, RM E113
9700 S. Cass Ave
Argonne, IL 60439

Molecular Environmental Science Group
skelly at anl.gov
phone: 630-252-7376

> -----Original Message-----
> From: ifeffit-bounces at millenia.cars.aps.anl.gov [mailto:ifeffit-
> bounces at millenia.cars.aps.anl.gov] On Behalf Of Lisa Giachini
> Sent: Friday, January 05, 2007 6:23 AM
> To: XAFS Analysis using Ifeffit; FEFF Users
> Cc: XAFS Analysis using Ifeffit
> Subject: [Ifeffit] R-factor uncertainty
> Dear all,
> I have a question about the R factor: how can I decide if the
> between the R factors of 2 fits is statistically significant, i.e, how
> I calculate the uncertainty which has to be associated to the R
> B.R.,
> Lisa
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> Ifeffit at millenia.cars.aps.anl.gov
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