[Ifeffit] statistical vicissitudes

Kelly, Shelly D. SKelly at anl.gov
Fri Jan 19 10:21:07 CST 2007

Hi Aaron,

In EXAFS the expected deviation in RCS(reduced chi square) is sqrt(2/nu)

So one fit is better than another fit if their difference is greater
than twice the fluctuation in the RCS values

(RCS1-RCS2)/RCS2 > 2 sqrt(2/nu)

We divide by RCS2 because our RCS-values are poorly scaled.
{in your link to the nist pages F = RCS1/RCS2 -1 and the statistically
significant variation in F is 2 * sqrt(2/nu)} 

If there are different values for nu in the two models then

(RCS1-RCS2) > 2sqrt(RCS2^2/nu2 + RCS1^2/nu1)

I think that the best explanation of these tests are given in Dani
Haskel's thesis pg 39 - 41
and Bevington, P. R.; Robinson, D. K. Data Reduction and Error Analysis
for the Physical Sciences; 2 ed.; McGraw-Hill: New York, 1992.


> -----Original Message-----
> From: ifeffit-bounces at millenia.cars.aps.anl.gov [mailto:ifeffit-
> bounces at millenia.cars.aps.anl.gov] On Behalf Of Aaron Slowey
> Sent: Thursday, January 18, 2007 4:50 PM
> To: ifeffit at millenia.cars.aps.anl.gov
> Subject: [Ifeffit] statistical vicissitudes
> Hello -
> The use of R-factors and reduced-chi-squared values, it's computations
> by IFEFFIT have been made clear by past writings, but the use of
> reduced-chi-squared as a comparative statistic has not, to my
> knowledge, been completely well-documented.
> Not withstanding the three disconnects between classical statistics
> and the realities of EXAFS mentioned in the IFEFFIT faq section
> http://cars9.uchicago.edu/iffwiki/FAQ/FeffitModeling#head-
> ed63cbd00d0b85def31ada3a695873243d08a76a
> can
> Is the criterion provided by Kelly et al. (2001) J. Phys. Chem. B
> http://www.mesg.anl.gov/pdf/JPC2001samms.pdf
> namely, redchi-sq_1 / redchi-sq_2) - 1 > 2 * (2 / deg_of_freedom)^0.5,
> derived from the F-test formalism and, if so, how?
> I tried to derive the above equation based on the F-test formalism
> provided by NIST:
> http://www.itl.nist.gov/div898/handbook/prc/section3/prc32.htm
> but was unsuccessfull. The Kemner et al. paper referenced by Kelly et
> al. to explain the statistical basis for the above equation does not
> clearly do so.
> I request that someone please provide a reference to a *first
> principles* basis for criteria to compare reduced-chi-square values of
> alternate EXAFS fits.
> Aaron
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