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 http://www.aps.anl.gov/xfd/people/haskel/dani.html and Bevington, P. R.; Robinson, D. K. Data Reduction and Error Analysis for the Physical Sciences; 2 ed.; McGraw-Hill: New York, 1992. HTH Shelly

-----Original Message----- From: ifeffit-bounces@millenia.cars.aps.anl.gov [mailto:ifeffit- bounces@millenia.cars.aps.anl.gov] On Behalf Of Aaron Slowey Sent: Thursday, January 18, 2007 4:50 PM To: ifeffit@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 105(27)

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 _______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit