[Ifeffit] statistical vicissitudes

[Aaron Slowey]

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