[Ifeffit] statistical parameters
Stefano Ciurli
stefano.ciurli at unibo.it
Wed Dec 14 15:05:17 CST 2005
Hi Shelly,
>Since 2dkdr/pi is not always an integer number, the degrees of freedom
>which is the NIP (number of independent points) - number of variables is
>not always an integer number.
but I notice that in all papers this is reported as an integer
number, which makes sense. DOes it mean I have to round it up to the
closest integer? Plus, in the conversion from chi^2 to reduced-chi^2,
does IFEFFIT consider it as an integer number or not?
> > Plus, I have found a
>> few documents in which Matt reports Nidp as 2dkdr/pi, some others in
>> which he reports 2dkdr/pi+1. In SK's thesis, which is available on
>> the net (thanks Shelly :-)) she says +2. I was simply wondering which
>> is the right formula used in IFEFFIT, and if it is different from
>> what reported in Stern, Phys. Rev. B, 1993, 48, 9825-9827, why it is
>> so.
>
>Most importantly, all of these expressions for the number of independent
>points are similar.
I know, but since I am reporting in a paper we are writing a table in
which we show chi^2, reduced chi^2, Nidp and Npar (and therefore the
degress of freedom) I was trying to be tidy and rigorous. But I am
facing numbers which I cannot make much sense of.
>The most important part is that the number of
>independent points goes like 2dkdr/pi. When fitting EXAFS data you
>really need to have a lot more independent points than the number of
>fitted variables. In that case the +0, +1, or +2 doesn't really matter
>as long as you are consistent.
of course, but see above.
>The +1 and +2 come from the information at the beginning of the data
>set. I think of the raw chi(k) data as being chopped up into pieces
>with the length of each piece about dk ~ pi/dr. For every multiple of
>this length you get two data points representing an amplitude and phase,
>hence the 2dkdr/pi part. If this length is -- then a data set like this
>.--.--.--.--.- Has 4.5 independent points, plus the one at the
>beginning hence +1 (count the "."). Now often Fourier transforms are
>done from r=0 to some other bigger r value. At the special value of r=0
>you only need one variable, the amplitude, since the phase is known,
>hence 2dkdr/pi + 1. For EXAFS analysis we never start at r=0 so we get
>two parameters for each length, hence 2drdk/pi + 2.
OK. This is the sense of the paper by Stern, which now I understand
better, thanks!
Stefano
--
____________________________________________
Stefano Ciurli
Professor of Chemistry
Laboratory of Bioinorganic Chemistry
Department of Agro-Environmental Science and Technology
University of Bologna
Viale Giuseppe Fanin, 40
I-40127 Bologna
Italy
Phone: +39-051-209-6204
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