[Ifeffit] statistical parameters

[Stefano Ciurli]

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
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