# [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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"Fatti non foste a viver come bruti,
ma per seguir virtute e canoscenza"
Dante Alighieri - Inferno - Canto XXVI

"Ihr seid bestimmt, nicht Tieren gleich zu leben,
Nein, Tugend zu erringen und Erkenntnis"
"Ye were not form'd to live the life of brutes,
But virtue to pursue and knowledge high"

```