# [Ifeffit] statistical parameters

Kelly, Shelly D. SKelly at anl.gov
Wed Dec 14 15:45:37 CST 2005

```Hi Stephano

> >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?

[Kelly, Shelly D.] Well, In my opinion that depends on where you are
publishing the data.  If you are publishing the data in PRB then you
should use the XX.X number.  If you are publishing in Science Magazine
then you should use the rounded number.  If the answer depends on
weather or not you round the number then I'd be suspicious.  Often we
round the number so that we don't have to explain why we have a
non-integer numbers.

You need ~ a factor of 2 for there to be a statistically significant
difference in the reduced chi squared.  So 33.5, 30, and 40 are all
about the same number.  Therefore I would round them all off to the
nearest whole number that works.   I like to show changes in the reduced
chi square rather than the absolute value.  Instead of showing a
reduced-chi-square of 100 and 350, I show them as 1 and 3.5. Then you
can say that 3.5 is much bigger than 1 so the model that gave 1 is the
best.  It is the relative change in the reduced chi square that matters.
We get the absolute value wrong for a number of reasons. By showing the
change you can side step all that explanation.

> >  > 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.

[Kelly, Shelly D.]
[Kelly, Shelly D.] That seems to be a problem.  Are you processing the
data with more than one k-weight in IFEFFIT?  Try a test case were you
use only one k-weight and see if you like the answers better.  If you
use more than one k-weight then the answers should be averages for all
three data sets.

>
> >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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>
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>
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