Hi
Shaofeng,
The parameter b does not have to do solely with the
difference in N_var between the two fits! As I say in the book,
“Changes in the theoretical standards used by the model can often be
accounted for as if they were changes in parameters. For example, if fit A
assumed that the nearest neighbors were oxygen and included coordination number,
bond length, and MSRD for those oxygen atoms as free parameters, while fit B
assumed the nearest neighbors were sulfur and used the same three parameters,
then a Hamilton test could be applied with the assumption that those three
parameters were “changed”—instead of applying to oxygen, they now apply to
sulfur. If E0 and S02 were also free parameters, they would not be considered to
be changed, as they are primarily a property of the absorber, not the
scatterer.”
In your case, it looks to me like two or three parameters are changed
between models (I count four free parameters in your table, one of which is E0,
so I’m not sure why you say there are only three…is there another constraint?)
Suppose there are two free parameters changed. b = 2/2 = 1.
x is the ratio of R-factors between the fits.
Using the values you list below, then, gives a result of 0.64, which
indicates such variation is quite likely to have taken place by chance.
You chose the worst case of your three, though; the pH 3 case. The pH 10
case shows the most improvement in the R-factor with x = 0.007/0.012 = 0.58. The
probability of getting that much improvement by chance drops to 0.30—less
likely, but still pretty close to a coin flip.
Even the fact that you got all three to show improvement doesn’t quite
reach the 95% confidence level, although it’s becoming suggestive.
Why, then, are fits that seem to have much lower R-factors not attaining
statistical significance? The main culprit is that you have a relatively small
number of independent points for studying this kind of system.
So where’s that leave you?
I’ll stand by the results of the Hamilton test…there’s not quite enough
data here, on its own, for me to decide in favor of your second model. If you
have other evidence pointing in that direction, these results could be used as
supporting evidence. But with the combination of the closeness of fit not
improving to a statistically significant degree and the sigma2 taking on
an unusual (but not impossible) value, there needs to be more to the argument,
in my opinion.
Best,
Scott Calvin
Lehman College of the City University of New York
Dear Scott,
I have learned the Hamilton test. However, this method seems
not suitable to distinguish our results because the Nvar are same
for the two fittings (3 when S02 was fixed). So the b value should be zero and
the calculator on the website http://www.danielsoper.com/statcalc/calculator.aspx?id=37
can not carry on.
In addition, I am not sure the value x. Is it the ratio of R-factors between two
fits? I calculated the results using a=2.18 (Nidp and variables (Nvar) were 7.35 and
3), b=0.00001, and x=0.818 (the ratio of two R-factors)
and got the Regularized lower incomplete beta function of 0.00000807. Does it
mean something?
Cheers,
Shaofeng
--------------------------------------
Shaofeng
Wang, Ph.D of Geochemistry
Environmental Molecular Science
Group
Institute of Applied Ecology, Chinese Academy of
Sciences
Shenyang, 110016, China
wangshaofeng@iae.ac.cnwww.iae.cas.cn
Sent: Thursday, January 05, 2017 11:50 AM
Subject: Fwd: about sigma2 for exafs fitting
Shaofeng
has given me permission to repost her question here on the ifeffit mailing
list. It is quoted below my response.
Dear Shaofeng,
As Bruce and I said before, a sigma2 of 0.0007 A^2 is not impossible,
although it indicates less disorder than is typically present. Your
attached table does seem to show some improvement by using the model from the
hydrogen-containing structure as compared to the arsenate. A more rigorous
test for statistical improvement can be conducted using the Hamilton test (you
mentioned you’ve consulted XAFS for Everyone; full details of the
Hamilton test are given there).
It’s also encouraging that the uncertainties on your sigma2
determinations using the hydrogen-containing model are quite small; it appears
that the fit is not getting confused by correlations even though it’s fitting
both coordination number and sigma2, as that would generally also cause high
uncertainties in the correlated parameters.
Is such a stiff sigma2 reasonable in this case? I have no idea. I
just don’t know enough about this particular system; perhaps someone else on
the list does. Oh, and one other question—was the data collected at room
temperature? If it were collected at cryogenic temperatures, that would tend
to reduce thermal disorder and thus lower sigma2’s.
Even if no one on the list has insight in to this particular system,
anyone have good published examples of room-temperature systems with sigma2’s
< 0.001? It might help Shaofeng with her referee…
Best,
Scott Calvin
Lehman College of the City University of New York
P. S. I certainly hope no reviewer is using the “typical values” I
provide for parameters in
XAFS for Everyone as rigid criteria for
rejecting results! It is most certainly not the way I use them in the book.
Some systems actually
are atypical!
Begin forwarded message:
Subject:
about
sigma2 for exafs fitting
Date:
January
4, 2017 at 8:31:33 PM CST
Dear Dr. Calvin,
I am a research from China. I know you are an expert on
XAFS analysis. So I write this letter to you for some xafs analysisi
problem.
Recently, I am attempting to study the incorporation of
arsenate into the barite structure. To investigate the species of arsenate
in barite, I fitted the exafs data using Ba3(AsO4)2 and a dft optimized
structure with HAsO4 incorporated in barite
supercell (configuration C2), respectively and got some results. Please see
the attached table. Smaller reduced chi2 and R-factor were obtained by using
configuration C2 as the initial model. Does this mean the species of
arsenate in barite is more likely to be
HAsO42- instead of
AsO43- ?
We also have other evidences including XANES and vibrational spectroscopy to
support this conclusion. However, using C2 as the initial model we obtained
samll sigma2 (~0.0007). This seems too small and out of the normal range
(0.002 每 0.03) as you mentioned in your publications (XAFS for everyone).
So, my question is if our data are reasonable. If yes, could you provid some
references to support?
By the way, I asked simialr question on the ifeffit forum
and you gave me some answer. However, the reviewer was not convinced and he
insited on that sigma2 must be in the range of 0.002-0.03. How can I
response this question?
Any help is very appreciated.
Best regards,
Shaofeng
--------------------------------------
Shaofeng
Wang, Ph.D of Geochemistry
Environmental Molecular Science
Group
Institute of Applied Ecology, Chinese Academy of
Sciences
Shenyang, 110016, China
wangshaofeng@iae.ac.cnwww.iae.cas.cn