# [Ifeffit] about sigma2 for exafs fitting

Scott Calvin scalvin at sarahlawrence.edu
Thu Jan 5 13:34:06 CST 2017

```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

On Jan 5, 2017, at 12:19 AM, Shaofeng Wang <wangshaofeng at iae.ac.cn<mailto:wangshaofeng at iae.ac.cn>> wrote:

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 at iae.ac.cn<mailto:wangshaofeng at iae.ac.cn>
www.iae.cas.cn

From: Scott Calvin<mailto:scalvin at sarahlawrence.edu>
Sent: Thursday, January 05, 2017 11:50 AM
To: XAFS Analysis using Ifeffit<mailto:ifeffit at millenia.cars.aps.anl.gov>
Cc: Shaofeng Wang<mailto:wangshaofeng at iae.ac.cn>
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:

From: Shaofeng Wang <wangshaofeng at iae.ac.cn<mailto:wangshaofeng at iae.ac.cn>>
Subject: about sigma2 for exafs fitting
Date: January 4, 2017 at 8:31:33 PM CST
To: <scalvin at sarahlawrence.edu<mailto:scalvin at sarahlawrence.edu>>
Reply-To: Shaofeng Wang <wangshaofeng at iae.ac.cn<mailto:wangshaofeng at iae.ac.cn>>

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 at iae.ac.cn<mailto:wangshaofeng at iae.ac.cn>
www.iae.cas.cn<http://www.iae.cas.cn/>

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