Via the Rietveld Users Mailing List at http://www.unige.ch/crystal/stxnews/riet/welcome.htm
|
From: "S. Nagesh Kini" [kini@mrc.iisc.ernet.in]
To: Rietveld Mailing List [rietveld_l@ill.fr]
Subject: Hamilton's test
Dear Rietvelders,
I would appreciate your help in the following problem,
Even with a stoichiometric mixture of starting materials, NdBa2Cu3Oy is
known to form a solid solution of the type Nd1+xBa2-xCu3Oy(Non
stoichiometric). So a small amount of BaCO3 and CuO are expected to be the
impurities.
I have taken two models
1.NdBa2Cu3O7 (Stoichiometric)
2.Nd(Ba1-xNdx)2Cu3O7 (Non-stoichiometric)
I have considered the following cases with XND.
Stoichiometric? Impurites included?
1. Yes No
2. No No
3. Yes Yes
4. No Yes
I have obtained different R factors. Now I want to decide which is the
most correct model. I have been suggested to use Hamilton R-factor
ratio test.
Could anybody give me the details of Hamilton R-factor ratio test?
Thanks
-Nagesh Kini
|
From: "Rory M Wilson (CDH) 13-7938" [R.M.Wilson@mds.qmw.ac.uk]
Organization: MDS QMW
To: rietveld_l@ill.fr
Date: Fri, 6 Apr 2001 15:39:15 BST
Subject: Re: Hamilton's test
Dear Nagesh
The R-factor is described in:
Volume 4 of International Tables for Crystallography section 4.2
pages 288 to 310.
if you have a look at Walter Hamilton's original paper:
Acta Crystallographica (1965), vol. 18, P502-510
you will see that it is based on the F-test which is covered in
most reasonable statistics text books.
Yours
Rory.
|
Date: Fri, 6 Apr 2001 10:37:40 -0700 (PDT) Subject: Re: Hamilton's test From: "Holger Kohlmann" [kohlmann@physics.unlv.edu] To: rietveld_l@ill.fr > I have obtained different R factors. Now I want to decide which is the > most correct model. I have been suggested to use Hamilton R-factor > ratio test. I would be careful with the Hamilton test in the case of powder diffraction, as your observations are not really independent from each other! -- Dr. Holger Kohlmann * High Pressure Science and Engineering Center * Department of Physics * University of Nevada, Las Vegas * 4505 South Maryland Parkway, Box 4002 * Las Vegas, Nevada 89154-4002, USA * phone [+1] (702)895 1716 * fax [+1](702)895 0804 * mailto:kohlmann@physics.unlv.edu |
Date: Fri, 06 Apr 2001 16:08:50 -0400
From: "Brian H. Toby" [Brian.Toby@nist.gov]
Organization: NIST Center for Neutron Research
To: rietveld_l@ill.fr
Subject: Re: Hamilton's test
> I would be careful with the Hamilton test in the case of powder
> diffraction, as your observations are not really independent from each
> other!
This is a common misconception. (If not common, at least it was my
misconception until I had several long conversations with Ted Prince.)
The Hamilton R-factor test is just a Student's t-Test. It tests if a
model is significantly improved by the addition of more adjustable
parameters compared to the more highly constrained model. One can use
ratios of Rwp for this. Personally, I find it easier to compute the
appropriate F distribution then to use the tables in Hamilton's paper.
The discussion on p128-9 in Ted's book (Mathematical Techniques in
Crystallography and Materials Science) is rather terse, but does derive
this.
The observations must be statistically independent, but need not be
independent in the sense of what they physically measure. If you measure
a full sphere of single crystal data, you will get the same R-factor
test result with that full data set as you would get by merging the data
to the unique subset, provided that the uncertainties are handled
correctly.
One additional note. Properly, the test cannot be used to compare
different models, rather it must be used where one model is a subset of
the other with respect to the varied parameters. If you fit data to "y =
mx + b", you can compare that to a fit of "y = mx", but you cannot
compare a fit of "y = mx + b" to a fit using "y = m cos(x)".
Brian
********************************************************************
Brian H. Toby, Ph.D. Leader, Crystallography Team
Brian.Toby@NIST.gov NIST Center for Neutron Research, Stop 8562
voice: 301-975-4297 National Institute of Standards & Technology
FAX: 301-921-9847 Gaithersburg, MD 20899-8562
http://www.ncnr.nist.gov/xtal
********************************************************************
|
|
|
Date: Mon, 09 Apr 2001 10:32:04 +0200 To: rietveld_l@ill.fr From: Jonathan WRIGHT [wright@esrf.fr] Subject: Re: Hamilton's test > The observations must be statistically independent, but need not be > independent in the sense of what they physically measure. It seems implicit from that sentence that the datapoints must be physically measuring some aspect of the model, is that the case? For example: Does a Hamilton test on two crystallographic models give the same results if you throw out the datapoints which only have background contributions? The "reducio ad absurdum" would be to use Rwp from a multipattern fit where only one pattern contains the phase of interest. Maybe that's statistically valid if some of the least squares parameters depend on all of the patterns? Bill David's work on deriving the number of independent peaks in a powder pattern seems to offer a route to significance testing for different crytallographic models (J.Appl.Cryst.(1999) 32:654). Perhaps it just adds to the confusion. Cheers, Jon Wright |
Date: Mon, 09 Apr 2001 08:11:07 -0600 To: rietveld_l@ill.fr From: vondreele@lanl.gov (Bob Von Dreele) Subject: Re: Hamilton's test >I would be careful with the Hamilton test in the case of powder >diffraction, as your observations are not really independent from each >other! Strictly speaking this is not true. The individual measurements of powder diffraction profile intensities are independent measurements. They do not depend on the order of their measurement, for example. The fact that a string of observations proceed over some feature of the diffraction profile (i.e. a Bragg peak) is not evidence of their "dependence". The only exception to this is profile measurements taken on a film or image plate where one observation may "bleed over" onto neighboring ones. Only in that case are the profile points correlated with each other in a statistical sense. Bob Von Dreele |
Date: Mon, 09 Apr 2001 17:08:34 +0200 From: Radovan Cerny [Radovan.Cerny@cryst.unige.ch] Subject: Re: Hamilton's test To: rietveld_l@ill.fr Organization: University of Geneva Bob Von Dreele wrote: >The only exception to this is profile measurements taken on a film or >image plate where one observation may "bleed over" onto neighboring >ones. Only in that case are the profile points correlated with each >other in a statistical sense. > > Bob Von Dreele In that case even the single crystal data resulting from the integration of images registred by an image plate are not strictly independent!!?? Information read from one pixel can depend on the information registred in a neigbouring pixel. -- Radovan Cerny Laboratoire de Cristallographie 24, quai Ernest-Ansermet CH-1211 Geneva 4, Switzerland Phone : [+[41] 22] 702 64 50, FAX : [+[41] 22] 702 61 08 mailto : Radovan.Cerny@cryst.unige.ch URL : http://www.unige.ch/crystal/cerny/rcerny.htm |
Date: Mon, 09 Apr 2001 09:24:58 -0600 To: rietveld_l@ill.fr From: vondreele@lanl.gov (Bob Von Dreele) Subject: Re: Hamilton's test Dear Radovan, At 05:08 PM 4/9/01 +0200, you wrote: >Bob Von Dreele wrote: > > >The only exception to this is profile measurements taken on a film > or >image plate where one observation may "bleed over" onto > neighboring >ones. Only in that case are the profile points correlated > with each >other in a statistical sense. > > > Bob Von Dreele > >In that case even the single crystal data resulting from the integration >of images registred by an image plate are not strictly independent!!?? >Information read from one pixel can depend on the information registred >in a neigbouring pixel. This would be true if the spots are close enough to each other so that they overlap (i.e. in protein patterns). Another case is that of 2-D area neutron detectors where one strong reflection can interfere with the measured intensities of other reflections seen in the same crystal setting because it can "blind" the whole detector. The main point is that one observation must somehow be correlated in the measuring process with other observations for them to not be statistically independent. The fact that the suite of observations are of the same object whether it be Bragg peaks in a powder pattern or some other experimentally observed feature does not make these observations "correlated". Bottom line is that Hamilton's test is just as valid for powder data as it is for single crystal data. Bob Von Dreele |
Date: Mon, 09 Apr 2001 18:10:01 +0200 From: Radovan Cerny [Radovan.Cerny@cryst.unige.ch] Subject: Re: Hamilton's test To: rietveld_l@ill.fr Organization: University of Geneva Bob Von Dreele wrote: > >In that case even the single crystal data resulting from the integration > >of images registred by an image plate are not strictly independent!!?? > >Information read from one pixel can depend on the information registred > >in a neigbouring pixel. > > This would be true if the spots are close enough to each other so that they > overlap (i.e. in protein patterns) No Bob, that was not my point. When you integrate one single crystal reflection, well separated from the others, what data do you use : information coded in individual pixels. Have they "bled over" into the neighboring pixels during the reading procedure? The pixels do not know whether it was powder or single crystal who sent the photons to them :-) I do not think that the powder data integrated from an image plate are more correlated than those measured with a point detector. Anybody who has developped the image plate software? Best regards -- Radovan Cerny Laboratoire de Cristallographie 24, quai Ernest-Ansermet CH-1211 Geneva 4, Switzerland Phone : [+[41] 22] 702 64 50, FAX : [+[41] 22] 702 61 08 mailto : Radovan.Cerny@cryst.unige.ch URL : http://www.unige.ch/crystal/cerny/rcerny.htm |
|
|
|
|
|
|
|
|
|
|
|
|
|
|