> 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
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Brian H. Toby, Ph.D. Leader, Crystallography Team
[EMAIL PROTECTED] 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
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