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On Tuesday 07 November 2006 11:40 am, Ulrich Genick wrote:
>
> a quick question for the data processing jocks.
>> How much do systematic and random errors contribute to the
> final sigmaF of a structure factor.

> Here is the scenario, I take a crystal and collect the same data set
> twice. Both data sets have a decent redundancy of 3-5 and there is
> no noticeable radiation-induced decay.
> Will the sigmaFs of the two data sets overestimate the difference
> between the two  data sets (i.e. is there systematic error that
> is reproduced between the data sets)
> or will the sigmaF predict the difference between the two data sets
> correctly (i.e. the error is random).

I'm winging this, so any experimental data to the contrary should
be taken in preference to my hand-waving :-)

As you say, there are both systematic and random sources of error.
If the major contribution to the uncertainty of each individual
replicate measurement in each data set is random, then the textbook
equation for combining two estimates of variance should yield the
expected variance between your two data sets.

However, if there is a major source of systematic error then it's
a different story.  Suppose for example that you mis-estimate the
polarization of the X-ray beam.  Then symmetry-equivalent reflections
within a single data set will have strong systematic differences
depending on where they fall on the detector.  This will increase
the internal estimated error for the data set, because the
supposedly equivalent reflections are systematically not equivalent.
But if you repeat the whole experiment - same crystal, same geometry,
same beam characteristics, same mis-estimate of polarization - 
then your two data sets should agree with each other quite well.
Thus in the presence of internal systematic error, the internal
sigmaFs of the individual data sets will overestimate the
differences between the data sets.

The experimentalist may argue that modern scaling procedures should
be good enough to correct for this particular error because it is
a well-defined function of position on the detector. But the general
argument still holds so long as there is a reproducible systematic
error. 


> Basically, I want to do some computation that involves the Fs from
> two consecutive data sets taken
> on the same crystal and in order to do
> error propagation I need to know, if the sigmaF's for the same
> reflection in the final merged data sets
> are independent or correlated. My gut feeling is that the errors will
> be mostly independent.
>
> I am positive somebody, (or probably a lot of people) know the answer
> to this question and it is
> probably written up somewhere in some old paper on scaling heavy
> metal derivatives.
>
>
> I am sure the answer will depend on the redundancy of the data sets,
> the quality of the crystals, the
> resolution  the stability of the beam etc. etc. My question is what
> will happen on average.
>
>
> Cheers,
>
> Ulrich

-- 
Ethan A Merritt
Biomolecular Structure Center
University of Washington, Seattle WA

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