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R-factors

492 bytes added, 11:42, 15 February 2008
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Historically, R-factors were introduced by ... ???
== Definitions ==
=== Data quality indicators ===
In the following, all sums over hkl extend only over unique reflections with more than one observation!
* R<sub>sym</sub> and R<sub>merge</sub> : the formula for both is
<math>
<br>
<br>
where <math>\langle I_{hkl}\rangle</math> is the average of symmetry- (or Friedel-) related observations of a unique reflection, and the first summation is over all unique reflections with more than one observation.* Redundancy-independant version of the above: R<submath>R_{meas} = \frac{\sum_{hkl} \sqrt \frac{n}{n-1} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}</submath><br><br>* measuring quality of averaged intensities/amplitudes: R for intensities use <submath>R_{p.i.m.} (or R_{mrgd-I}) = \frac{\sum_{hkl} \sqrt \frac{1}{n} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}</submath> <br><br> and Rsimilarly for amplitudes: <submath>R_{mrgd-F} = \frac{\sum_{hkl} \sqrt \frac{1}{n} \sum_{j=1}^{n} \vert F_{hkl,j}-\langle F_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}F_{hkl,j}}</submath><br><br> 
=== Model quality indicators ===
* R and R<sub>free</sub> : the formula for both is
<math>
R=\frac{\sum_{hkl_{unique}hkl}\vert F_{hkl}^{(obs)}-F_{hkl}^{(calc)}\vert}{\sum_{hkl_{unique}hkl} F_{hkl}^{(obs)}}
</math>
<br>
<br>
where <math>F_{hkl}^{(obs)}</math> and <math>F_{hkl}^{(calc)}</math> have to be scaled w.r.t. each other. R and R<sub>free</sub> differ in the set of reflections they are calculated from: R is calculated for the [[working set]], whereas R<sub>free</sub> is calculated for the [[test set]].
== what do R-factors try to measure, and how to interpret their values? ==
* relative deviation of
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