R-factors: Difference between revisions
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where <math>\langle I_{hkl}\rangle</math> is the average of symmetry- (or Friedel-) related observations of a unique reflection, and the summation is over all | 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<sub>meas</sub> | * Redundancy-independant version of the above: R<sub>meas</sub> | ||
* measuring quality of averaged intensities/amplitudes: R<sub>p.i.m.</sub> and R<sub>mrgd-F</sub> | * measuring quality of averaged intensities/amplitudes: R<sub>p.i.m.</sub> and R<sub>mrgd-F</sub> | ||
Revision as of 16:11, 14 February 2008
Historically, R-factors were introduced by ...
Definitions
Data quality indicators
- Rsym and Rmerge : the formula for both is
[math]\displaystyle{
R = \frac{\sum_{hkl} \sum_{j} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}
}[/math]
where [math]\displaystyle{ \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: Rmeas
- measuring quality of averaged intensities/amplitudes: Rp.i.m. and Rmrgd-F
Model quality indicators
- R and Rfree : the formula for both is
[math]\displaystyle{
R=\frac{\sum_{hkl_{unique}}\vert F_{hkl}^{(obs)}-F_{hkl}^{(calc)}\vert}{\sum_{hkl_{unique}} F_{hkl}^{(obs)}}
}[/math]
where [math]\displaystyle{ F_{hkl}^{(obs)} }[/math] and [math]\displaystyle{ F_{hkl}^{(calc)} }[/math] have to be scaled w.r.t. each other. R and Rfree differ in the set of reflections they are calculated from: R is calculated for the working set, whereas Rfree is calculated for the test set.
what do R-factors try to measure, and how to interpret their values?
- relative deviation of
Data quality
- typical values: ...
Model quality
what kinds of problems exist with these indicators?
- (Rsym / Rmerge ) should not be used, Rmeas should be used instead (explain why ?)
- R/Rfree and NCS: reflections in work and test set are not independant