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R-factors: Difference between revisions
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Historically, R-factors were introduced by ... | Historically, R-factors were introduced by ... ??? | ||
== Definitions == | == Definitions == | ||
=== Data quality indicators === | === 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 | * R<sub>sym</sub> and R<sub>merge</sub> : the formula for both is | ||
<math> | <math> | ||
| Line 9: | Line 10: | ||
<br> | <br> | ||
<br> | <br> | ||
where <math>\langle I_{hkl}\rangle</math> is the average of symmetry- (or Friedel-) related observations of a unique reflection | where <math>\langle I_{hkl}\rangle</math> is the average of symmetry- (or Friedel-) related observations of a unique reflection | ||
* Redundancy-independant version of the above: | * Redundancy-independant version of the above: | ||
* measuring quality of averaged intensities/amplitudes: | <math> | ||
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}} | |||
</math> | |||
<br> | |||
<br> | |||
* measuring quality of averaged intensities/amplitudes: | |||
for intensities use | |||
<math> | |||
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}} | |||
</math> | |||
<br> | |||
<br> | |||
and similarly for amplitudes: | |||
<math> | |||
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}} | |||
</math> | |||
<br> | |||
<br> | |||
=== Model quality indicators === | === Model quality indicators === | ||
* R and R<sub>free</sub> : the formula for both is | * R and R<sub>free</sub> : the formula for both is | ||
<math> | <math> | ||
R=\frac{\sum_{ | R=\frac{\sum_{hkl}\vert F_{hkl}^{obs}-F_{hkl}^{calc}\vert}{\sum_{hkl} F_{hkl}^{obs}} | ||
</math> | </math> | ||
<br> | <br> | ||
<br> | <br> | ||
where <math>F_{hkl}^{ | 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? == | == what do R-factors try to measure, and how to interpret their values? == | ||
* relative deviation of | * relative deviation of | ||