# Changes

,  11:42, 15 February 2008
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Historically, R-factors were introduced by ...
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Historically, R-factors were introduced by ... ???

== Definitions ==

== Definitions ==

=== Data quality indicators ===

=== Data quality indicators ===
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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

$[itex] Line 9: Line 10: <br> <br> <br> <br> where [itex]\langle I_{hkl}\rangle$ 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.
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where $\langle I_{hkl}\rangle$ is the average of symmetry- (or Friedel-) related observations of a unique reflection
* Redundancy-independant version of the above: R<sub>meas</sub>
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* Redundancy-independant version of the above:
* measuring quality of averaged intensities/amplitudes: R<sub>p.i.m.</sub> and R<sub>mrgd-F</sub>
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<math>
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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}}
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</math>
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<br>
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<br>
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* measuring quality of averaged intensities/amplitudes:
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for intensities use
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<math>
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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}}
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</math>
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<br>
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<br>
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and similarly for amplitudes:
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<math>
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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}}
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</math>
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<br>
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<br>
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=== 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

$[itex] R=\frac{\sum_{hkl_{unique}}\vert F_{hkl}^{(obs)}-F_{hkl}^{(calc)}\vert}{\sum_{hkl_{unique}} F_{hkl}^{(obs)}} + R=\frac{\sum_{hkl}\vert F_{hkl}^{obs}-F_{hkl}^{calc}\vert}{\sum_{hkl} F_{hkl}^{obs}}$

[/itex]

<br>

<br>

<br>

<br>
where $F_{hkl}^{(obs)}$ and $F_{hkl}^{(calc)}$ 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]].
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where $F_{hkl}^{obs}$ and $F_{hkl}^{calc}$ 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
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