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,  15:40, 18 February 2008
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where $\langle I_{hkl}\rangle$ is the average of symmetry- (or Friedel-) related observations of a unique reflection.

where $\langle I_{hkl}\rangle$ is the average of symmetry- (or Friedel-) related observations of a unique reflection.
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It can be shown that this formula results in higher R-factors when the redundancy is higher <ref name="DiKa97">K. Diederichs and P.A. Karplus (1997). Improved R-factors for diffraction data analysis in macromolecular crystallography. Nature Struct. Biol. 4, 269-275 [http://strucbio.biologie.uni-konstanz.de/strucbio/files/nsb-1997.pdf]</ref>. In other words, low-redundancy datasets appear better than high-redundancy ones, which obviously violates the intention of having an indicator of data quality!
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It can be shown that this formula results in higher R-factors when the redundancy is higher (Diederichs and Karplus <ref name="DiKa97">K. Diederichs and P.A. Karplus (1997). Improved R-factors for diffraction data analysis in macromolecular crystallography. Nature Struct. Biol. 4, 269-275 [http://strucbio.biologie.uni-konstanz.de/strucbio/files/nsb-1997.pdf]</ref>). In other words, low-redundancy datasets appear better than high-redundancy ones, which obviously violates the intention of having an indicator of data quality!

* Redundancy-independant version of the above:

* Redundancy-independant version of the above:

$[itex] R_{meas} = \frac{\sum_{hkl} \sqrt \frac{n}{n-1} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}} R_{meas} = \frac{\sum_{hkl} \sqrt \frac{n}{n-1} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}$

[/itex]
which unfortunately results in higher (but more realistic) numerical values than R<sub>sym</sub> / R<sub>merge</sub> <ref name="DiKa97"/> (M.S. Weiss and R. Hilgenfeld (1997) On the use of the merging R-factor as a quality indicator for X-ray data. J. Appl. Crystallogr. 30, 203-205[http://dx.doi.org/10.1107/S0021889897003907]).
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which unfortunately results in higher (but more realistic) numerical values than R<sub>sym</sub> / R<sub>merge</sub>
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(Diederichs and Karplus <ref name="DiKa97"/> ,
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Weiss and Hilgenfeld <ref name="WeHi97">M.S. Weiss and R. Hilgenfeld (1997) On the use of the merging R-factor as a quality indicator for X-ray data. J. Appl. Crystallogr. 30, 203-205[http://dx.doi.org/10.1107/S0021889897003907]</ref>).

* measuring quality of averaged intensities/amplitudes:

* measuring quality of averaged intensities/amplitudes:
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for intensities use (M.S. Weiss. Global indicators of X-ray data quality. J. Appl. Cryst. (2001). 34, 130-135 [http://dx.doi.org/10.1107/S0021889800018227])
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for intensities use
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(Weiss <ref name="We01">M.S. Weiss. Global indicators of X-ray data quality. J. Appl. Cryst. (2001). 34, 130-135 [http://dx.doi.org/10.1107/S0021889800018227]</ref>)

$[itex] R_{p.i.m.} = \frac{\sum_{hkl} \sqrt \frac{1}{n} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}} R_{p.i.m.} = \frac{\sum_{hkl} \sqrt \frac{1}{n} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}$

[/itex]
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<math>R_{mrgd-I}</math> is similarly defined in Diederichs and Karplus <ref name="DiKa97"/>.
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R<sub>mrgd-I</sub> is similarly defined in Diederichs and Karplus <ref name="DiKa97"/>.

Similarly, one should use R<sub>mrgd-F</sub> as a quality indicator for amplitudes <ref name="DiKa97"/>, which may be calculated as:

Similarly, one should use R<sub>mrgd-F</sub> as a quality indicator for amplitudes <ref name="DiKa97"/>, which may be calculated as:
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