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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.
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It can be shown that this formula results in higher R-factors when the redundancy is higher (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]). 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 <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:  
 
  <math>
 
  <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}}
 
  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>
 
  </math>
which unfortunately results in higher (but more realistic) numerical values than R<sub>sym</sub> / R<sub>merge</sub> (Diederichs and Karplus (1997)[http://strucbio.biologie.uni-konstanz.de/strucbio/files/nsb-1997.pdf], and 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> <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]).
    
* measuring quality of averaged intensities/amplitudes:
 
* measuring quality of averaged intensities/amplitudes:
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  </math>
 
  </math>
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<math>R_{mrgd-I}</math> is similarly defined in Diederichs and Karplus (1997).
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<math>R_{mrgd-I}</math> 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 (Diederichs and Karplus (1997) [http://strucbio.biologie.uni-konstanz.de/strucbio/files/nsb-1997.pdf]), which may be calculated as:  
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Similarly, one should use R<sub>mrgd-F</sub> as a quality indicator for amplitudes <ref name="DiKa97"/>, which may be calculated as:  
 
  <math>
 
  <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}}
 
  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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- R/R<sub>free</sub> and NCS: reflections in work and test set are not independant
 
- R/R<sub>free</sub> and NCS: reflections in work and test set are not independant
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==Notes==
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<references/>
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