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R-factors

889 bytes added, 18:25, 17 February 2008
m
Data quality indicators
R = \frac{\sum_{hkl} \sum_{j} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}
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where <math>\langle I_{hkl}\rangle</math> is the average of symmetry- (or Friedel-) related observations of a unique reflection.
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!
* Redundancy-independant version of the above:
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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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<br>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]). 
* measuring quality of averaged intensities/amplitudes:
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])
<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}}
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<math>R_{mrgd-I}</math> is similarly defined in Diederichs and similarly Karplus (1997). 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:
<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>
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with <math>\langle F_{hkl}\rangle</math> defined analogously as <math>\langle I_{hkl}\rangle</math>.
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