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R-Factor/Free R-Factor

Rfactor (or Rwork) 
The common crystallographic R-factor (most common measure for the quality of a crystal structure, or correctness of a model structure) is:

where h,k,l are the reciprocal lattice points of the crystal, Fobs and Fcalc are the observed and calculated structure factor amplitudes, and k is a scale factor. "The R-factor measures the average discrepancy between the scattering amplitudes Fc(hkl) calculated from the refined model and those measured experimentally (Fo(hkl))" Matthews BW (2009) Protein Sci.

Free R-Factor (Rfree)

hklT means all reflections belonging to test set T of unique reflections. Refinement is carried out with the remaining reflections (the working set). Rfree 
is used in cross validation during the refinement of macromolecular structures using X-ray data, its advantage being that it is unbiased by the refinement process. 
"A test set of reflections is set aside from the working set and the progress of the refinement is monitored by the calculation of a free R factor which is based only on the excluded reflections".

Brunger, Free R value: a novel statistical quantity for assessing the accuracy of crystal structures, Nature (1992) vol. 355 (6359) pp. 472-5 

For Tables in manuscripts use the following:
Rwork = Σ||F(obs)|- |F(calc)||/Σ|F(obs)|
Rfree = as for Rwork, but calculated for 5.0% of the total reflections that were chosen at random and omitted from refinement

The importance of R-factor, from: