Another useful quantity is the so-called Bragg R-factor, which are computed on the reflection intensities rather than the data points. They are defined in various ways, but I will use here the values on structure factors, \(F_{hkl}\) and \(F_{hkl}^2\), which are: \[R_F = \frac {\sum _{hkl} |F_{obs, hkl}| - |F_{calc, hkl}| } {\sum _{hkl} |F_{obs, hkl}|} \] and \[R_{F^2} = \frac {\sum _{hkl} F^2_{obs, hkl} - F^2_{calc, hkl} } {\sum _{hkl} F^2_{obs, hkl}} \] These R-factors are analogous to single-crystal R-factors, but in single-crystal work, the structure factors are measured and have uncertainties that can be used for weighted R-factors. How the \(F_{obs, hkl}\) values are obtained is discussed in Chapter 20, but that method is both indirect and approximate. Further, we do not have uncertainties, so unlike single-crystal work, these R-factors have no statistical basis. The reason though that they are useful is that the focus on how well the structure is reproducing the peak intensities and are much less affected by other aspects of the overall fit.