R_free and the R_free ratio. II. Calculation of the expected values and variances of cross-validation statistics in macromolecular least-squares refinement

The free R factor is used routinely as a cross-validation tool in macromolecular crystallography. However, without any means of deriving quantitative estimates of its expected value and variance, its application has been rather subjective and its usefulness therefore somewhat limited. In the first part of this series, estimates of the expected value of the ratio of the free R factor to the standard R factor at the convergence of the structure refinement were given. Here, estimates of the variance of this ratio are given and are compared with the observed deviations from the expected values for a selection of refined structures. It is discussed how errors in the functional form of the structure-factor model as well as other types of errors might influence this ratio.