The statistics of cross-validation residuals - Theory
The statistics of cross-validation residuals - Theory
The R-factor expressions used so far in this paper have been based
on the generalised R-factor, 
. However identical expressions
can be derived for the estimated values of the standard free R-factor,
, and the standard ratio. For example, in
Appendix II the following estimate of the ratio in
unrestrained refinement is derived which is based on standard
R-factors.
The numerator and denominator in the above equation are
first order binomial approximations to square roots and therefore
another estimate of the standard ratio is
The right hand side is now the same as for the 
ratio
(equation 12). These expressions may be compared with
the estimate used by Bacchi, Lamzin & Wilson (1996) which in our
notation is
The derivation of simple estimates for the standard and its
ratio requires the assumption that the variances of all structure
amplitudes are equal. The use of generalised R-factors, whose
estimates do not require this assumption, is to be preferred.
The statistics of cross-validation residuals - Theory