# Free R factor

Facteur R libre (Fr). Freier R-Faktor (Ge). Fattore R libero (It). 自由Ｒ因子 (Ja). Factor R libre (Sp).

## Definition

A residual function calculated during structure refinement in the same way as the conventional R factor, but applied to a small subset of reflections that are not used in the refinement of the structural model. The purpose is to monitor the progress of refinement and to check that the R factor is not being artificially reduced by the introduction of too many parameters.

## Discussion

Many macromolecular structure refinements now use the statistical cross-validation technique of monitoring a `free' R factor Rfree. It is calculated in the same way as the conventional least-squares R factor

$R = {{\sum | F_{obs} - F_{calc} | } \over {\sum |F_{obs} |}}$,

but uses a small subset of randomly selected reflections that are set aside from the beginning and not used in the refinement of the structural model. Thus Rfree tests how well the model predicts experimental observations that are not themselves used to fit the model. A fixed percentage of the total number of reflections is usually assigned to the free group.

A weighted free R factor may also be calculated over the set of reflections not used in the refinement:

$wR = \left( {\sum | w | Y_o - Y_c |^2{| }\over{\sum |wY^2_o}| }\right)^{1/2}$,

where Y represents F, F2 or I.

After each cycle of refinement, the free R factor and the R factor for the working set of reflections are both calculated. However, as the refinement converges, the working and free R factors both approach stable values. It is common practice, particularly in structures at high resolution, to stop monitoring Rfree at this point and to include all the reflections in the final rounds of refinement.

## History

The idea of the free R factor was introduced by Brünger, A. T. [(1997). Methods Enzymol. 277, 366–396. Free R value: cross-validation in crystallography.]