# Free R factor

### From Online Dictionary of Crystallography

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 $R_\textrm{free}$. 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 $R_\textrm{free}$ 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, $F^2$ 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 $R_\textrm{free}$ 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.]