# 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*).

## Contents

## 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 [math]R_\textrm{free}[/math]. It is calculated in the same way as the conventional least-squares *R* factor

[math]R = {{\sum | F_{obs} - F_{calc} | } \over {\sum |F_{obs} |}}[/math],

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 [math]R_\textrm{free}[/math] 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:

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

where *Y* represents *F*, [math]F^2[/math] 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 [math]R_\textrm{free}[/math] 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.*]

## See also

- Validation of protein crystal structures. G. J. Kleywegt.
*International Tables for Crystallography*(2006).*Vol. F*, ch. 21.1, pp. 497-506 doi:10.1107/97809553602060000707