# R-factors

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Historically, R-factors were introduced by ...

## Definitions

### Data quality indicators

• Rsym and Rmerge : the formula for both is

$\displaystyle{ R = \frac{\sum_{hkl} \sum_{j} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}} }$

where $\displaystyle{ \langle I_{hkl}\rangle }$ is the average of symmetry- (or Friedel-) related observations of a unique reflection, and the summation is over all observations, leaving out those that have no symmetry mates (or Friedel) in the dataset.

• Redundancy-independant version of the above: Rmeas
• measuring quality of averaged intensities/amplitudes: Rp.i.m. and Rmrgd-F

### Model quality indicators

• R and Rfree : the formula for both is

$\displaystyle{ R=\frac{\sum_{hkl_{unique}}\vert F_{hkl}^{(obs)}-F_{hkl}^{(calc)}\vert}{\sum_{hkl_{unique}} F_{hkl}^{(obs)}} }$

where $\displaystyle{ F_{hkl}^{(obs)} }$ and $\displaystyle{ F_{hkl}^{(calc)} }$ have to be scaled w.r.t. each other. R and Rfree differ in the set of reflections they are calculated from: R is calculated for the working set, whereas Rfree is calculated for the test set.

## what do R-factors try to measure, and how to interpret their values?

• relative deviation of

### Data quality

• typical values: ...

## what kinds of problems exist with these indicators?

- (Rsym / Rmerge ) should not be used, Rmeas should be used instead (explain why ?)

- R/Rfree and NCS: reflections in work and test set are not independant