# R-factors

Historically, R-factors were introduced by ...

## Definitions

### Data quality indicators

- R
_{sym}and R_{merge}: the formula for both is

[math]\displaystyle{
R = \frac{\sum_{hkl} \sum_{j} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}
}[/math]

where [math]\displaystyle{ \langle I_{hkl}\rangle }[/math] is the average of symmetry- (or Friedel-) related observations of a unique reflection, and the first summation is over all unique reflections with more than one observation.

- Redundancy-independant version of the above: R
_{meas} - measuring quality of averaged intensities/amplitudes: R
_{p.i.m.}and R_{mrgd-F}

### Model quality indicators

- R and R
_{free}: the formula for both is

[math]\displaystyle{
R=\frac{\sum_{hkl_{unique}}\vert F_{hkl}^{(obs)}-F_{hkl}^{(calc)}\vert}{\sum_{hkl_{unique}} F_{hkl}^{(obs)}}
}[/math]

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

### Model quality

## what kinds of problems exist with these indicators?

- (R_{sym} / R_{merge} ) should not be used, R_{meas} should be used instead (explain why ?)

- R/R_{free} and NCS: reflections in work and test set are not independant