R factor - Revision history

BrianMcMahon: Tidied translations.

2017-12-15T10:32:36Z

Tidied translations.

BrianMcMahon: Tidied translations and added German and Spanish (U. Mueller)

2017-11-17T16:45:52Z

Tidied translations and added German and Spanish (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-16T14:55:35Z

Style edits to align with printed edition

MassimoNespolo: languages

2016-04-12T11:16:45Z

languages

BrianMcMahon at 10:24, 4 April 2008

2008-04-04T10:24:00Z

New page

== Definition ==

The term ''' ''R'' factor''' in crystallography is commonly taken to refer to the 'conventional' ''R'' factor

<math>R = {{\sum | F_{obs} - F_{calc} | } \over {\sum |F_{obs} |}}</math>,

a measure of agreement between the amplitudes of the [[structure factor]]s calculated from a crystallographic model and those from the original X-ray diffraction data. The ''R'' factor is calculated during each cycle of least-squares structure refinement to assess progress. The final ''R'' factor is one measure of model quality.

More generally, a variety of ''R'' factors may be determined to measure analogous residuals during least-squares optimization procedures. Where the refinement attempts to minimize the deviates of the squares of the structure factors (refinement against <math>F^2</math>), the ''R'' factor based on <math>F^2</math> is used to monitor the progress of refinement:

<math>R(F^2) = {{\sum | F^2_{obs} - F^2_{calc} | } \over {\sum |F^2_{obs} |}}</math>.

Likewise, refinement against ''I'' can be tracked using the [[Bragg R factor|Bragg ''R'' factor]]

<math>R_B = {{\sum | I_{obs} - I_{calc} | } \over {\sum |I_{obs} |}}</math>.

Even for refinement against <math>F^2</math> or ''I'', the 'conventional' ''R'' factor may be calculated and quoted as a measure of model quality, in order to compare the resulting quality of models calculated at different times and with different refinement strategies.

The ''R'' factor is sometimes described as the '''discrepancy index'''.

== ''R'' factor as a measure of structure quality ==

Theoretical values of ''R'' range from zero (perfect agreement of calculated and observed intensities) to about 0.6 for a set of measured intensities compared against a set of random intensities. ''R'' factors greater than 0.5 indicate very poor agreement between observed and calculated intensities, and many models with <math>R \ge 0.5</math> will not respond to attempts at improvement. An early model with <math>R \le 0.4</math> can usually be improved during refinement. A desirable target ''R'' factor for a protein model refined with data to 2.5 Å is considered to be <math>\sim 0.2</math>. Small organic molecules commonly refine to <math>R < 0.05</math>. However, the ''R'' factor must always be treated with caution, as an indicator of precision and not accuracy. Partially incorrect structures have been reported with ''R'' values below 0.1; many imprecise but essentially correct structures have been reported with higher ''R'' values.

== Weighted ''R'' factors ==

In practice, ''weighted'' ''R'' factors are more often used to track least-squares refinement, since the functions minimized are weighted according to estimates of the precision of the measured quantity ''Y'':
<math>\sum w (Y_o - Y_c)^2</math>
(''Y'' being ''F'', <math>F^2</math> or ''I''). The general term for a weighted residual is

<math>wR = ({{\sum |w |Y_o - Y_c|^2|}\over{\sum |wY^2_o}|})^{1/2}</math>

The sum is usually computed over all reflections measured in the experiment. However, occasionally reflections are omitted from the calculation, either because they are believed to result from a systematic experimental error or are recorded with an intensity small compared with background noise. Any such selection may introduce statistical artefacts, and must always be described when reporting ''R'' factors.

[[Category:Structure determination]]

← Older revision		Revision as of 10:32, 15 December 2017
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−	<font color="blue">Facteur ''R''</font> (''Fr''). <font color="red">R-Faktor, Übereinstimmungsfaktor</font> (''Ge''). <font color="black">Fattore ''R''</font> (''It''). <font color="~~brown~~">R~~-фактор~~</font> (''Ru''). <font color="~~purple~~">R 因子</font> (''Ja''). <font color="green">Factor R</font> (''Sp'').	+	<font color="blue">Facteur ''R''</font> (''Fr''). <font color="red">R-Faktor, Übereinstimmungsfaktor</font> (''Ge''). <font color="black">Fattore ''R''</font> (''It''). <font color="purple">R 因子</font> (''Ja''). <font color="brown">R-фактор</font> (''Ru''). <font color="green">Factor R</font> (''Sp'').

← Older revision		Revision as of 16:45, 17 November 2017
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−	<font color="blue">Facteur ''R''</font> (''Fr''). <font color="black">Fattore ''R''</font> (''It''). <font color="brown">R-фактор</font> (''Ru''). <font color="purple">R 因子</font> (''Ja'').	+	<font color="blue">Facteur ''R''</font> (''Fr''). <font color="red">R-Faktor, Übereinstimmungsfaktor</font> (''Ge''). <font color="black">Fattore ''R''</font> (''It''). <font color="brown">R-фактор</font> (''Ru''). <font color="purple">R 因子</font> (''Ja''). <font color="green">Factor R</font> (''Sp'').

← Older revision		Revision as of 11:16, 12 April 2016
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		+	<font color="blue">Facteur R</font> (''Fr''); <font color="black">Fattore R</font> (''It''); <font color="brown">R-фактор</font> (''Ru''); <font color="purple">R 因子</font> (''Ja'').
		+
		+
	== Definition ==		== Definition ==

@@ Line 1: / Line 1: @@
-<font color="blue">Facteur R</font> (''Fr''); <font color="black">Fattore R</font> (''It'');  <font color="brown">R-фактор</font> (''Ru''); <font color="purple">R 因子</font> (''Ja'').
+<font color="blue">Facteur ''R''</font> (''Fr''). <font color="black">Fattore ''R''</font> (''It'').  <font color="brown">R-фактор</font> (''Ru''). <font color="purple">R 因子</font> (''Ja'').
@@ Line 10: / Line 10: @@
 a measure of agreement between the amplitudes of the [[structure factor]]s calculated from a crystallographic model and those from the original X-ray diffraction data. The ''R'' factor is calculated during each cycle of least-squares structure refinement to assess progress. The final ''R'' factor is one measure of model quality.
-More generally, a variety of ''R'' factors may be determined to measure analogous residuals during least-squares optimization procedures. Where the refinement attempts to minimize the deviates of the squares of the structure factors (refinement against <math>F^2</math>), the ''R'' factor based on <math>F^2</math> is used to monitor the progress of refinement:
+More generally, a variety of ''R'' factors may be determined to measure analogous residuals during least-squares optimization procedures. Where the refinement attempts to minimize the deviates of the squares of the structure factors (refinement based on <math>F^2</math>), the ''R'' factor based on <math>F^2</math> is used to monitor the progress of refinement:
 <math>R(F^2) = {{\sum | F^2_{obs} - F^2_{calc} | } \over {\sum |F^2_{obs} |}}</math>.
-Likewise, refinement against ''I'' can be tracked using the [[Bragg R factor|Bragg ''R'' factor]]
+Likewise, refinement based on ''I'' can be tracked using the [[Bragg R factor|Bragg ''R'' factor]]
 <math>R_B = {{\sum | I_{obs} - I_{calc} | } \over {\sum |I_{obs} |}}</math>.
-Even for refinement against <math>F^2</math> or ''I'', the 'conventional' ''R'' factor may be calculated and quoted as a measure of model quality, in order to compare the resulting quality of models calculated at different times and with different refinement strategies.
+Even for refinement based on <math>F^2</math> or ''I'', the 'conventional' ''R'' factor may be calculated and quoted as a measure of model quality, in order to compare the resulting quality of models calculated at different times and with different refinement strategies.
 The ''R'' factor is sometimes described as the '''discrepancy index'''.
@@ Line 32: / Line 32: @@
 (''Y'' being ''F'', <math>F^2</math> or ''I''). The general term for a weighted residual is
-<math>wR = ({{\sum |w |Y_o - Y_c|^2|}\over{\sum |wY^2_o}|})^{1/2}</math>
+<math>wR = \Big({{\sum |w |Y_o - Y_c|^2|}\over{\sum |wY^2_o}|}\Big)^{1/2}</math>.
 The sum is usually computed over all reflections measured in the experiment. However, occasionally reflections are omitted from the calculation, either because they are believed to result from a systematic experimental error or are recorded with an intensity small compared with background noise. Any such selection may introduce statistical artefacts, and must always be described when reporting ''R'' factors.
 [[Category:Structure determination]]