Tables for
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 11.4, p. 292   | 1 | 2 |

Section Merging and signal validation

Z. Otwinowski,a* W. Minor,b D. Boreka and M. Cymborowskib

aUT Southwestern Medical Center at Dallas, 5323 Harry Hines Boulevard, Dallas, TX 75390–9038, USA, and bDepartment of Molecular Physiology and Biological Physics, University of Virginia, 1300 Jefferson Park Avenue, Charlottesville, VA 22908, USA
Correspondence e-mail: Merging and signal validation

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Symmetry-related scaled measurements I(hkl) and their uncertainty estimates σE are used to obtain merged intensities by a standard weighted averaging formula:[\langle I\rangle={\textstyle\sum_jI_j/\sigma^2_{E,j}\over \textstyle\sum_j 1/\sigma^2_{E,j}}.\eqno(]This allows for calculations of validation statistics, called goodness-of-fit or normalized χ2, for each unique index:[\chi^2=\left({1\over n-1}\right)^{1/2}\displaystyle\sum_j{(I_j-\langle I\rangle)^2\over\sigma^2_{E,j}},\eqno(]where n represents the number of observations of a given unique index. This χ2 statistic is then averaged in resolution shells or over intensity bins or batch number. If the error model accounts properly for all effects, the χ2 statistic should fluctuate around a value of unity. If χ2 values depart from this expectation it may indicate a number of possibilities, e.g. various problems at earlier stages (poorly edited beam-stop shadow, hardware failures, mis­takes in processing or other source of outliers etc.), inadequacy of the error model or variations in the structure factors within the symmetry-related observations. The instrumental problems or mistakes in processing should be corrected. The effects that cannot be corrected may be handled by adjusting the error model. However, if the more detailed analysis eliminates the obvious source for such problems, then the most likely source of discrepancies between symmetry-related measurements results from violation of Friedel symmetry. SCALEPACK cal­culates merging statistics both for the Bijvoet pairs merged together and separately. Differences in χ2 values between these two merging outputs are very reliable estimates of anomalous signal strength. When a more detailed analysis eliminates the obvious reasons for high χ2 values, the most likely remaining source of error is non-isomorphism (Borek et al., 2007[link], 2010[link]).


Borek, D., Cymborowski, M., Machius, M., Minor, W. & Otwinowski, Z. (2010). Diffraction data analysis in the presence of radiation damage. Acta Cryst. D66, 426–436.
Borek, D., Ginell, S. L., Cymborowski, M., Minor, W. & Otwinowski, Z. (2007). The many faces of radiation-induced changes. J. Synchrotron Rad. 14, 24–33.

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