International Journal of Materials Chemistry and Physics
Articles Information
International Journal of Materials Chemistry and Physics, Vol.1, No.3, Dec. 2015, Pub. Date: Jan. 16, 2016
Two Common Sources of Systematic Errors in Charge Density Studies
Pages: 417-430 Views: 1819 Downloads: 1522
Authors
[01] Julian Henn, Bayreuth, Germany.
[02] Kathrin Meindl, Centre for Genomic Regulation (CRG), Barcelona, Spain.
Abstract
Resolution independent residuals  should not show any discontinuities, when plotted against the resolution . The density of reflections per resolution range, however, changes with resolution, which limits the information value from these plots. Residuals plotted against ranked resolution values, should be uniform and are easy to interpret. These plots of individual ranked residuals show more details compared to binned data, and additionally the important spread of the data. Therefore, plots of individual ranked residuals, which are currently only very rarely applied (see for example Friese et al. (2013)), are superior over the plots of binned values and should be used for the detection of systematic errors. Plots against the ranked intensity, significance and standard uncertainties, respectively, can be chosen, too. This work concentrates on the resolution dependence. Any discontinuity is evidence for data processing errors e.g. from merging resolution batches. Applications to artificial data and to experimental data are given. Non-uniform features are observed in the experimental data. Characteristic features in the residuals resulting from distorted standard uncertainty (s.u.) values are discussed by means of normal probability plots, plots of observed vs. calculated intensities, and plots of residuals vs. resolution for 23 experimental data sets and 3 artificial data sets with accurate, overestimated and underestimated large s.u.s. Distorted s.u. values seem to be a very common source of errors as demonstrated here. The underlying cause for distorted s.u. values is that the integration software from detector data severely underestimates the s.u.s of the strong reflections. Underestimation of the s.u.s of the strong reflections also leads to artificially reduced  values. When a weighting scheme is applied, there remains a tendency to not fully compensate for the underestimation. In virtually all data sets the s.u.s are underestimated as is seen by Goodness of Fit (GoF) values larger than one and slopes larger than one in the normal probability plots. Underestimated s.u. values artificially increase the number of rare events and manifest in form of outliers in other diagnostic tools based on the s.u.s, however, when no other systematic errors are present, the plots of observed vs. calculated intensities do not show outliers, even in the case of distorted s.u. values. The appearance of outliers in plots of residuals vs. resolution not accompanied by outliers in plots of  vs. is therefore consequently taken as an indicator for distorted s.u. values. Individual outliers in plots of observed vs. calculated intensities are surprisingly also observed.
Keywords
Quality Indicator, Fit Data, Ranked Residuals, Systematic Errors, Charge Density
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