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The use of the Durbin–Watson d statistic in Rietveld analysis
Author(s) -
Hill R. J.,
Flack H. D.
Publication year - 1987
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889887086485
Subject(s) - statistic , mathematics , rietveld refinement , statistics , neutron diffraction , measure (data warehouse) , diffraction , physics , computer science , optics , data mining
A weighted form of the Durbin–Watson d statistic [Durbin & Watson (1971). Biometrika , 58 , 1–19] has been used to quantify the serial correlation between adjacent least‐squares residuals in Rietveld refinements of step‐scan powder diffraction data. Analyses of X‐ray and neutron data from a range of materials have shown that the d statistic: provides a sensitive measure of the progress of a refinement and remains discriminating when other agreement indices fail, for example, when comparing results at different step widths; provides quantitative information about the significance of serial correlation present in the residuals; provides a convenient means of assessing the reliability of the estimates of the parameter variances; and provides a basis for the selection of values of step width and intensity corresponding to optimum and/or minimum use of experimental beam time.