The use of the Durbin-Watson d statistic in Rietveld analysis

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.