International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 8.6, p. 712

Section 8.6.2.5. Statistical validity

A. Albinatia and B. T. M. Willisb

aIstituto Chimica Farmaceutica, Università di Milano, Viale Abruzzi 42, Milano 20131, Italy, and bChemical Crystallography Laboratory, University of Oxford, 9 Parks Road, Oxford OX1 3PD, England

8.6.2.5. Statistical validity

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Sakata & Cooper (1979[link]) criticized the Rietveld method on the grounds that different residuals [ y_{i}\left ({\rm obs.}\right) -y_{i}\left ({\rm calc.}\right) ]related to the same Bragg peak are correlated with one another, and they asserted that this correlation leads to an uncertainty in the standard uncertainties of the structural parameters. Prince (1981[link]) has challenged this conclusion and stated that the s.u.'s given by the Rietveld procedure are correct if the crystallographic model adequately fits the data. However, even if the s.u.'s are correct, they are measures of precision rather than accuracy, and attempts to assess accuracy are hampered by lack of information concerning correlations between systematic errors (Prince, 1985[link], 1993[link]).

References

Prince, E. (1981). Comparison of profile and and integrated-intensity methods in powder refinement. J. Appl. Cryst. 14, 157–159.
Prince, E. (1985). Precision and accuracy in structure refinement by the Rietveld method. Structure and statistics in crystallography, edited by A. J. C. Wilson. New York: Adenine Press.
Prince, E. (1993). Mathematical aspects of Rietveld refinement. The Rietveld method. IUCr Monographs on Crystallography, No. 5, edited by R. A. Young, pp. 43–54. Oxford University Press.
Sakata, M. & Cooper, M. J. (1979). An analysis of the Rietveld profile refinement method. J. Appl. Cryst. 12, 554–563.








































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