International Tables for Crystallography

Statistical significance tests
E. Prince and C. H. Spiegelman. International Tables for Crystallography (2006). Vol. C, ch. 8.4, pp. 702-706  [ doi:10.1107/97809553602060000612 ]


Chapter 8.4 introduces the χ2 distribution and shows how it can be used to assess whether a model produced by a least-squares fit is consistent with the data. The F distribution, the distribution of the ratio of two independent random variables that both have χ2 distributions, is derived. The F distribution and two others derived from it, Student's t distribution and Hamilton's R-factor ratio distribution, can be used to decide whether one model is significantly better than another. The projection matrix is defined and the concept of leverage is introduced. The projection matrix can be used to determine which data points have the most influence in determining particular refined parameters.

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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The series consists of nine volumes and comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.