Chapter 8.4 Statistical significance tests

Mathematical, physical and chemical tables

First Online Edition (2006)

Part 8. Refinement of structural parameters

  1. E. Prince1,
  2. C. H. Spiegelman2

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000612

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Prince, E. and Spiegelman, C. H. 2006. Statistical significance tests. International Tables for Crystallography. C:8:8.4:702–706.

Author Information

  1. 1

    NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

  2. 2

    Department of Statistics, Texas A&M University, College Station, TX 77843, USA

Publication History

  1. Published Online: 1 JAN 2006


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.


  • chi-squared distributions;
  • influential data points;
  • statistical significance tests;
  • statistical validity