International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.8, p. 325

Section 3.8.2.1. Spearman's rank order coefficient

C. J. Gilmore,a G. Barra and W. Donga*

aDepartment of Chemistry, University of Glasgow, University Avenue, Glasgow, G12 8QQ, UK
Correspondence e-mail:  chris@chem.gla.ac.uk

3.8.2.1. Spearman's rank order coefficient

| top | pdf |

Consider two diffraction patterns, i and j, each with n measured points n((x1, y1), …, (xn, yn)). These are transformed to ranks R(xk) and R(yk). The Spearman test (Spearman, 1904[link]) then gives a correlation coefficient (Press et al., 2007[link]),[{R_{ij}} = {{\displaystyle\sum\limits_{k = 1}^n {R({x_k})R({y_k}) - n{{\left(\displaystyle{{{n + 1}\over 2}} \right)}^2}} } \over {{{\left({\displaystyle\sum\limits_{k = 1}^n {R{{({x_k})}^2} - n{{\left(\displaystyle{{{n + 1}\over 2}} \right)}^2}} } \right)}^{1/2}}{{\left({\displaystyle\sum\limits_{k = 1}^n {R{{({y_k})}^2} - n{{\left(\displaystyle{{{n + 1}\over 2}} \right)}^2}} } \right)}^{1/2}}}}, \eqno(3.8.1)]where [ - 1\, \le \,{R_{ij}}\, \le \,1].

References

Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. (2007). Numerical Recipes. 3rd ed. Cambridge University Press..Google Scholar
Spearman, C. (1904). The proof and measurement of association between two things. Am. J. Psychol. 15, 72–101.Google Scholar








































to end of page
to top of page