Sums of ranking differences and inversion numbers for method discrimination


Correspondence to: James A. Koziol, PhD, Department of Molecular and Experimental Medicine, The Scripps Research Institute, 10550 N. Torrey Pines Road, La Jolla, CA 92037, USA



Héberger and colleagues [Trends Anal Chem 2010;29:101–109; J Chemometrics 2011;25:151–158] have introduced the sum of ranking differences as a measure for comparing models or methods and have demonstrated its applicability in a variety of settings. The sum of ranking differences is closely related to another distance measure for permutations, namely, the inversion number. In this note, we describe the inversion number along with some of its distributional properties and draw comparisons with the sum of ranking differences for model comparison. Copyright © 2013 John Wiley & Sons, Ltd.