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Journal of Probability and Statistics
Volume 2015 (2015), Article ID 375491, 6 pages
http://dx.doi.org/10.1155/2015/375491
Research Article

On Association Measures for Continuous Variables and Correction for Chance

GION, University of Groningen, Grote Rozenstraat 3, 9712 TG Groningen, Netherlands

Received 24 June 2015; Revised 20 October 2015; Accepted 28 October 2015

Academic Editor: Heinz Holling

Copyright © 2015 Matthijs J. Warrens. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies correction for chance for association measures for continuous variables. The set of linear transformations of Pearson’s product-moment correlation is used as the domain of the correction for chance function. Examples of measures in this set are Tucker’s congruence coefficient, Jobson’s coefficient, and Pearson’s correlation. An equivalence relation on the set of linear transformations is defined. The fixed points of the correction for chance function are characterized. It is shown that each linear transformation is mapped to the fixed point in its equivalence class.