# Nonlinear Rank Correlations

Tarsitano, A. (2008) Nonlinear Rank Correlations. Working Paper. Agostino Tarsitano, Italy. (In Press)

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Rank correlation is a fundamental tool to express dependence in case in which the data are arranged in order. There are, by contrast, circumstances where the ordinal association is of a nonlinear type. In this paper we have investigated the effectiveness of thirty measures of rank correlation for assessing agreement between two evaluators in the presence of non costant scale of terms. These measures have been divided into three classes: unweighted rank correlations, weighted rank correlations, correlations of scores. Our findings suggest that none is systematically better than the other in all circumstances. However, a simply weighted version of the Kendall’s $\tau$ provides plausible answers to many special situations where intercategory distances are not the same.