Rank correlation - an alternative measure

Within the bounds of a general theory of rank correlation two particular measures have been adopted widely: Spearman's rank correlation coefficient, ρ, in which ranks replace variates in Pearson's product-moment correlation calculation; and Kendall's τ, in which the disarray of x-ordered data due to a y-ordering is measured by counting the minimum number, s, of transpositions (interchanges between adjacent ranks) of the y-ordering sufficient to recover the x-ordering. Based on insights from the calculation of Kendall's coefficient, this paper develops a graphical approach which leads to a new rank correlation coefficient akin to that of Spearman. This measure appears to stand outside general theory but has greater power of discrimination amongst differing reorderings of the data whilst simultaneously being strongly correlated with both ρ and τ. The development is focused on situations where agreement over ordering is more important for top place getters than for those lower down the order as, for example, in subjectively judged Olympic events such as ice skating. The basic properties of the proposed coefficient are identified. © Australian Statistical Publishing Association Inc. 2000. Published by Blackwell Publishers Ltd.