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Theory & Methods: Rank Correlation — an Alternative Measure
Author(s) -
Blest David C.
Publication year - 2000
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00110
Subject(s) - mathematics , rank correlation , rank (graph theory) , measure (data warehouse) , spearman's rank correlation coefficient , pearson product moment correlation coefficient , correlation coefficient , statistics , correlation , partial correlation , moment (physics) , order (exchange) , combinatorics , geometry , data mining , computer science , physics , finance , classical mechanics , economics
Within the bounds of a general theory of rank correlation two particular measures have been adopted widely: Spearman7apos;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 theorybut 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.