Measures of Ordinal Association II

Kenneth J. Berry and Janis E. Johnston

Chapter Chapter 10 in Statistical Methods: Connections, Equivalencies, and Relationships, 2023, pp 435-493 from Springer

Abstract: Abstract Chapter 10 is the second of two chapters describing connections, equivalencies, and relationships relating to measures of ordinal association. First, Kendall’s τ b $$\tau _{b}$$ measure of ordinal association and Stuart’s τ c $$\tau _{c}$$ measure of ordinal association are described and the connection linking Kendall’s τ b $$\tau _{b}$$ , Stuart’s τ c $$\tau _{c}$$ , and permutation test statistic δ $$\delta $$ is established. An example illustrates the connections among τ a $$\tau _{a}$$ , τ b $$\tau _{b}$$ , τ c $$\tau _{c}$$ and δ $$\delta $$ . Second, Goodman and Kruskal’s γ $$\gamma $$ measure of ordinal association is presented and the connection linking Goodman and Kruskal’s γ $$\gamma $$ and permutation test statistic δ $$\delta $$ is detailed. Third, Somers’ d y x $$d_{yx}$$ and d x y $$d_{xy}$$ measures of ordinal association are described and the connections linking Somers’ d y x $$d_{yx}$$ and d x y $$d_{xy}$$ and permutation test statistic δ $$\delta $$ are established. Fourth, Wilson’s e measure of ordinal association is described and the connection linking Wilson’s e and test statistic δ $$\delta $$ is delineated. Fifth, the connection linking Kendall’s S measure of ordinal association and Mann and Whitney’s U two-sample rank-sum statistic is described. Finally, Cohen’s weighted kappa measure of inter-rater agreement is presented and the connection linking κ w $$\kappa _{w}$$ and permutation measure ℜ $$\Re $$ is described.

Date: 2023
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DOI: 10.1007/978-3-031-41896-9_10

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