Measures of Fourfold Association II

Kenneth J. Berry and Janis E. Johnston

Chapter Chapter 14 in Statistical Methods: Connections, Equivalencies, and Relationships, 2023, pp 701-746 from Springer

Abstract: Abstract Chapter 14 is the second of two chapters describing connections, equivalencies, and relationships relating to fourfold ( 2 × 2 $$2 \times 2$$ ) contingency tables. First, the connections linking Pearson’s χ 2 $$\chi ^{2}$$ , Pearson’s ϕ 2 $$\phi ^{2}$$ , Tschuprov’s T 2 $$T^{2}$$ , and Cramér’s V 2 $$V^{2}$$ for symmetrical 2 × 2 $$2 \times 2$$ contingency tables are described and illustrated. Second, the connections linking Pearson’s r x y $$r_{xy}$$ product-moment correlation coefficient, regression coefficients b y x $$b_{yx}$$ and b x y $$b_{xy}$$ , Leik and Gove’s d N c $$d_{N}^{\,c}$$ measure of nominal association, and Goodman and Kruskal’s t y $$t_{y}$$ and t x $$t_{x}$$ asymmetric measures of nominal association are described. Third, the connections linking Kendall’s τ b $$\tau _{b}$$ measure of ordinal association, Stuart’s τ c $$\tau _{c}$$ measure of ordinal association, percentage differences Δ y $$\Delta _{y}$$ and Δ x $$\Delta _{x}$$ , and Somers’ d y x $$d_{yx}$$ and d x y $$d_{xy}$$ asymmetric measures of ordinal association are described. Fourth, the connections linking Yule’s Y measure of nominal association, Cohen’s unweighted κ $$\kappa $$ measure of inter-rater agreement, and Goodman and Kruskal’s λ y $$\lambda _{y}$$ and λ x $$\lambda _{x}$$ measures of nominal association are described. Finally, the connections linking Cohen’s unweighted κ $$\kappa $$ measure with a variety of other measures are described and illustrated.

Date: 2023
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DOI: 10.1007/978-3-031-41896-9_14

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