Measures of Nominal Association II

Kenneth J. Berry and Janis E. Johnston

Chapter Chapter 12 in Statistical Methods: Connections, Equivalencies, and Relationships, 2023, pp 559-632 from Springer

Abstract: Abstract Chapter 12 is the second of two chapters describing connections, equivalencies, and relationships relating to measures of nominal association. First, Cohen’s unweighted kappa measure of inter-rater agreement is described. Second, Mielke and Berry’s ℜ $$\Re $$ chance-corrected measure of agreement is introduced and the connection linking Cohen’s kappa and Mielke and Berry’s ℜ $$\Re $$ is described and illustrated. Third, Cohen’s weighted kappa measure of inter-rater agreement is described for both linear and quadratic weighting. Fourth, the connections linking Cohen’s weighted kappa and Mielke and Berry’s ℜ $$\Re $$ chance-corrected measure of agreement is described and illustrated. Fifth, the connection linking Pearson’s chi-squared test of independence and Pearson’s r x y $$r_{xy}$$ product-moment correlation coefficient is presented. Sixth, Leik and Gove’s d N c $$d_{N}^{\,c}$$ measure of nominal association is described. Seventh, Agresti’s δ ̂ $$\hat {\delta }$$ measure of nominal association is described. Eighth, Somers’ d y s $$d_{ys}$$ asymmetric measure of nominal association is described. Ninth, Freeman’s θ $$\theta $$ measure of association between a nominal-level independent variable and an ordinal-level dependent variable is described. Finally, the connections linking Leik and Gove’s d N c $$d_{N}^{\,c}$$ , Agresti’s δ ̂ $$\hat {\delta }$$ , Somers’ d y x $$d_{yx}$$ , and Freeman’s θ $$\theta $$ are described and illustrated with an example analysis.

Date: 2023
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DOI: 10.1007/978-3-031-41896-9_12

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