Measures of Nominal Association II

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.