Chance-corrected measures for 2 x 2 tables that coincide with weighted kappa

Cohen's kappa is presently a standard tool for the analysis of agreement in a 2 x 2 reliability study, and weighted kappa is a standard statistic for summarizing a 2 x 2 validity study. The special cases of weighted kappa, for example Cohen's kappa, are chance-corrected measures of association. For various measures of 2 x 2 association it has been observed in the literature that, after correction for chance, they coincide with a special case of weighted kappa. This paper presents the general function, linear in both numerator and denominator, that becomes weighted kappa after correction for chance.