The Cohen’s kappa coefficient is a widely accepted mecisure of agreement on categorical variables and has replaced some older simpler measures. Observational and statistical properties of the kappa coefficient in 2 x 2 tables are investigated. The asymmetrical measure “Cohenized implication” is proposed. The decomposition of the symmetrical measure kappa into two asymmetrical components is shown. These statistically motivated measures are discussed as weakened forms of strict logical notions of equivalence and implication. Applications of kappa and “Cohenized implication” are recommended; on the one hand in the medical research as a supplement to traditional measures of sensitivity and speciíity, on the other hand as quantifiers in the GUHA proceduře ASSOC as a statistically contemporary operationalization of the weakened equivalence.