(i) The procedure introduced here for the clustering of frequency vectors takes into account the uncertainty arising from dealing with small observed frequencies. The smaller observed absolute frequencies, the more uncertainty about the “true” probability vector. The object is not represented by a single point in the multidimensional space but rather by the fuzzy set spread around this point. Consequently, the distance between two such objects is a fuzzy value, too. The expected mean distance between two objects generally differs from the simple distance: for instance, two objects with the same frequency vectors have a positive mean distance. The exact formula for estimation of the mean distance is given; this makes the algorithmization of the proposed procedure possible. The approach corresponds to that of the Bayesian estimation. The matrix of expected mean distances is an input to the hierarchical cluster analysis. (ii) The conventional hierarchical cluster analysis investigates similarities between objects from a given class. A modified general procedure is proposed seeking analogies between two classes of objects. The “two-class cluster analysis” is applicable to any kind of objects to be clustcred; it is not confined to the herein discussed special case of frequency vectors. (iii) The development of the procedure was developed initially for the field of the psychotherapy research - investigation of relationship patterns found within verbatirn protocols of sessions using the “guided imagery”, a psychotherapy technique dealing with evoked daydrearns. This constitutes an application example.
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.