Dominance, information, and hierarchical scaling of variance space

Abstract

A method for computation of dominance relations and for construction of their corresponding hierarchical structures is presented. It is shown that variance can be computed from the squared pairwise differences between scores and that dominance indices are actually linear transformations of variances. The interpretation of variance as a quantitative measure of information is suggested and conceptual partition of variance into components associated with relational spaces is proposed. The link between dominance and variance allows integration of the mathematical theory of information with least squares statistical procedures without recourse to logarithmic transformations of the data.