On the definition of quadratic indices of correlation between standardized deviations

Abstract

This work is strictly related to two previous works written by the author in collaboration with A. Gili and published on issues No.4, 1984 and No.1, 1986 of "Statistica". The main aim of the first work was to propose a methodology introducing to the general theory of concordance between deviations, also including, therefore, partial concordance between deviations. For this purpose proportionality equations were used as a conceptual instrument, which proved particularly suitable for better penetrating the logical fundamental of partial concordance. In the second of the two works mentioned above, on the basis of ginian conception which differentiates the indices of concordance in indices of omophilia and indices of correlation, depending on whether the notion of relative maximum or absolute maximum of concordance is referred to, a general theory of quadratic indices of correlation between deviations was treated, which also introduces indices whose logical structure is the one of partial indices of correlation. In the work which has just been published the author, always basing the construction on the conceptual instrument represented by proportionality equations, proposes the theory of quadratic indices of correlation again, thus referring to the ginian notion of absolute maximum of concordance but, this time, as regards statistical distributions of standardized deviations. A general formulation of quadratic indices of correlation between standardized deviations is given, and the Yule partial correlation coefficient and Bravais-Pearson linear correlation coefficient are determined as particular expressions of it.