Modified Phi Correlation Coefficients for the Multivariate Analysis of Ordinally Scaled Variables

Abstract

The Pearson-Bravais correlation coefficient is the most widely used intervariable association index with multivariate analysis of underlying structure. However, it is a suboptimal coefficient when assumptions of multivariate normality are violated because of its tendency to become attenuated. A nonparametric class of intervariable association indexes is presented that follows the logic of point symmetry adjustment of the Pearsonian phi. This approach is extended to multipoint scales. These indexes may be shown to have useful Euclidean properties and to be attractive alternatives to the Pearson correlation coefficient for multivariate analyses.