The purpose of this paper is to describe one of the methods of analyzing a configuration of psychological tests or traits in the problem of isolating primary factors. In factorial analysis a set of traits or tests is represented by a set of radial vectors which are so related to each other that the scalar product of each pair is equal to the corresponding experimentally observed correlation coefficient. Each radial vector represents a trait. The dimensionality of the trait configuration is the rank of the reduced correlational matrix. The reduced correlational matrix has communalities in the diagonal cells.

If there are n trait vectors in the configuration and if the dimensionality is r, then each of the n traits can be described as a linear function, a weighted sum, of any set of r linearly independent vectors. It is assumed here that n > r. These r traits in terms of vchich one may describe or comprehend each of the traits in the configuration have been denoted reference traits.