In seeking a suitable topic for the address at this annual event of the psychometricians, I tried to keep in mind the motto of our official publication, Psychometrika, to promote “the development of psychology as a quantitative, rational science.” The best that I have been able to do falls short of this ideal in two important respects. Although the material that I am to bring before you pretends to be quantitative, in the sense that measurements have been made, the problem has not been rationalized and the data have thus far yielded only to graphical treatment.

A technique for determining a set of weights for the linear combination of a number of measures is applied to a concrete problem. The set of weights meets the criterion of maximum separation of the total scores of two different occupational groups.

Correlation coefficients derived from an hypothetical simple structure for twenty tests and four factors were “loaded” with chance error components. Centroid analyses and rotations to give least square determinations of the hypothetical simple structure were made for several conditions. It is concluded that the experimental situation of inaccurate coefficients and estimated communalities permits accurate determination of primary trait loadings provided that the rank of the centroid matrix is equal to or greater than that of the underlying primary trait matrix. Of several criteria for the completeness of factorization which were tested, none was wholly satisfactory.

A mechanism for localizing different stimulus intensities within the nervous system, essentially as described by Rashevsky, is considered in first approximation. The mechanism is central, and therefore general. There results a one-parameter family of theoretical curves, graphs of the Weber (discriminal) ratio against stimulus intensity. Comparisons are made with experimental visual, acoustical, and tactual data.

With the mechanism of common elements we designed numerous sets of variates correlated with each other in a known manner and also correlated with the primary and specific factors in the same predetermined fashion. To the correlations from theoretical populations, and also from experimental samples, Thurstone's centroid method of factoring was applied. The resulting centroid co-ordinates were rotated to yield the test vectors. These vectors were close approximations to the theoretical and sample correlations.