ABSTRACT
In the preceding two chapters, rotation of factor axes according to simple structure criteria has been described, with positive manifold used as a supplementary aid in achieving this goal. Thurstone (1947, pp. 140ff.) attempted to prove the value of simple structure by presenting a solution to his famous “box” problem. He collected a sample of 20 boxes and took various mathematical functions of the three basic dimensions to obtain a total of 20 variables. with x, y, and z being the basic dimensions, Thurstone used as variables x 2, logx, x 2 + y 2, x 2 + z 2, 2x + 2y, x 2 + y 2 + z 2, and ex , with similar functions for y and z. From the intercorrelations of these variables he obtained three centroid factors, none of which matched the basic dimension variables of length, width, or height, the presumed underlying factors in the system. Rotation to simple structure, however, produced factors that were readily identifiable with the three basic box dimensions of length, width, and height.
