Influence of Chance Error on Simple Structure: An Empirical Investigation of the Effect of Chance Error and Estimated Communalities on Simple Structure in Factorial Analysis

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.