Factor analysis; some effects of chance error

Ignorance concerning the standard error of individual factor loadings and their differences has been a major obstacle to the proper interpretation of factorial results. The effects of three types of experimental error (selection of variables, selection of subjects and selection of scores) are here reported. In order to handle the errors of rotation systematically, it has been necessary to introduce a new semi-analytical criterion for the attainment of simple structure. Variability in results which may theoretically be eliminated is discussed under the heading of non-essential error.