EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT

FACTOR analysis is used for two different theoretical purposes: to search for structure among correlated measures for purposes of theory construction, and to test hypotheses, derived perhaps from previous factor analyses, about measures. For purposes of the first sort a variety of computer programs for both oblique and orthog-onal rotation of factors is available. Visually guided rotations are also still used. For purposes of the second sort visually guided rotations are also used, but either orthogonal or oblique rotations by computer to a target matrix is a typical procedure. The question arises with respect to either of these theoretical purposes, and to either visually guided or computer rotations, as to the extent to which the investigator can capitalize on chance. In multiple regression, for example, the investigator capitalizes on chance to an extent which is a function of the number of variables (n) and the number of observations (N). The investigator can &dquo;shrink&dquo; his multiple correlation, if he is interested in the popula-tion value, or he can cross-validate, when he wishes to apply weights to independent samples. While an analogous phenomenon is expected in the factor analytic rotational process, the investigator has no statistical basis for estimating population values nor has he an empirical technique comparable to cross-validation at his disposal. There is one empirical study which indicates the practical impor-tance of the problem. Horn (1967) factored the intercorrelation