Capitalization on Chance in Rotation of Factors

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 orthogonal 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