On the assumption that principle component scores are to be computed by what is known as the direct solution (in contrast to estimation procedures), the weighted internal consistancy reliability coefficient for a component is reduced to a form so that it easily can be seen that when a latent root becomes as small as 1.0, the reliability becomes zero (as indicated in Kaiser-Caffrey alpha factor analysis). If the root becomes less than 1.0, the internal consistency becomes negative. These findings are extended to common-factor analysis under an assumption that the observed scores are approximated by their common-factor parts; it is seen that the internal consistency for a common factor will become zero when the common variance for the factor becomes as small as 1.0. It is recognized that the model for simple structure factor analysis implies that only a few from among all variables of a set will have nonrandom relationships to a given factor. It follows that to calculate the internal consistency for a simple structure factor by means of the procedures outlined above is rather like calculating the reliability for a composite formed by adding relatively many random variables to relatively few indicators of an attribute. The implication is that if one really wants to estimate the internal consistency of simple structure factors—perhaps as a basis for determining when to stop factoring—he should first rotate the factors and then use only salient variables in calculating a reliability coefficient. The criterion for size of the internal consistency coefficient would then be set in accordance with the psychometric standards applied generally to variables in a particular substantive area. © 1969, Taylor & Francis Group, LLC. All rights reserved.
