On the Internal Consistency Reliability of Factors

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.