  The present study investigates to what degree the common variance of the
factor score predictor with the original factor, i.e., the determinacy
coefficient or the validity of the factor score predictor, depends on the
mean-difference between groups. When mean-differences between groups in the
factor score predictor are eliminated by means of covariance analysis,
regression, or group specific norms, this may reduce the covariance of the
factor score predictor with the common factor. It is shown that in a one-factor
model with the same group mean-difference on all observed variables, the common
factor cannot be distinguished from a common factor representing the group
mean-difference. It is also shown that for common factor loadings equal or
larger than .60, the elimination of a d = .50 mean-difference between two
groups in the factor score predictor leads to only small decreases of the
determinacy coefficient. A compensation-factor k is proposed allowing for the
estimation of the number of additional observed variables necessary to recover
the size of the determinacy coefficient before elimination of a group
mean-difference. It turns out that for factor loadings equal or larger than .60
only a few additional items are needed in order to recover the initial
determinacy coefficient after the elimination of moderate or large group
mean-differences.
