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.

翻译：本研究探究因子得分预测变量与原始因子的共同方差（即确定性系数或因子得分预测变量的效度）在多大程度上依赖于组间均值差异。当通过协方差分析、回归或分组特定常模消除因子得分预测变量中的组间均值差异时，可能会降低因子得分预测变量与公共因子的协方差。研究表明，在单因子模型下，若所有观测变量存在相同的组间均值差异，则无法将公共因子与代表组间均值差异的公共因子区分开来。同时，当公共因子载荷等于或大于0.60时，在因子得分预测变量中消除两组间d=0.50的均值差异仅会导致确定性系数的小幅下降。本文提出补偿因子k，用于估计恢复消除组均值差异前确定性系数大小所需的额外观测变量数量。结果表明，当因子载荷等于或大于0.60时，在消除中等或较大组间均值差异后，仅需增加少量项目即可恢复初始确定性系数。