# An empirical verification of the statistical properties of factor score estimates and the effects of the differentially estimated factor scores on the resulting probability values in a multivariate analysis of variance design

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## Abstract

The present study was conducted to provide an empricial verification of the theoretically-based reports on the statistical properties of differentially computed factor score estimates in combination with alternative factor extraction solutions. With each rank-reduction solution, factors were extracted from the intercorrelations based upon the total variance and based upon the pooled-within group variance. Each initial solution was subjected to an orthonormal transformation. Subsequent to securing each derived solution, factor score estimates were calculated by the regression method, the ideal variable method, the Bartlett method, and the Anderson-Rubin method. For each derived set of factor score estimates, the statistical properties of maximum validity, orthogonality univocality, and unbiasedness were assessed, and the relative effect on the magnitude of the probability value in a multivariate analysis of variance was evaluated. Results indicated that the interactive effect on the statistical properties of differentially computed factor score estimates is dependent upon whether a component model or common factor model is employed. Due to computational simplicity, the ideal variable method is suggested when the univocal property is desired. The factor score estimates, calculated subsequent to a principal factor solution, using a total correlation matrix in the extraction process, may provide the best means of obtaining significant results. Limitations of the study and recommendations for future research are given.