Invariance in measurement and prediction: Their relationship in the single-factor case

Two forms of bias in psychological measurement are often distinguished. Predictive bias concerns systematic inaccuracies in predictions based on a test-Measurement bias concerns systematic inaccuracies in the information provided by a test about the latent variable or variables to be measured. although both forms of bias are important, their relationship has not been clearly described in the literature. Their relationship is here described under a single-factor model for the predictor battery and the criterion. Several theorems establish the general inconsistency between factorial invariance and slope Invariance (i.e., invariance of regression slopes). Predictor-criterion sets that are factorially invariant are not slope invariant under realistic conditions. The implications of this inconsistency for research on Spearman's ''g'' in employment testing, and for the general study of test bias, are discussed.