Convergent Validity of Variables Residualized By a Single Covariate: the Role of Correlated Error in Populations and Samples

This study examined the bias and precision of four residualized variable validity estimates (C0, C1, C2, C3) across a number of study conditions. Validity estimates that considered measurement error, correlations among error scores, and correlations between error scores and true scores (C3) performed the best, yielding no estimates that were practically significantly different than their respective population parameters, across study conditions. Validity estimates that considered measurement error and correlations among error scores (C2) did a good job in yielding unbiased, valid, and precise results. Only in a select number of study conditions were C2 estimates unable to be computed or produced results that had sufficient variance to affect interpretation of results. Validity estimates based on observed scores (C0) fared well in producing valid, precise, and unbiased results. Validity estimates based on observed scores that were only corrected for measurement error (C1) performed the worst. Not only did they not reliably produce estimates even when the level of modeled correlated error was low, C1 produced values higher than the theoretical limit of 1.0 across a number of study conditions. Estimates based on C1 also produced the greatest number of conditions that were practically significantly different than their population parameters