Subscores and Validity

In educational testing, subscores may be provided based on a portion of the items from a larger test. One consideration in evaluation of such subscores is their ability to predict a criterion score. Two limitations on prediction exist. The first, which is well known, is that the coefficient of determination for linear prediction of the criterion score by the subscore cannot exceed the reliability coefficient of the subscore. The second limitation is on incremental validity. The coefficient of determination for linear prediction of the criterion score by both the total score and the subscore is at least as great as the coefficient of determination for linear prediction of the criterion score by only the total score. Incremental validity may be measured by the difference between these two coefficients of determination. This difference is no greater than the reliability of the residual from linear prediction of the subscore by the total score.