Correcting the predictive validity of a selection test for the effect of indirect range restriction

The validity of selection tests is underestimated if it is determined by simply calculating the predictor-outcome correlation found in the admitted group. This correlation is usually attenuated by two factors: (1) the combination of selection variables which can compensate for each other and (2) range restriction in predictor and outcome due to the absence of outcome measures for rejected applicants.

Here we demonstrate the logic of these artifacts in a situation typical for student selection tests and compare four different methods for their correction: two formulas for the correction of direct and indirect range restriction, expectation maximization algorithm (EM) and multiple imputation by chained equations (MICE). First we show with simulated data how a realistic estimation of predictive validity could be achieved; second we apply the same methods to empirical data from one medical school.

The results of the four methods are very similar except for the direct range restriction formula which underestimated validity.

For practical purposes Thorndike's case C formula is a relatively straightforward solution to the range restriction problem, provided distributional assumptions are met. With EM and MICE more precision is obtained when distributional requirements are not met, but access to a sophisticated statistical package such as R is needed. The use of true score correlation has its own problems and does not seem to provide a better correction than other methods.