Validating a selection test,a predictive probability approach

The problem of inferring the validity of a selection test (x) as a predictor of some criterion (y) when completexy data are not available is investigated. The basic approach is to construct the predictive probability distribution of the unobservedy scores and then derive interval estimates of the least squares regression weights, the difference in averagey scores for selected and unselected cases, and the residual variance in predictingy fromx. Further, an approximation to the predictive distribution of the squared correlation betweenx andy in a future group is derived.