This paper describes several situations in which generalization of statistical results is not possible by representative sampling but which is attempted using corrections for selection of groups. The situations include hiring, admissions, differential classification, guidance, test score equating, and test score scaling. Evidence of inaccuracies of the assumptions underlying the corrections is adduced. The Pearson equations which rest on these assumptions are mentioned as a basis for scaling and equating procedures in existence. An alternative approach is suggested, and its application to anchored equating, vertical equating, scaling, and equating with mixed essay and objective material is described. The alternative approach consists of a principle for choosing objective functions whose optimization would lead to a selection of conversion constants for equating. The principle is that equal equating test scores should be associated with equal reported scores on the average. Constrained optimizations are suggested where policy considerations so indicate. (Author)