FORMAL MODELS FOR A CENTRAL PREDICTION SYSTEM1

Abstract

ABSTRACTThree quantitative models are considered for merging secondary school grades from various schools to composite predictor variables for estimating expected performances of students at various colleges. Previous formulations of possible solutions for developing a universal grading scale have been limited to univariate models. The models discussed are not so limited and may involve several composite scores. These multiple solutions could have considerable importance both in college admission procedures and in counseling of students.In the first model, a total variance and covariance canonical correlation model, composite variables are developed for both school grades and for college grades so as to maximize the correlation between the school and college variables. A major defect found in this model is the influence of existing differences in school grades between groups of students attending various colleges. The second canonical correlation model utilized within college deviation scores for the variances and covariances used in the canonical correlations. This model provided some improvement over the preceding model but still had some defects generated from differential sizes of groups from particular secondary schools attending particular colleges. Both canonical models are formulated to obtain pairs of variates, one from the secondary school grades and one from the college grades, which correlate maximally. Prediction of student performances on specific criteria, such as grades at particular colleges, would be a secondary step and might not be accomplished effectively.The third model, a predictive model, is formulated to develop composite scores which provide predictions of grades at the various colleges. This model appears to provide the soundest basis for practical actions, both in student guidance and in college admissions.