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Predicted Differences and Differences Between Predictions

Mollenkopf, William G.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Difference Scores, Predictive Measurement, Predictor Variables


When K tests are given to N individuals, and for each individual there are available two criterion measures, then (1) the multiple regression weight to be applied to the standard score for each test to predict the criterion-difference score is equal to the difference of the weights for predicting each criterion separately; (2) the difference between the predicted scores for the two criteria is the same as the predicted difference in criterion scores (each test being assigned the appropriate multiple regression weight); (3) the square of the multiple correlation between predicted and actual criterion-difference scores is equal to the sum of the squares of the multiple correlations of the battery with each criterion, less the product of these correlations and the correlation between predicted scores, all divided by twice the quantity one minus the criterion intercorrelation; and (4) the variance of the errors of estimating the criterion- difference score is equal to the sum of the variances of the errors of estimating each criterion score, minus twice the criterion intercorrelation, plus twice the correlation between predicted scores multiplied by the product of the square root of one minus the variance of the errors of estimating one criterion and the corresponding square root for the second criterion.

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  • 10.1002/j.2333-8504.1950.tb00018.x