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Fitting A Model of School Learning to Aptitude and Achievement Data Over Grade Levels

Carroll, John B.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Achievement Tests, Aptitude Tests, Learning Theories, Mathematical Models, Multiple Regression Analysis, Time Factors (Learning)


A model of school learning proposed by the writer in 1962, concerned with relations among aptitude, achievement, and time to learn, is extended to the analysis of regressions of achievement on aptitude over multiple grade levels. This mathematical model provides good fits to empirical data from series of vertically-equated scales of aptitude and achievement obtained by G. R. Burket for Grades 1 through 12, and appears to be able to indicate which of a given pair of tests is more like an aptitude test. An aptitude component connected with learning rate is found for a Memory test as a predictor of Arithmetic achievement, and for a Vocabulary test as a predictor of Reading achievement. (43pp.)

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