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In 1993 John Carroll (1916 - 2003) published "Human cognitive abilities: A survey of factor-analytic studies", which outlined his hierarchical, Three-Stratum Theory of cognitive abilities.  The theory is based on a factor analytic study of correlation of individual differences variables from measures including psychological tests, school marks, and competence ratings. The factor analysis suggests three layers or strata, with each layer attempting to account for the variation in factor loadings at the next lower level. Thus, the three strata are defined as representing narrow, broad, and general cognitive ability.
Carroll argues that factors are not mere artifacts of a mathematical process. The factors do describe stable and observable differences among individuals in the performance of tasks. The existence of physiological explanations for the differences in ability (e.g., muscle firing rates) does nothing to limit the effectiveness of factors in accounting for behavioral differences.
Carroll proposes a taxonomic dimension in the distinction between level factors and speed factors. The tasks that contribute to the identification or level factors can be sorted by difficulty and individuals differentiated by whether they have acquired the skill to perform the tasks. Tasks that contribute to speed factors are distinguished by the relative speed with which individuals can complete them. Carroll suggests that the distinction between level and speed factors may be the broadest taxonomy of cognitive tasks that can be offered. Carroll distinguishes his hierarchical approach from taxonomic approaches such as Guilford’s Structure of Intellect model (three-dimensional model with contents, operations, and products).
- J. B. Carroll. (1997). The three-stratum theory of cognitive abilities. In Contemporary intellectual assessment: Theories, tests, and issues. D. P. Flanagan, J. L. Genshaft and et al., New York, NY, USA, Guilford Press122-130]
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