Introduction
The evolution of the factor theory of intelligence marks a major psychometric transition from Charles Spearman's unifactorial unity, through L.L. Thurstone's group-factor pluralism, to J.P. Guilford's multi-dimensional taxonomy. This conceptual development was closely driven by advancements in factor-analytic methodologies and divergent assumptions regarding the structure of human cognitive abilities.
1. Spearman’s Two-Factor Theory: The Unifactorial Foundation
In 1904, Charles Spearman formulated the Two-Factor Theory, arguing that performance on any intellectual task is governed by two components: a general cognitive capacity (g factor) representing cortical mental energy, and task-specific factors (s factors).
- Methodological Basis: Spearman observed the 'positive manifold'—the universal tendency for diverse cognitive ability tests to correlate positively.
- Mathematical Formulation: To prove the existence of a single general factor, Spearman formulated the criterion of tetrad differences: r13r24 - r23r14 = 0. Vanishing tetrad differences indicated that after partialling out a single latent common factor (g), the remaining partial correlations approached zero.
2. Thurstone’s Primary Mental Abilities: The Group-Factor Departure
L.L. Thurstone (1938) rejected the overarching unitary g factor, proposing that intelligence consists of seven distinct and relatively independent Primary Mental Abilities (PMAs): Verbal Comprehension, Word Fluency, Number Facility, Spatial Visualization, Associative Memory, Perceptual Speed, and Inductive Reasoning.
- Methodological Innovation: Thurstone pioneered Multiple Factor Analysis using oblique rotation (non-orthogonal axes), which allowed factors to correlate to satisfy his criteria for 'simple structure'.
- Psychometric Critique: Thurstone's isolation of independent factors was influenced by sample bias, as his initial validation used highly homogeneous samples of university students. When administered to broad, heterogeneous populations, these PMAs yielded positive intercorrelations. Second-order factor analysis of these correlated PMAs mathematically extracted a higher-order general factor, thereby reaffirming the necessity of a hierarchical g.
3. Guilford’s Structure-of-Intellect (SOI) Model: Multi-Dimensional Taxonomy
J.P. Guilford (1956) departed completely from hierarchical models by formulating a three-dimensional morphological taxonomy. Originally comprising 120 distinct cognitive abilities (5 × 4 × 6), the model was later expanded to 180 components (6 Operations × 5 Contents × 6 Products):
- Operations (6): Cognition, Memory Recording, Memory Retention, Divergent Production, Convergent Production, and Evaluation.
- Contents (5): Visual, Auditory, Symbolic, Semantic, and Behavioral.
- Products (6): Units, Classes, Relations, Systems, Transformations, and Implications.
- Methodological Artifact: Guilford employed forced orthogonal rotation (such as Varimax), which constrained factor axes to 90 degrees. This mathematically mandated that all extracted abilities remain uncorrelated (r = 0), artificially constructing factor independence where natural cognitive intercorrelations actually existed.
Conclusion
The historical divergence among Spearman's unifactorial construct, Thurstone's group factors, and Guilford's cross-classification was subsequently reconciled by modern hierarchical frameworks like the Cattell-Horn-Carroll (CHC) theory. By utilizing confirmatory factor analysis, contemporary psychometrics integrates Spearman's general factor at Stratum III, Thurstone's broad abilities at Stratum II, and Guilford's specific cognitive operations at Stratum I.