By the late twentieth century, intelligence research had accumulated an awkward abundance of results. Spearman had identified general covariance. Thurstone had emphasized broad abilities. Cattell and Horn had developed an increasingly differentiated map of cognitive domains. Hundreds of factor-analytic studies had produced factors with overlapping names and sometimes competing interpretations. John Carroll tried to find out what structure survived across that accumulated evidence. The result was the Three-Stratum theory of cognitive abilities, published in Human Cognitive Abilities in 1993. Carroll’s synthesis placed relatively narrow abilities at the first stratum, broader domains at the second, and a highly general factor at the third. Its importance is not that the mind literally contains three layers. It is that Carroll offered a way to reconcile a century-old argument: cognitive abilities can be meaningfully different at one level while remaining related at another.
What did Carroll actually do?
This part is often compressed into “Carroll analyzed lots of tests.” The scale matters. For Human Cognitive Abilities (1993), Carroll systematically surveyed and reanalyzed hundreds of factor-analytic datasets from the twentieth-century literature using a comparatively consistent methodological framework. These datasets contained correlations among cognitive tests administered to many different samples. He was not combining everyone’s raw answers into one giant test. Conceptually, the process was:
existing cognitive-test datasets → correlation matrices → factor analyses → comparison of recurring factor patterns → hierarchical synthesis
The result was a taxonomy of abilities organized at different levels of generality.
What are the three strata?
Stratum I: narrow abilities
These are relatively specific dimensions of cognitive performance. Examples include narrower forms of reasoning, memory, perceptual, language, or speed-related ability. They are broader than one item but narrower than major domains.
Stratum II: broad abilities
These organize clusters of narrower abilities. Carroll identified broad factors including fluid intelligence, crystallized intelligence, general memory and learning, broad visual perception, broad auditory perception, broad retrieval ability, broad cognitive speediness, and processing/decision speed. Terminology has evolved, and later CHC frameworks do not map perfectly onto Carroll’s original labels.
Stratum III: general ability
At the highest level, Carroll identified a general factor associated with covariance among the broad abilities, which he interpreted in relation to Spearman’s g.
From individual tests to a hierarchy
Imagine a battery containing twelve fictional tests:
- three novel reasoning tasks;
- three knowledge/language tasks;
- three visual-spatial tasks;
- three memory tasks.
Within each cluster, the tests correlate especially strongly. So we can represent four broad domains:
reasoning
acquired knowledge
visual-spatial ability
memory-related ability
But those four broad domains are also positively correlated. A hierarchical model can therefore represent:
12 observed tests → 4 broad factors → 1 general factor
The model does not say that the four broad factors disappear because g exists. Nor does it say that the general factor disappears because broad abilities exist. It represents covariance at several levels.
Does the hierarchy describe one person’s mind?
This needs care. Factor structures are estimated from differences among people. If spatial and verbal tests correlate across a sample, factor analysis can identify dimensions that organize those individual differences. That does not mean we have directly watched a “spatial factor” or “g” operating inside one person’s brain. The factors are statistical constructs inferred from population-level covariance. Individual scores can then be estimated within that measurement framework.
Is Carroll’s hierarchy the final map?
No. Carroll’s synthesis was enormously influential, but later researchers using confirmatory factor analysis and other methods have questioned aspects of the number, replicability, and interpretive usefulness of some broad factors. One modern reanalysis of selected Carroll datasets concluded that Carroll may have extracted too many Stratum II factors in some cases and argued that some broad factors provided little incremental interpretive information beyond general intelligence in those datasets. That criticism does not erase the evidence for differentiated cognitive domains. It demonstrates that identifying a factor in a structural model and proving that its score adds practical interpretive value are different questions.
Why is Carroll still important?
Because the three-stratum framework made explicit something that simpler arguments obscure:
“general” and “specific” are levels of description, not necessarily rival theories.
A broad overall factor can summarize common variance. Broad abilities can represent additional covariance among related tasks. Narrow abilities can represent still more specific regularities. This hierarchical insight remains foundational even where researchers disagree about exact factor labels or preferred models.
A map of covariance, not a map of the brain
Carroll did not discover three physical layers inside the brain. He synthesized a very large body of correlational evidence into a three-level model of cognitive individual differences. The hierarchy is a model of structure. What biological and cognitive mechanisms generate that structure remains a further theoretical question.
References
- Carroll, J. B. (1993). Human Cognitive Abilities: A Survey of Factor-Analytic Studies. Cambridge University Press. DOI
- McGrew, K. S. (2009). CHC theory and the human cognitive abilities project. Intelligence, 37, 1–10. DOI
- Canivez, G. L., & Youngstrom, E. A. (2019). Challenges to the Cattell-Horn-Carroll theory: Empirical, clinical, and policy implications. Applied Measurement in Education, 32. DOI
- Dombrowski, S. C., McGill, R. J., & Canivez, G. L. (2018). Revisiting Carroll’s survey of factor-analytic studies: Implications for the clinical assessment of intelligence. Psychological Assessment, 30. DOI
- McGrew, K. S. (2023). Carroll’s Three-Stratum cognitive ability theory at 30 years. Journal of Intelligence, 11, 32. DOI
