The science of intelligence
Cattell-Horn-Carroll (CHC) theory
Short answer
Cattell-Horn-Carroll (CHC) theory is a hierarchical model of human cognitive abilities built on John Carroll’s 1993 reanalysis of more than 460 data sets. General ability (g) sits at the top, broad abilities such as fluid reasoning, comprehension-knowledge, visual processing, working memory and processing speed sit in the middle, and narrow skills sit below.
Want your own number? The test is 25 visual puzzles, about 12 minutes, no sign-up.
Three theories under one name
CHC is named for three researchers whose models were merged. Raymond Cattell distinguished fluid intelligence, reasoning with novel material, from crystallized intelligence, acquired knowledge, in 1963 (Wikipedia: Fluid and crystallized intelligence). John Horn is the second name in the title. John Carroll arrived at a similar picture from a different direction: his 1993 book reanalyzed more than 460 data sets from the factor-analytic literature and presented a hierarchical, three-stratum theory of cognitive ability (Carroll, 1993).
In 1999 Richard Woodcock brokered the Cattell-Horn-Carroll umbrella term with Horn and Carroll, for practical reasons (McGrew, 2023). Kevin McGrew, writing 30 years after Carroll's book, recommends treating these as a family of related CHC theories rather than a single theory (McGrew, 2023).
The three strata
- Stratum III, general ability. The general factor, g, first proposed by Charles Spearman in 1904 (Wikipedia: g factor). It reflects the fact that different abilities correlate, about 0.30 on average at the observed level (Plomin & Deary, 2015). See the g factor guide.
- Stratum II, broad abilities. Groups of related skills such as fluid reasoning or processing speed.
- Stratum I, narrow abilities. The specific skills a single subtest draws on.
Try one · Logical Reasoning
Which tile completes the second pair?
Tap the option you think is right, or show the answer.
Show the answer
The missing panel shows a small hatched triangle pointing up, with small solid shapes: a triangle at the top-left corner and a triangle at the right side (option 2).
How to solve it
- Compare the first two panels and name exactly what changed.
- The whole figure turns a quarter turn clockwise.
- The large shape becomes hatched.
- Nothing else changes.
- Apply the same changes to the third panel: a small outlined triangle pointing left, with small solid shapes: a triangle at the bottom-left corner and a triangle at the top.
- So the missing panel shows a small hatched triangle pointing up, with small solid shapes: a triangle at the top-left corner and a triangle at the right side.
That was 1 puzzle. The full test has 25.
The broad abilities
A 2023 network analysis of the Woodcock-Johnson IV norm sample (ages 9 to 19) measured these broad abilities and found that the results supported them (McGrew et al., 2023):
| Code | Broad ability | What it covers |
|---|---|---|
| Gf | Fluid reasoning | Solving unfamiliar problems, finding rules |
| Gc | Comprehension-knowledge | Vocabulary, general knowledge, verbal understanding |
| Gv | Visual processing | Imagining and manipulating shapes and space |
| Ga | Auditory processing | Analyzing sounds, including speech sounds |
| Gwm | Short-term working memory | Holding and working with information briefly |
| Gr | Retrieval fluency | Producing ideas or names from memory quickly |
| Gs | Processing speed | Fast, accurate work on simple tasks |
The same study suggested that the working memory and attentional control complex may be central to how the abilities connect (McGrew et al., 2023). That fits research finding a median correlation of .72 between working memory capacity and fluid reasoning (Kane et al., 2005); see working memory. For the speed side, see processing speed.
Why the broad abilities are worth separating
If every ability moved in lockstep, a single g score would be enough. They do not. Processing speed and some reasoning measures peak in the late teens and twenties, while vocabulary and accumulated knowledge keep rising into the sixties (Hartshorne & Germine, 2015). A model that only had g would hide that. The fluid vs crystallized guide covers the oldest and best known of these splits.
How well the model holds up
McGrew describes Carroll's treatise as a milestone in psychometric intelligence research that still influences how intelligence tests are built and interpreted 30 years later (McGrew, 2023). A 2023 bifactor reanalysis supported Carroll's conclusion that his three-stratum model represents the structure of intelligence better than two prominent alternative models (McGrew, 2023). The network analysis reached a similar answer by a different statistical route, supporting the primary broad abilities (McGrew et al., 2023).
CHC and IQ tests
McGrew's point that Carroll's model still shapes how tests are built and interpreted is easiest to see on the named-test pages. The Woodcock-Johnson and the WAIS-5 pages describe two of them. Our own test samples mainly fluid reasoning and visual processing, so it reports an estimated IQ from those areas rather than a full CHC profile. Compare the models on theories of intelligence.
Sources
- Fluid and crystallized intelligence. Wikipedia. en.wikipedia.org/wiki/Fluid_and_crystallized_intelligence
- Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. Cambridge University Press. doi.org/10.1017/CBO9780511571312
- McGrew, K. S. (2023). Carroll's three-stratum (3S) cognitive ability theory at 30 years. Journal of Intelligence, 11(2), 32. doi.org/10.3390/jintelligence11020032
- McGrew, K. S., Schneider, W. J., Decker, S. L., & Bulut, O. (2023). A psychometric network analysis of CHC intelligence measures. Journal of Intelligence, 11(1), 19. doi.org/10.3390/jintelligence11010019
- g factor (psychometrics). Wikipedia. en.wikipedia.org/wiki/G_factor_(psychometrics)
- Plomin, R., & Deary, I. J. (2015). Molecular Psychiatry, 20, 98-108. doi.org/10.1038/mp.2014.105
- Hartshorne, J. K., & Germine, L. T. (2015). Psychological Science, 26(4), 433-443. doi.org/10.1177/0956797614567339
- Kane, M. J., Hambrick, D. Z., & Conway, A. R. A. (2005). Working memory capacity and fluid intelligence are strongly related constructs: Comment on Ackerman, Beier, and Boyle (2005). Psychological Bulletin, 131(1), 66-71. doi.org/10.1037/0033-2909.131.1.66