“…an intelligence test is no more than a sample of the kinds of skills we regard as intelligent.” - Vernon (1969, p.11).
Discussions of early developments in the construction of hierarchical models of intelligence generally begin with Charles Spearman’s (1927) factor-analytically derived “two-factor theory.” Spearman proposed that intelligence is comprised of a general factor (g) and a set of specific factors (s). According to Spearman g is responsible for the positive manifold (observed relations) among
intelligence tests. Specific factors are instead responsible for the variance in test scores not explained by g. This is because specific factors concern the specific, unique requirements of tasks independent of one’s general intelligence. Spearman (1923) divided g into the components of education and
reproduction. These components are thought to work together, but to be only moderately correlated and measured separately. Education was conceptualised as the ability to make sense of information encountered. Reproduction was conceptualised as the ability to recall and articulate that information at some future point. These factors are very conceptually similar to Cattell’s (1941) model of fluid and crystallised intelligence (Hogan, R., Hogan, J., & Barrett, 2008).
The fluid/crystallised intelligence theory posited that cognitive abilities involving some degree of intelligence are most usefully organised at a general level into two principal classes or dimensions. Fluid intelligence (Gf) was conceptualised as raw intellectual potential and considered dependent upon biological factors such as genotype and central nervous system development (Cattell, 1943b, 1963, 1987c; Horn, 1985; Horn & Cattell, 1966c). The conceptualisation of Gf as innate has achieved considerable popularity among intelligence theorists. However, evidence from behavioural-genetic studies is currently insufficient to substantiate or refute this claim (Richardson, 1998). Crystallised intelligence (Gc) was conceptualised as the primary manifestation of the impact of experiential, educative, and acculturation influences upon intellectual development (Cattell, 1943b, 1963, 1987c;
61 Horn, 1985; Horn & Cattell, 1966c). Another way to conceptualise this distinction is based upon fluid intelligence reflecting fundamental abilities in reasoning and its related higher mental processes, while crystallised intelligence reflects the size of an individual’s knowledge base (Drasgow, 2003). Cattell’s fluid and crystallised theory of intelligence has remained one of the most influential within the context of intelligence testing and theorisation (Demetriou & Papdopoulos, 2004; Roberts, Markham,
Matthews, & Zeidner, 2005; Sternberg, 2004).
Fluid and crystallised intelligence both rely upon the cognitive processes of perceiving
relationships, abstracting, reasoning, problem solving, and concept formation (Horn & Cattell, 1966c). Tests of Gf and Gc can be undertaken via either speed or maximum capability (power) measures based on pictorial-spatial, verbal-semantic, and verbal-symbolic materials (Stankov et al., 1995). For
example, Gf is related to speed of reasoning, whereas Gc is related to reading speed. Fluid and crystallised intelligence are also influenced by the relationships among a variety of other factors. Examples of such factors and their relationships include the relationship between one’s visual
perception/spatial ability and perceptual speed, one’s ideational fluency and retrieval capacity, and the relationship between one’s reaction time and processing speed (Bates & Shieles, 2003). Horn and Blankson (2005) view Gf and Gc abilities as opposites. Whereas Gc measures indicate the extent to which an individual has incorporated a culture’s general and procedural knowledge, Gf measures indicate abilities that depend only minimally on knowledge of the culture.
Fluid intelligence derives its label from its capacity to be channelled into just about any task or activity that requires the exercise of intelligence (Horn, 1977). The construct domain of Gf is
comprised of one’s general reasoning ability; particularly reasoning that involves figural, symbolic, or nonverbal content (Horn, 1976; Horn & Cattell, 1966c). Fluid intelligence is assessed by tests in which the parameters of elementary relation perceiving and/or correlate-inducing abilities establish one’s level of performance (Horn, 1977; Jensen, 1998b). Some characterise the dimension of Gf as nonverbal intelligence (although verbal measures can assess it), or performance IQ. Gf is usually measured by tests involving content such matrices, mazes, letter series, figure classifications, and word groupings (Horn, 1976). A variety of researchers and theorists has attempted to equate Gf with
62 Spearman’s g factor (e.g., Cronbach, 1984; Deary, 2000; Gustafsson, 1988; Jensen, 2002; Kyllonen & Christal, 1990). Yet this identification has not been borne out by further investigation (Horn &
Blankson, 2005; Kline, 2000; McGrew, 2005; Stankov, 2002). Perhaps the most compelling refutation of the Gf = g hypothesis is that presented within Carroll’s (1993) seminal work on cognitive ability and its structure. Carroll performed a Schmid-Leiman hierarchical factor analysis and found that an identified second-order Gf remained after the extraction of the third-order g.
Crystallised intelligence gets its name from the intellectual abilities it comprises appearing to “crystallise out of experience” (Horn, 1967, p.150). Horn and Cattell (1966c) construe Gc tests as most commonly measuring that aspect of intelligence involving the use of verbal or conceptual knowledge. Gc is seen as concerning one’s awareness of terms and concepts pertaining to a wide variety of topics. Gc is generally considered the product of fluid intelligence functioning (Sternberg, 2004). Crystallised intelligence is assessed by items demanding the knowledge and skills it is reasonable to expect of people of the relevant age within a particular culture (Kline, 2000). Crystallised intelligence is normally measured via vocabulary tests and tests that measure general and/or specific knowledge, such as mathematics. Rightly or wrongly, because of its association with the knowledge tested in school aptitude tests etc., Gc is the dimension most usually considered indicative of intelligence (Horn, 1976, 1977). Crystallised abilities are often referred to in attempts to specify what is most important about human intelligence (Horn & Blankson, 2005).
The next major advance in hierarchical models of intelligence was Carroll’s (1993) three- stratum theory of intelligence. The three-stratum theory of cognitive ability extends and expands all previous theories of intelligence (Carroll, 1997). Many consider it the most definitive study into the structure of intelligence measured by tests (Grubb et al., 2004; Stankov et al., 1995; Sternberg et al., 2003). McGrew (2005) has even gone so far as to attribute to Carroll the provision of a “Rosetta stone” by which to understand intelligence (p.147). After reanalysing more than 450 data sets
covering a full spectrum of tool and participant group diversity, and observing the consistencies across results, Carroll concluded that a hierarchical model of intelligence was the most practically useful and theoretically sound model of intelligence. On the basis of this investigation Carroll proffered a
63 “Three-Stratum” hierarchy of intelligence. According to this model the stratum of a cognitive ability is assigned on the basis of its perceived breadth or narrowness (Carroll, 1997).
The structure of intelligence within this hierarchy is comparable to a pyramid. Spearman’s g
is equivalent to the apex of the pyramid (Stratum III). The body of the pyramid (Stratum II) is comprised of eight factors. Each of these factors represent enduring characteristics affecting an individual’s performance in any given area requiring intellectual acumen. The most prevalent of Stratum II factors are fluid and crystallised intelligence. The base of the pyramid, or Stratum I, is comprised of a number of specific factors. Examples of stratum I factors include mathematical reasoning and verbal ability (Carroll, 1997).
Carroll’s (1997) rationale for the creation of his three-stratum theory was to allow the
facilitation of a provisional statement about the identification, enumeration, and structuring of the total range of cognitive abilities discovered or known thus far. To this end Carroll’s theory was expected to expand, replace, or supplement previous theories of the structure of cognitive abilities. This included: Thurstone’s (1938) theory of primary mental abilities, Horn and Cattell’s (1966c) Gf-Gc theory, Guilford’s (1967) structure-of-intellect theory, and Wechsler’s (1974) theory of performance and verbal components of intelligence. The next stage in the refinement of a model incorporating both g
and Gf and Gc was McGrew’s (2005) Cattell-Horn-Carroll (CHC) theory of cognitive abilities. According to McGrew (2005) the CHC theory of intelligence is “the tent that houses the two most prominent psychometric theoretical models of human cognitive abilities” (p.137). The CHC theory is a hybridisation of Horn and Cattell’s Gf-Gcand Carroll’s three-stratum theory of
intelligence. The first published account of the CHC link is contained within Flanagan, McGrew, and Ortiz (2000). This report assigned credit for the CHC link to McGrew’s (1997) attempt to create a single Gf-Gc taxonomy for interpreting and evaluating intelligence test batteries. Neither the Cattell- Horn nor the Carroll model of intelligence was selected over the other in CHC development. The CHC instead synthesised the Carroll and Horn-Cattell Gf-Gcframeworks (McGrew, 1997; 2009). According to McGrew and Flanagan (1997) the empirical evidence strongly suggests that the Horn- Cattell Gf-Gc theory (Horn, 1994; Horn & Noll, 1997) and the three-stratum theory of cognitive
64 abilities (Carroll, 1993, 1997) represent the most well researched and comprehensive frameworks of the structure of intelligence to date (also see Flanagan & McGrew, 1997; McGrew & Flanagan, 1996; Messick, 1992). Although Carroll’s model incorporated Gf-Gc factors, it did not assign sufficient weight to the place of these factors in common intelligence testing. The CHC model represents the most accurate model of the factors underlying commonly measured intelligence. This makes CHC taxonomy the obvious “cognitive cornerstone” of modern intelligence theory and test design (Carroll, 1997; Flanagan & McGrew, 1995a, 1998; McGrew, 1997, 2005; Woodcock, 1990).
The validity of CHC over Carrollian second-stratum abilities alone has received considerable support from large and small factorial studies (McGrew, 2005; Shu-chen, Jordanova, & Lindenberger, 1998; Stankov, Seizova-Cajie, & Roberts, 2001). Contemporary CHC modelling has also garnered considerable support from outcome criterion prediction, developmental, heritability, and
neurocognitive studies (Floyd, McGrew, Barry, Rafael, & Rogers, 2009; Horn & Noll, 1997). The CHC model includes a stratum III general intelligence factor. Yet this does not make compulsory its inclusion in research involving the CHC. According to McGrew (2005) researchers employing the CHC model need to themselves decide whether g is to be included in the application of the CHC in their research. An evaluation of the relative merits of the g versus no-g approaches to intelligence theorisation are beyond the scope of this dissertation; at least four substantial books or major papers have been exclusively devoted to the topic (Brand, 1996; Jensen, 1998b; Nyborg, 2003; Sternberg & Grigorenko, 2002) and no consensus has been reached. Regardless of the reality of g,
there is no doubt that Spearman’s conceptualisation has had, and continues to have a profound impact upon intelligence theorisation and test construction. A considerable amount of empirical evidence suggests that general intelligence is among the most dominant and enduring factors connected with environmental adaptation; occupational success; and physical propensity and morbidity (McGrew & Flanagan, 1997; McDermott, Fantuzzo, & Glutting, 1990). The use of g in psychometrics remains such an emotive topic that authors such as Deary (2000, 2001) claim theories failing to account for g
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Figure 2.3. CHC Hierarchical Model of Intelligence (adapted from McGrew, 2005). Circles represent latent factors (PMA = primary mental ability). Squares represent manifest measures (T = test).
This dissertation will adopt a conservative approach to the inclusion of g. A general intelligence factor will be included within analysis, but will assume a secondary role to Gf and Gc within the discussion. Evidence that secondary abilities such as Gf and Gc make important contributions to understanding cognitive performance above and beyond that accounted for by g is substantial (McGrew & Flanagan, 1997; McGrew, 2005, 2009). Yet the inclusion of g remains important from a practical perspective. Composite intelligence tests involving g comprise several different abilities. This means they are often better predictors of overall performance ratings than measures of Gc or Gf alone (Horn, 1994). This is important from a validity perspective, yet similar arguments apply to those made earlier made regarding a focus on the Big Five or their facets.