The Cattell-Horn-Carroll (CHC) theory of cognitive abilities is the most comprehensive and empirically supported psychometric theory of the structure of cognitive abilities to date. It represents the integrated works of Raymond Cattell, John Horn, and John Carroll (Alfonso, Flanagan, & Radwan, 2005; Horn & Blankson, 2005; McGrew, 2005; Schneider & McGrew, 2012). Because it has an impressive body of empirical support in the research literature (e.g., developmental, neurocognitive, outcome-criterion) it is used extensively as the foundation for selecting, organizing, and interpreting tests of intelligence and cognitive abilities (e.g., Flanagan, Alfonso, & Ortiz, 2012; Flanagan, Ortiz, & Alfonso, 2007). Most recently, it has been used for classifying intelligence and achievement batteries and neuropsychological tests to: (a) facilitate interpretation of cognitive performance; and (b) provide a foundation for organizing assessments for individuals suspected of having a learning disability (Flanagan, Alfonso, Mascolo, & Sotelo-Dynega, 2012; Flanagan, Alfonso, Ortiz, & Dynda, 2010; Flanagan, Ortiz, & Alfonso, in press). Additionally, CHC theory is the foundation on which most new and recently revised intelligence batteries were based (see Flanagan & Harrison, 2012 for comprehensive coverage of these batteries). A brief overview of the evolution of CHC theory follows. The original Gf-Gc theory was a dichotomous conceptualization of human cognitive ability put forth by Raymond Cattell in the early 1940s. Cattell based his theory on the factor-analytic work of Thurstone conducted in the 1930s. Cattell believed that Fluid Intelligence (Gf) included inductive and deductive reasoning abilities that were influenced by biological and neurological factors as well as incidental learning through interaction with the environment. He postulated further that Crystallized Intelligence (Gc) consisted primarily of acquired knowledge abilities that reflected, to a large extent, the influences of acculturation (Cattell, 1957, 1971). In 1965, John Horn expanded the dichotomous Gf-Gc model to include four additional abilities, including visual perception or processing (Gv), short-term memory (Short-term Acquisition and Retrieval—SAR or Gsm), long-term storage and retrieval (Tertiary Storage and Retrieval—TSR or Glr), and speed of processing (Gs). Later he added auditory processing ability (Ga) to the theoretical model and refined the definitions of Gv, Gs, and Glr (Horn, 1968; Horn & Stankov, 1982). In the early 1990s, Horn added a factor representing an individual's quickness in reacting (reaction time) and making decisions (decision speed). The acronym or code for this factor is Gt (Horn, 1991). Finally, quantitative (Gq) and broad reading-writing (Grw) factors were added to the model based on the research of Horn (e.g., 1991) and Woodcock (1994), respectively. Based largely on the results of Horn's thinking and research, Gf-Gc theory expanded into an eight-factor model that became known as the Cattell-Horn Gf-Gc theory (Horn, 1991; see Horn and Blankson, 2005, for a comprehensive review of Horn's contribution to Gf-Gc theory). In his review of the extant factor-analytic research literature, Carroll differentiated factors or abilities into three strata that varied according to the "relative variety and diversity of variables" (Carroll, 1997, p. 124) included at each level. The various G abilities are the most prominent and recognized abilities of the model. They are classified as broad or stratum II abilities and include abilities such as Gf and Gc, the two original factors. According to Carroll (1993), broad abilities represent "basic constitutional and long standing characteristics of individuals that can govern or influence a great variety of behaviors in a given domain" and they vary in their emphasis on process, content, and manner of response (p. 634). Broad abilities, like Gf and Gc, subsume a large number of narrow or stratum I abilities of which approximately 70 have been identified (Carroll, 1993, 1997). Narrow abilities "represent greater specializations of abilities, often in quite specific ways that reflect the effects of experience and learning, or the adoption of particular strategies of performance" (Carroll, 1993, p. 634). The broadest or most general level of ability in the Gf-Gc model is represented by stratum III, located at the apex of Carroll's (1993) hierarchy. This single cognitive ability, which subsumes both broad (stratum II) and narrow (stratum I) abilities, is interpreted as representing a general factor (i.e., g) that is involved in complex higher-order cognitive processes (Gustaffson & Undheim, 1996; Jensen, 1997; McGrew & Woodcock, 2001). It is important to note that the abilities within each level of the hierarchical Gf-Gc model typically display nonzero positive intercorrelations (Carroll, 1993; Gustafsson & Undheim, 1996). For example, the different stratum I (narrow) abilities that define the various Gf-Gc domains are correlated positively and to varying degrees. These intercorrelations give rise to and allow for the estimation of the stratum II (broad) ability factors. Likewise, the positive nonzero correlations among the stratum II (broad) Gf-Gc abilities allow for the estimation of the stratum III (general) g factor. The positive factor intercorrelations within each level of the Gf-Gc hierarchy indicate that the different Gf-Gc abilities do not reflect completely independent (uncorrelated or orthogonal) traits. However, they can, as is evident from the vast body of literature that supports their existence, be reliably distinguished from one another and therefore represent unique, albeit related, abilities (see Keith & Reynolds, 2012). Simplified versions of the Cattell-Horn and Carroll models of the structure of abilities (i.e., where the narrow abilities are omitted) are presented together in Figure 1, which shows a number of important similarities and differences between the two models. In general, these models are similar in that they both include multiple broad abilities with similar descriptions (e.g., Gs) and similar classification of narrow abilities. However there are four major structural differences between the Cattell-Horn and Carroll models. First, Carroll's theory includes g (global or general ability) at stratum III and the Cattell-Horn theory does not, as these theorists disagreed over the existence of an overarching intellectual ability. This dispute is an ongoing debate in the field (see Schneider & McGrew, 2012 for a discussion on the existence of g). Second, in the Cattell-Horn model, Gq is comprised of quantitative knowledge and quantitative reasoning; however, Carroll classified quantitative reasoning as a narrow ability subsumed by Gf. Third, the Cattell-Horn theory includes a distinct broad reading/writing (Grw) factor, whereas Carroll's theory includes reading and writing as narrow abilities subsumed by Gc. Fourth, the Cattell-Horn and the Carroll models differ in their treatment of certain narrow memory abilities. Carroll combined both short-term memory and the narrow abilities of associative, meaningful, and free-recall memory with learning abilities under (Gy). Horn (1991) made a distinction between immediate apprehension (e.g., short-term memory span) and storage and retrieval abilities. Notwithstanding the important differences between the Cattell-Horn and the Carroll models, in order to realize the practical benefits of using theory to guide test selection, organization, and interpretation, it is necessary to define a single taxonomy—one that can be used to classify ability tests. A first effort to create a single taxonomy for this purpose was an integrated Cattell-Horn and Carroll model proposed by McGrew (1997). McGrew and Flanagan (1998) subsequently presented a slightly revised integrated model, which was further refined by Flanagan et al. (2000). The integrated model presented by McGrew and colleagues was accepted by both John Horn and John Carroll and thus became known as the Cattell-Horn-Carroll (CHC) theory, reflecting the order in which these theorists made their contributions. The original integration of the Cattell-Horn Gf-Gc theory and Carroll's three-stratum theory, or simply CHC theory, is presented in Figure 2. This figure depicts the original structure of CHC theory and reflects the manner in which the Cattell-Horn and Carroll models have been integrated. In this figure, CHC theory includes 10 broad cognitive abilities, which are subsumed by over 70 narrow abilities. A paramount feature of the CHC theory is that it is not static, but rather a dynamic model that is continuously reorganized and restructured based on current research. Recently, Schneider and McGrew (2012) conducted an extensive review on CHC theory by (1) analyzing the current theory and potential errors, (2) reviewing whether contemporary intellectual research validates or refutes the CHC model, (3) redefining constructs to be more meaningful for clinicians, (4) adding, deleting, and restructuring the broad and narrow abilities within the model, and (5) highlighting which aspects of the model are more central to CHC theory. While a thorough explanation and description of the changes made to CHC theory is beyond the scope of this entry, the interested reader is referred to Schneider and McGrew (2012). The current model of CHC theory is presented in Figure 3. In this model, CHC theory includes 16 broad cognitive abilities, which are subsumed by over 80 narrow abilities. The ovals represent broad abilities and rectangles represent narrow abilities. The darker rectangles represent those narrow abilities that are most consistently represented on tests of cognitive and academic abilities. Additionally, the overall g or general ability is omitted from this figure intentionally due to space limitations. The conceptual groupings of abilities (i.e., reasoning, acquired knowledge, memory and efficiency, sensory, motor, and speed and efficiency) were suggested by Schneider and McGrew and provide an integrated framework of both cognitive and neuropsychological perspectives (Flanagan et al., 2010). The CHC theory represented a culmination of more than 60 years of factor-analysis research in the psychometric tradition. However, in addition to structural evidence, there are other sources of validity evidence, some quite substantial, that support CHC theory. Prior to defining the broad and narrow abilities that comprise CHC theory, a brief overview of the validity evidence in support of this structure of cognitive abilities is presented. It is beyond the scope of this entry to provide a fully detailed account and review of all the validity evidence currently available in support of the CHC structural model as well as the broad and narrow ability constructs it encompasses. The interested reader is referred to Carroll (1993, 2005), Flanagan and Harrison (2012), Horn and Blankson (2005), and Schneider & McGrew (2012) for a more thorough discussion. Briefly, the CHC structure of abilities is supported by factor-analytic (i.e., structural) evidence as well as developmental, neurocognitive, and heritability evidence (see Horn & Blankson, 2005). Additionally, there is a mounting body of research available on the relations between the broad cognitive CHC abilities and many academic outcomes (summarized in Flanagan et al., 2006; McGrew & Wendling, 2010), and occupational outcomes (Ackerman & Heggestad, 1997; McGrew & Flanagan, 1998). Furthermore, studies have shown that the factor structure of CHC theory is invariant across the lifespan (Bickley, Keith, & Wolfe, 1995; Keith, 2005; Woodcock et al., 2001) and across gender, ethnic, and cultural groups (e.g., Carroll, 1993; Gustafsson & Balke, 1993; Keith, 1997, 1999). In general, CHC theory is based on a more extensive network of validity evidence than other contemporary multidimensional ability models (see Daniel, 1997; Schneider & McGrew, 2012; Sternberg & Kaufman, 1998). Given the breadth of empirical support for the CHC structure of intelligence, it provides one of the most useful frameworks for designing and evaluating psychoeducational batteries, including intelligence, achievement, and neuropsychological tests (Flanagan et al., in press; Keith & Reynolds, 2012). Moreover, in light of the well-established structural validity of CHC theory, external validity support for the various CHC constructs, derived through sound research methodology, can be used confidently to guide test interpretation (see Bensen, 1998; Evans, Floyd, McGrew, & Leforgee, 2002; Flanagan, 2000; Floyd, Evans, & McGrew, 2003; Vanderwood, McGrew, Flanagan, & Keith, 2002). As previously mentioned, it is important to recognize that research related to CHC theory is not static. Rather, research on the hierarchical structure of abilities (within the Gf-Gc and now CHC framework) has been systematic, steady, and mounting for decades. Definitions of the broad and narrow abilities currently comprising CHC theory are presented in the next section. These definitions presented here were derived from an integration of the writings of Carroll (1993), Gustafsson and Undheim (1996), Horn (1991), McGrew (1997, 2005), and Schneider and McGrew (2012). The narrow ability definitions are presented in Tables C.1 through C.15. Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Narrow Stratum I Name (Code) Fluid intelligence refers to mental operations that an individual uses when faced with a relatively novel task that cannot be performed automatically. These mental operations may include forming and recognizing concepts, perceiving relationships among patterns, drawing inferences, comprehending implications, problem solving, extrapolating, and reorganizing or transforming information. Gf can also be described as "deliberate but flexible control of attention to solve novel, 'on-the-spot' problems that cannot be performed by relying exclusively on previous learned habits, schemas, and scripts" (Schneider & McGrew, 2012, p. 111). Inductive and deductive reasoning are generally considered to be the hallmark narrow ability indicators of Gf. Although most practitioners would agree that this ability is typically not measured directly by individually administered achievement batteries, some tests of achievement clearly involve the use of specific Gf abilities. For example, many tests of reading comprehension require individuals to draw inferences from the text. Aside from general inductive and deductive reasoning abilities, Gf also subsumes more specific types of reasoning, most notably Quantitative Reasoning (RQ). Unlike the other narrow Gf abilities, RQ is more directly related to formal instruction and classroom-related experiences. Definitions of the narrow abilities subsumed by Gf are presented in Table C.1. Crystallized intelligence refers to the breadth and depth of a person's acquired knowledge and skills that are valued by one's culture. This store of primarily verbal or language-based knowledge represents those abilities that have been developed largely through the "investment" of other abilities during educational and general life experiences (Horn & Blankson, 2005). Gc includes both declarative (static) and procedural (dynamic) knowledge. Declarative knowledge includes factual information, comprehension, concepts, rules, and relationships, especially when the information is verbal in nature. Declarative knowledge is held in long-term memory and is activated when related information is in working memory (Gsm). Procedural knowledge refers to the process of reasoning with previously learned procedures in order to transform knowledge. For example, a child's knowledge of his or her street address would reflect declarative knowledge, whereas a child's ability to find his or her way home from school would require procedural knowledge (Gagne, 1985). A rather unique aspect of Gc not seen in the other broad abilities is that it appears to be both a store of acquired knowledge (e.g., lexical knowledge, general information, information about culture) as well as a collection of processing abilities (e.g., communication ability, listening ability). The narrow ability of General Information (K0), for example, is clearly a repository of learned information, whereas the narrow Listening Ability (LS) appears to represent the ability to effectively comprehend and process information presented orally. Although research is needed to discern the nature of acquired knowledge versus processing abilities within the Gc domain, assessment of Gc should pay close attention to the narrow abilities that define this broad domain. Despite the interrelatedness of all narrow abilities under Gc, there may well be times when focus on the abilities that are more process oriented, as opposed to those that are knowledge oriented, is most important, and vice versa. Definitions of the narrow abilities subsumed by Gc are presented in Table C.2. General (domain-specific) knowledge (Gkn) is the "depth, breadth, and mastery of specialized knowledge (knowledge not all members of a society are expected to have)" (Schneider & McGrew, 2012, p. 123). This newly introduced broad ability was created from four narrow abilities previously accounted for in the Gc domain (i.e., Foreign Language [KL], Geography Achievement [A5], General Science Information [K1], and Knowledge of Culture [K2]) because they represent the acquired knowledge from specialized domains. This specialized knowledge is usually developed through an individual's work experience, hobbies, or passions. The Gkn broad ability is unique in that it is a domain that does not have a true G ability because the aggregates are of specific and distinct abilities. Furthermore, an individual should not be assessed in comparison with same age-peers in the general populations, but rather individuals who possess the same specialized knowledge base. For example, a sociologist's knowledge of human social behavior (i.e., Gkn narrow ability of should be to other not the general an number of specialized of knowledge the broad ability of Gkn an number of narrow abilities. However, of Gkn narrow abilities are and in Table (Schneider & McGrew, 2012). Quantitative knowledge represents an individual's and breadth of knowledge related to (Schneider & McGrew, 2012, p. The Gq store of acquired knowledge represents the ability to use quantitative information and Gq abilities are typically measured by achievement tests. For example, most comprehensive tests of achievement include of problems problem and general knowledge. Although some intelligence batteries aspects of Gq (e.g., on the Quantitative Reasoning on the they typically do not this ability It is important to the between Gq and the Quantitative Reasoning ability that is subsumed by Gf. the Gq represents an individual's store of acquired knowledge, including the ability to (i.e., procedural Quantitative Reasoning represents the ability to and when quantitative Gq is most evident when a task skills (e.g., and general knowledge (e.g., the on the other would be to solve for a number in a task (e.g., for narrow abilities are and under Gq in Table ability is an acquired store of knowledge that includes reading and writing skills for the comprehension of and the of It includes both abilities (e.g., reading and and complex abilities (e.g., comprehending writing a is considered to be an domain has been measured by tests of academic In Carroll's (1993) three-stratum model, narrow reading and writing abilities are subsumed by Gc
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