Dumont Willis: CHC

 CHC Theory *


Probably the best known and most widely accepted theories of intellectual factors among practitioners derive from the Horn-Cattell Gf-Gc model [e.g., Cattell (1941, 1971, 1987), Cattell & Horn (1978), Horn (1988), Horn (1991), Horn & Noll (1997)]. Gf and Gc refer, respectively, to “fluid” and “crystallized” intelligence.  See Carroll (1993); Flanagan & McGrew (1997); Flanagan, McGrew, & Ortiz (2000); Flanagan & Ortiz (2001); Flanagan, Ortiz, Alfonso, & Mascolo (2002); Horn (1985, 1988, 1991); Horn and Cattell (1966); Horn & Noll (1997); McGrew (1997); McGrew & Flanagan (1998); Woodcock (1990); and Woodcock & Mather (1989) for discussions of Gf-Gc, now referred to as the Cattell-Horn-Carroll (CHC) theory.

Building upon the foundation of CHC theory and the work of Richard Woodcock (e.g., 1990, 1993), McGrew and Flanagan created the McGrew, Flanagan, and Ortiz Integrated Cattell-Horn-Carroll Gf-Gc Cross-Battery Approach to assessment. The most complete and practically useful expositions of the application of CHC theory in the McGrew, Flanagan, and Ortiz Integrated Cattell-Horn-Carroll Gf-Gc Cross-Battery Approach available at this writing are in Kevin McGrew & Dawn Flanagan’ s The Intelligence Test Desk Reference (ITDR): Gf-Gc Cross-Battery Assessment (Allyn & Bacon, 1998), Flanagan, McGrew, and Samuel Ortiz’s (2000). The Wechsler Intelligence Scales and Gf-Gc theory: A contemporary approach to interpretation, Flanagan and Ortiz’s (2001). Essentials of Cross-Battery Assessment, and Flanagan, Ortiz, Vincent Alphonso, and Jennifer Mascolo’s (2002) The Achievement Test Desk Reference (ATDR).   Kevin McGrew’s Institute for Applied Psychometrics (IAP) (http://www. iapsych.com/) contains an incredible amount of information related to CHC theory and free membership in the IAP listserv.

The following discussion draws very heavily upon these sources, which should be consulted for more accurate and detailed information.  There is considerable similarity between the Carroll and the Cattell-Horn models.  See, for example, Figure 2.2, p. 25 and pp. 25-27 in Flanagan, Ortiz, Alfonso, & Mascolo (2002).[1]  The Carroll model emphatically includes g.  The Cattell-Horn model does not.   The McGrew, Flanagan, and Ortiz Integrated CHC model omits g.  “The exclusion of g does not mean that the integrated model does not subscribe to a separate general human ability or that g does not exist.  Rather, it was omitted by McGrew (1997) (and is similarly omitted in the current integrated model) since it has little practical relevance to cross-battery assessment and interpretation.  That is the cross-battery approach was designed to improve psychoeducational assessment practice by describing the unique (Gf-Gc pattern of abilities of individuals that in turn can be related to important occupational and achievement outcomes and other human traits (see last section of this chapter)” (McGrew & Flanagan, 1998, p. 14, emphasis in original).[2]  The McGrew, Flanagan, and Ortiz Integrated model uses, with slight modifications, the terminology used by Carroll (1993, pp. 792-795) to label (stratum I) abilities (e.g., RG = General Sequential Reasoning, I = Induction, and K2 = Information about culture).

The Gf-Gc model increasingly drives the construction of cognitive ability tests.  The Kaufman Adult & Adolescent Intelligence Test (KAIT) (Kaufman & Kaufman, 1993), for example, is explicitly organized into Crystallized and Fluid Scales.  The Woodcock-Johnson III   (Woodcock, McGrew, & Mather, 2001) is organized into Cattell-Horn-Carroll factors.

In addition to the Gf and Gc factors, the Cattell-Horn-Carroll theory, which continues to be revised and expanded by various theorists, includes many other factors, some of which are listed below. It is important to remember that, while the factors derived from actual factor-analytic studies are more-or-less objective (depending on the factor analytic method and the sample used), the names of the factors are arbitrary and subjective.  Carroll (1993, p. 644) observes, “The naming of a factor in terms of a process, or the assertion that a given process or component of mental architecture in involved in a factor, can be based only on inferences and makes little if any contribution to explaining or accounting for that process unless clear criteria exist for defining and identifying processes.”  Consider, for example, the so-called “Freedom from Distractibility” factor on the WISC-III (Wechsler, 1991), which, at least under acceptable testing conditions, has little to do with distractibility, much to the confusion of readers and writers of psychological reports.  The misleading name for that factor has stuck for almost 40 years (Cohen, 1959), although the Wechsler Adult Intelligence Scale (3rd ed.) (Wechsler, 1997) uses the term “Working Memory.”  For another example, examiners are often embarrassed when they must explain a large difference between a student’s “Processing Speed” scores on the WISC-III (Wechsler, 1991) and on the Woodcock-Johnson III (WJ III) (Woodcock, McGrew, & Mather, 2001), factors with identical names and apparently very similar content, but often very different scores for the same student.  Much confusion derives from the names assigned to the factors. We must not confuse the factor labels with the actual mental operations that may be involved.  One virtue of the increasing popularity of CHC theory may be agreement on a common nomenclature, ideally, in our opinion, using the more neutral G symbols rather than potentially misleading names for the factors.

GF *

Gf, usually called “fluid intelligence” or “fluid reasoning,” refers to inductive and deductive reasoning with materials and processes that are new to the person doing the reasoning.  The vast majority of fluid reasoning tests use nonverbal stimuli, but require an integration of verbal and nonverbal thinking.  Examples include the Concept Formation and Analysis-Synthesis subtests of the Woodcock-Johnson III (Woodcock, McGrew, & Mather, 2001), Sequential and Quantitative Reasoning on the Differential Ability Scales (Elliott, 1990a) and various matrix tests [e.g., Stanford-Binet Fourth Edition (Thorndike, Hagen, & Sattler, 1986); Raven Progressive Matrices (Raven, 1939; Raven, Court,  & Raven, 1986; and Raven, Court, & Raven, 1983); Differential Ability Scales (Elliott, 1990); and Wechsler Adult Intelligence Scale (3rd ed.) (Wechsler, 1997)].  It has been argued (e.g., Gustafsson (1988) that Gf may be synonymous with g, and Carroll (1993, p. 114) does not rule out this possibility, but Gf is treated as a broad (stratum II) ability in the CHC model.  In the latest CHC model (Flanagan, Ortiz, Alfonso, & Mascolo, 2002) Gf includes four narrow abilities.

GC *

Gc usually called “crystallized” or “crystallized verbal” ability [but called Comprehension-Knowledge on the Woodcock-Johnson III (Woodcock, McGrew, & Mather, 2001], refers to the application of acquired knowledge and learned skills to answering questions and solving problems presenting at least broadly familiar materials and processes.  Most verbal subtests of intelligence scales primarily involve crystallized intelligence.  Subtests of general knowledge and vocabulary are relatively pure measures of crystallized intelligence.  In the latest CHC model (Flanagan, Ortiz, Alfonso, & Mascolo, 2002) Gc includes 12 narrow abilities.

GV *

 Gv involves a range of visual processes, ranging from fairly simple visual perceptual tasks to higher level, visual, cognitive processes. Woodcock and Mather (1989) define Gv in part: “In Horn-Cattell theory, ‘broad visualization’ requires fluent thinking with stimuli that are visual in the mind’s eye . . .” Although Gf tasks are also often nonverbal (e.g., matrix tests), Gv does not include the aspect of dealing with novel stimuli or applying novel mental processes that characterizes Gf tasks.  The WISC-III (Wechsler, 1990) Performance Scale subtests probably measure Gv much more than Gf  (Kaufman, 1996; McGrew & Flanagan, 1996; Willis, 1996), although there might be more Gf the first time a student encounters puzzles similar to Wechsler Performance tasks, when they are still novel to the student (which may occur before the student ever takes a Wechsler scale).  As Kaufman (1994, p. 31) observes with regard to Wechsler profiles, “You get one shot,” after which novel tasks are no longer novel.  The Differential Ability Scales (DAS) School-Age scale (Elliott, 1990a, 1990b) includes a Spatial scale, which measures Gv.  The DAS Nonverbal Reasoning scale actually measures Gf (Keith, 1990).  In the latest CHC model (Flanagan, Ortiz, Alfonso, & Mascolo, 2002) Gv includes 11 narrow abilities including visual memory (MV), which is elsewhere in Gv in Carroll’s (1993) classification. 

Some Gv tasks on tests are contaminated by a visual memory component.  A student with reasonably average visual memory would probably score at the same level on the memory-loaded Gv task as on other Gv tasks, but a student with exceptionally strong or weak visual memory skills might not.  This does not seem to be an issue for groups of students, even for groups of students with specific learning disabilities (C. D. Elliott, personal communication June 22, 2000), but might influence the score of an individual with an extreme strength or weakness in visual memory.  Demands on attention, concentration, short-term memory, and working memory potentially contaminate many otherwise “pure” measures of factors for students with various disorders of attention, concentration, short-term memory, and working memory, such as Attention-Deficit/Hyperactivity Disorder (ADHD).  Many measures of Gv also have time limits and bonus points for fast work.  For example, on the WISC-III, if a child solves every item correctly within the time limit, but does not earn any bonus points for speed, the child’s scaled score will be lower than 10 (50th percentile) after age 10-7 on Picture Arrangement and after age 11-11 on Block Design and Object Assembly.  For some students, examiners may wish to use Gv measures that do not require speed, such as the alternative procedure for the DAS Pattern Construction or the Stanford-Binet IV Pattern Analysis.  Otherwise, a potential strength in Gv might be missed in an examinee who worked slowly and reflectively

Many writers seem to consider Gv a relatively low-level cognitive ability, more perceptual than intellectual.  However, the “fluent thinking with stimuli that are visual in the mind’s eye” may well be a higher level intellectual process on a par with Gc and Gf.  Engineers, auto mechanics, architects, nuclear physicists, sculptors, carpenters, and parts department managers all use Gv to deal with the demands of their jobs.  Measures of Gv have lower correlations with academic achievement and other variables than do measures of Gc and Gf.   However, those lower correlations may reflect the way that school subjects are usually taught and tested.

Ga *

 Ga is auditory processing, such as recognizing similarities and differences between sounds and recognizing degraded spoken words, such as words with sounds omitted or separated (e.g., “tell – own” and /t/ /ě/ /l/ /ě/ /f/ /ō/ /n/ both as “telephone”). Phonemic awareness skills, terribly important for acquisition of beginning reading (e.g., Rath, 2001), are Ga tasks.  There is an interaction between Ga and working memory (a narrow ability within Gsm below) on many phonemic awareness tasks, for example, repeating dictated words with a sound omitted (say “blend” without the /l/) or substituted (say “blend”; now say it again, but say /a/ instead of /e/”) or repeating words with the sounds reversed (e.g., “knife” backwards is “fine”).  Readers are encouraged to take Rath’s (2001, pp. 96-97) “Phonemic Awareness Quiz for Reading Teachers.”  In the current state of the CHC model, there are only two narrow phonemic awareness abilities, Analysis and Synthesis within Ga.  For practical assessment purposes, it is important to further analyze the various phonemic awareness task characteristics as Flanagan, Ortiz, Alfonso, and Mascolo (2002, pp. 507-523) have very helpfully done with reading, writing, math, listening, and speaking tests.  In the latest CHC model (Flanagan, Ortiz, Alfonso, & Mascolo, 2002) Ga includes 14 narrow abilities, some of which are purely auditory [e.g., sound localization (UL)] and others of which are more language-based [e.g., phonetic coding analysis (PC:A), phonetic coding synthesis (PC:S), and speech sound discrimination (US).

Gs *

Gs, or processing speed, refers to measures of clerical speed and accuracy, for example, the Processing Speed subtests of the WISC-III and WJ III.  As noted above, it is often difficult to determine why a particular student achieves radically different scores on the four or five subtests that make up the Processing Speed factors of those two instruments.  The WJ III also includes three tests of academic fluency: reading, writing, and math fluency, each of which may be tapping certain aspects of Gs. In the latest CHC model (Flanagan, Ortiz, Alfonso, & Mascolo, 2002) Gs includes four narrow abilities.

Gf *

 Gt is the speed of reacting, or making decisions, correctly.   The vigilance tests used as part of assessments for ADHD [e.g., Test of Variables of Attention (TOVA, 19…). Conners’ Continuous Performance Test (CPT, 19…), Intermediate Visual and Auditory Continuous Performance Test (IVA, 19,,,)] may assess Gt. In the latest CHC model (Flanagan, Ortiz, Alfonso, & Mascolo, 2002) Gt includes four narrow abilities.

Gsm *

Gsm is short-term or immediate memory.  On the WJ III, Gsm is measured primarily by Memory for Words and Numbers Reversed.  Many tests, including the Stanford-Binet IV, use repetition of dictated sentences as a memory test.  Those tests offer good examples of potential contamination of factor measures by other influences.  For instance, memory for sentences may tap language comprehension more than auditory memory.  Children usually cannot repeat sentences they cannot understand.  Strong language abilities often prop up the otherwise shaky auditory abilities of students repeating dictated sentences.  For example, factor analysis of the Stanford-Binet IV (Sattler, 1992, 2001a) revealed that the sentence memory test was a verbal ability measure more than a memory test.  Students who score much higher or lower on sentence memory than on word memory subtests are often revealing relatively strong or weak oral language abilities.  Repeating dictated digits in the order they were dictated (e.g., Recall of Digits on the DAS) appears to be primarily an auditory memory task (although anxiety and discomfort with numbers might interfere), but repeating dictated numbers in correct, reversed order (e.g., Digits backward on the Wechsler Scales and Numbers Reversed on the WJ III) appears to include a substantial component of visual memory as well as working memory[3] for many students. In the latest CHC model (Flanagan, Ortiz, Alfonso, & Mascolo, 2002) Gsm includes three narrow abilities.

Glr *

 Glr involves memory storage and retrieval over longer periods of time than Gsm.  How much longer varies from task to task.  For example, on the WJ III, Glr can include both relatively short-term tasks, such as learning nonsense names and “reading” rebus symbols for words and relatively longer-term tasks of recalling those rebus symbols thirty minutes to eight days later.  Glr is the ability to store and retrieve information, not the information itself.  In the latest CHC model (Flanagan, Ortiz, Alfonso, & Mascolo, 2002), Glr includes 13 narrow abilities.

Grw *

Grw, or reading and writing abilities, are part of Gc (Cattell & Horn), or the separate domain of knowledge and achievement in Carroll’s (1993) formulation. In the latest CHC model (Flanagan, Ortiz, Alfonso, & Mascolo, 2002), these have been grouped as eight narrow abilities in Grw.

Gq *

Gq, or quantitative knowledge, includes Mathematical Knowledge (KM) and Mathematical Achievement (A3), which are parts of Carroll’s (1993) domain of knowledge and achievement, not his cognitive abilities.  Mathematical Reasoning (RQ) is part of Gf, not Gq.

The last two broad abilities raise the question of the distinction between “ability” and “achievement.”  Carroll (1993, p. 510, emphasis in the original) discusses this problem:  “It is hard to draw the line between factors of cognitive abilities and factors of achievement.  Some will argue that all cognitive abilities are in reality learned achievements of one kind or another.”  Carroll suggests we “conceptualize a continuum that extends from the most general abilities to the most specialized types of knowledges.”   Flanagan, Ortiz, Alfonso, and Mascolo (2002) also quote Carroll (1993, p. 510) and Horn (1988, p. 655), “Cognitive abilities are measures of achievements, and measures of achievements are just as surely measures of cognitive ability,” and reach the same conclusion as Carroll: “Thus, rather than conceiving of cognitive abilities and academic achievements as mutually exclusive, they may be better thought of as lying on an ability continuum that has the most general types of abilities at one end and the most specialized types of knowledge at the other (Carroll, 1993)” (p. 21).  This continuum, of course, tends to make a hash of the IDEA stipulation [§300.541(a)]: “A team may determine that a child has a specific learning disability if— (1) The child does not achieve commensurate with his or her age and ability levels in one or more of the areas listed in paragraph (a)(2) of this section, if provided with learning experiences appropriate for the child’s age and ability levels; and  (2) The team finds that a child has a severe discrepancy between achievement and intellectual ability in one or more of the following areas:  (i) Oral expression.  (ii) Listening comprehension.  (iii) Written expression.  (iv) Basic reading skill.  (v) Reading comprehension.  (vi) Mathematics calculation.  (vii) Mathematics reasoning.”   Flanagan, Ortiz, Alfonso, and Mascolo (2000) address this issue at length in chapters 1, 11, 13, and 14.  Please see also Dumont, Willis, and McBride (2001) and the Severe Discrepancy chapter in this book.           

CHC theory and the McGrew, Flanagan, and Ortiz Integrated Cross-Battery Approach are not, of course, universally accepted.   See, for example, Floyd’s (2002) discussion; Watkins, Youngstrom, and Glutting’s (2002) commentary; and Ortiz and Flanagan’s (2002a, 2002b) reply.

Additional References: *

A “cute”  video on CHC (courtesy of but not by Kevin McGrew)

For additional on-line information regarding CHC theory, click on:

Cattell-Horn-Carroll Theory

See also Flanagan, McGrew, & Ortiz (2000, pp. 24-29); and Flanagan & Ortiz (2001, pp. 5-8), and McGrew & Flanagan (1998, pp. 10-14).

[2]  See also Flanagan, McGrew, & Ortiz (2000, p. 28); Flanagan & Ortiz (2001, p. 6); and Flanagan, Ortiz, Alfonso, & Mascolo (2002, p. 27)

[3] We are using the term “working memory” to refer to a mental “scratch pad” which allows the student to hold data in memory and manipulate those data, for instance repeating digits in reversed order, reciting the alphabet backwards, counting backwards by sevens from 103, or performing mental arithmetic.