4.1 A. Internal CHC structural extensions
During the past decade, significant factor analytic research has been limited primarily to five well- established CHC domains—Gv, Ga, Gsm, Gc, and Gs.
Gv abilities have been cursed by with a schizophrenic relationship with intelligence researchers. Despite inclusion in most all models of human cognitive abilities, and being one of the more studied domains of human cognitive functioning (Carroll, 1993), “spatial abilities have long been relegated to a secondary status in accounts of human intelligence” (Lohman, 1996, p.97).  According to Lohman (1996), Gvs second class status is due, in part, to the fact that: (1) beyond a minimum level of proficiency, Gv abilities do not consistently predict success in school or work, (2) the relations between Gv and outcome criteria are dwarfed when other more powerful predictors (e.g., Gc, Gf) are included in prediction studies, (3) the typical criterion variables used in prediction studies tend to be biased in favor of verbal and language- based measures, (4) existing Gv measures used in studies may be poor measures of visual-spatial functioning, and (5) the typical practice of first entering a g proxy in prediction studies may mask potential important Gv-outcome relations.  The love-hate status Gv has experienced in the intelligence research is also due to the fact that Gv has concurrently been associated with both highly acclaimed and prestigious achievements in demanding professions such as engineering, architecture, physics, chemistry and mathematics, as well as more pedestrian trades such as carpentry, auto mechanics, and technical/industrial occupations (Lohman, 1996; Shea et al., 2001). 
[Note.  However, according to Lohman (1994), tests of spatial abilities are: (1) among some of the best predictors training of machine and bench workers, and air crews, (2) have been moderately associated with grades in engineering and trade schools, and (3) are listed among 84 job categories from the United States Employment Service (1957).]
Recently, Gv has enjoyed a renaissance in status due to the linkage of high Gv abilities with: (1)  higher- order thinking in science, math and the achievement, (2) incremental prediction of performance (above and beyond verbal and quantitative abilities) in gifted and talented populations (Shea, Lubinski & Benbow, 2001), and (3) the observation of creative “insights by means of thought experiments on visualized systems of waves and physical bodies in states of relative motion” (Lohman, 1996, p. 99).  For example, high spatial ability, particularly the ability to visual complex dynamic systems, has been reported to play a prominent role in the accomplishments of such imminent scientists and inventors as Albert Einstein, Michael Faraday, Herman Von Helmholtz, Benjamin Frankin, Francis Galton and Leonardo da Vinci (Lohman, 1996; West, 1991).  As an example, “on several occasions Albert Einstein reported that verbal processes seemed not to play a role in his creative thought.  Rather, he claimed that he achieved insights by means of thought experiments on visualized systems of waves and physical bodies in states of relative motion” (Lohman, 1994, p. 1000).
With the exception of studies investigating the role of Gv in information processing/working memory models (Lohman, 1996), only a handful of investigations have studied the structural characteristics of the Gv domain during the past decade.  Juhel (1991), using Carroll-based exploratory factor methods and procedures in a sample of college students, confirmed the existence of the well documented Visualization (Vz), Spatial Relations (SR), and Visual Memory (MV) abilities (see Carroll, 1993; Lohman, 1979; 1996).  More importantly, contrasts of subgroups categorized as high or low on Vz and MV reinforced the notion that Gv tasks vary as a function of cognitive complexity. Vz abilities were reported to require the most complex cognitive processing (i.e., require greater complex mental manipulations and transformations; load highest on Gv).  MV was found, in a relative sense, to be a lower level (less complex) ability in the domain of visual-spatial abilities.   This finding is consistent with Lohman’s (1979) statement, regarding the narrow Gv abilities of MV, P, and CS, that these “factors consistently fall near the periphery of scaling representations, or at the bottom of a hierarchical model” (p. 126-127). Although MV may be viewed as an ability of lower stature within the Gv domain (e.g., relatively lower g-loadings than Vz and SR), Juhel’s (1991) research suggested that the more complex Gv abilities are partially dependent on, and supported by, MV. 
 Miyake, Friedman, Rettinger, Shah, Hegarty’s (2001) structural equation-based investigation of the relations between measures of information processing and psychometric measures of Gv (Vz, SR, P) reinforces the findings of Juhel (1991).  These investigators hypothesized (and confirmed) that Vz, SR, and P abilities differed as a function of the relative demands each placed on the working memory system, particularly the visuo-spatial sketchpad and executive function components.  Similar to prior research (Carroll, 1993; Lohman, 1979), Miyake et al. (2001) found it difficult to structurally differentiate the Vz and SR factors. However, the Vz and SR factors, as well as the P factor, were clearly differentiated as a function of degree of information processing demands.  Miyake et al. (2001) concluded that Vz, SR and P differed in the degree of executive involvement, with Vz requiring the most and P the least.  It is possible that the higher complexity attributed to Vz and SR tasks is due to a greater use of verbal analytic processing during these task (Justin & Carpenter, 1985). Furthermore, the “three spatial abilities require a substantial degree of visuo-spatial storage, but the maintenance of visuo-spatial representations involved in the performance on these spatial ability tests (particularly the Spatial Visualization and Spatial Relations tests) may be strongly tied to executive functioning or controlled attention. Finally, these relations between the WM-related constructs and the spatial ability factors are substantial. In fact, they are so substantial that, together, the Executive Functioning and Visuo-spatial STM-WM variables were able to essentially fully explain the pattern of the intercorrelations between the three spatial ability factors” (Miyake et al. 2001. p 637).
“Imagery refers to the mental depiction or recreation of people, objects, and events that are not actually present” (Finke & Freyd, 1994, p. 561).  Visual imagery has been linked to a variety of abilities such as: (1) Gf--thinking hypothetically; constructing mental models of complex conceptual systems; “seeing” relationships and solutions to problems, (2) efficient retrieval of Gc information, (3) Gv--mental rotation of objects or patterns, and (4) mental extrapolations involved in complex motor activities (e.g., driving a car; athletic performance) (Finke & Freyd, 1994).  According to Carroll (1993), imagery was not clearly defined by the factor studies available at the time of his review.  Following Carroll’s (1993) recommendation for further IM research, Burton and Fogarty (2003) reported exploratory and confirmatory factor analysis of 26 cognitive ability measures, 5 self-report visual imagery inventories, 7 experimental imagery tasks, and 2 tasks requiring creative imagery.  Consistent with the extant Gv structural literature (Carroll, 1993; Lohman, 1979), support was found for the narrow abilities of Vz, SR, MV, and CS.  In addition, three first-order IM factors (quality, self- report, and speed) were suggested.  The IM (quality) and IM (speed) factors shared moderate amounts of variance with the Vz, SR, MV, and CS factors, while the IM (self- report) factor did not. [Note.   It is very likely that the IM (self-report) factor represents a “method” factor as it was the only factor defined in this investigation by the subjects self-reports.] Burton and Fogarty’s (2003) findings consistent with research that suggests that IM may be a multidimensional construct characterized along the dimensions of generation, vividness, clarity, controllability, transformation and/or maintenance (Kosslyn, 1980; Poltrock & Agnoli, 1986).  Burton and Fogerty’s study reinforces the specification of the visual IM (i.e., the IM quality factor) ability alongside the other major Gv narrow abilities. Left unanswered by this study is whether the IM (quality) and IM (speed) abilities represent the level and rate aspects of the imagery domain.
In the long history of research on individual differences in human cognitive abilities, Ga has played the role of “stepchild” to its elder visual-spatial processing (Gv) sibling.   According to Carroll (1993), auditory abilities have “received little attention in the factor-analytic literature” (p. 364).   Fortunately, interest and research in the Ga domain has increased due to: (1) technological advances that have made research in the Ga domain easier (Stankov, 1994), (2) an increased interest in the psychophysics of auditory perception (Hirsh & Watson, 1996), (3)  an explosion of research focused on the relations between the Ga abilities of phonological processing or phonemic awareness (Phonetic Coding-PC as per Carroll, 1993) and early reading development and reading disabilities (see Bus & van IJzendoorn,1999; Ehri, Nunes, Willows, Schuster, Yoghoub-Zadeh & Shanahan, 2001; McBride-Chang, Chang, & Wagner, 1997; McBride-Chang, 1995, 1996; Metsala, Stanovich, & Brown, 1998 Stahl & Murray, 1994; Stone & Brady,1995; Torgesen, Wagner, Rashotte, Rose, Lindamood, Conway & Garvan, 1999 Wagner, Torgesen, Laughon, Simmons & Rashotte, 1993; Wagner, Torgesen & Rashotte, 1994), (4) the increased  interest in Central Auditory Processing Disorder (CAPD; Ricco & Hynd, 1996) in the professions of  speech-language pathology and audiology, and (5)  the inclusion of the Ga abilities of pitch, rhythm and sound discrimination in Howard Gardner’s (1983) musical and linguistic intelligences.
In 1998, Flanagan and I (McGrew & Flanagan, 1998) were persuaded by a small number of exploratory and confirmatory research studies with young children (Wagner, Torgesen, Laughon, Simmons & Rashotte, 1993; Yopp, 1988)  that Phonetic Coding (PC) should be split into two narrow PC abilities—PC:Analysis (PC:A) and PC:Synthesis (PC:S).   Research during the past decade, which includes an “about face” by Wagner et al. (1993), now largely supports a unidimensional PC ability.
In a longitudinal study of 244 young children (grades K-2), Wagner, Torgesen and Rashotte (1994) specified their previously hypothesized PC:A and PC:S factors in a confirmatory modeling research study.  However, the high latent factor correlations between the two PC abilities proved problematic (high multi-colinearity) when both were included in prediction models.  In a subsequent longitudinal investigation of 216 kindergarten thru fourth grade students, Wagner, Torgesen, Rashotte, Hecht, Barker, Burgess, Donahue & Garon (1997) again reported very high PC:A/PC:S latent factor correlations, with the actual correlation approaching a perfect 1.0 at third grade.  Wagner et al. (1997) concluded that the two factors were representing the same construct and subsequently respecified their model to include a single PC (phonemic awareness) ability.
The unidimensional interpretation of PC was recently echoed by Van Bon and Van Leeuwe (2003) who may have provided the most comprehensive listing of studies (viz., de Jong & van der Leij, 1999; Høien et al., 1995; Holopainen et al., 2000; Lundberg Frost & Petersen, 1988; Mommers, 1987; Muter,  Hulme, Snowling,  & Taylor, 1997; Schatschneider et al., 1999; Stahl & Murray, 1994; Stanovich et al., 1984; Valtin, 1984; Wagner & Torgesen, 1987; Wagner et al., 1997) in support of a unidimensional PC ability.  Van Bon and Van Leewe (2003) further report that their independent reanalysis of Yopp’s (1988) data supported a single PC ability.  The one exception noted in the literature by Van Bon and Van Leeuwe (2003) was the tendency for rhyming abilities to stand separate from PC.  Consistent with this conclusion, Hatcher and Hulme’s (1999) exploratory factor analysis revealed separate rhyming and phonemic manipuation (PC) factors derived from the five phonological measures used in their study of 124 children experiencing reading difficulties.  In their own longitudinal study of 171 Dutch students in the primary grades, Van Bon and Van Leeuwe’s (2003) exploratory and confirmatory analysis of measures of phoneme recognition, blending, counting, deletion, segmentation, and pseudoword repetition and rhyme judgment reinforced the presence of a unidimensional PC ability.
     In a welcome contribution to the internal (structural) and external Ga validity literature, Anvari, Trainor, Woodside and Levy (2002) explored the relations between phonological awareness (PC), music perception, and early reading in a sample of 100 four- and five-year old children.  Consistent with the above reviewed literature, factor analyses of the four Anvari et al. (2002) PC measures (rhyme generation, oddity, blending, and the Rosner task) revealed a single factor at both age levels.  Exploratory analysis of the music tasks (same/different melody, same/different chord, chord analysis, same/different rhythm, and rhythm production tasks) revealed a single music factor for four-year olds and two factors (pitch perception; rhythm perception) for five-year olds.  The musical factors appear to measures aspects of the Musical Discrimination and Judgment (U1, U9) and Sound- Frequency Discrimination (U5) reported by Carroll (1993).  Moderate factor correlations (.33 to .59) supported the independence of the music perception and PC ability factors.  Further support for separate music perception and PC abilities was the intriguing finding that “music perception skill predicts reading even after the variance shared with phonemic awareness is removed. This suggests that phonemic awareness and music perception ability tap some of the same basic auditory and/or cognitive skills needed for reading but that they each also tap unique processing skills” (Anvari et al., 2002, p.127).
In the final structurally relevant Ga study, Schatschneider, Francis, Foorman, Fletcher and Mehta (1999) investigated the dimensionality (via factor and IRT analyses) of a battery of seven phonological awareness measures in a large kindergarten to second grade sample (n = 945).  Results of a confirmatory factor analysis supported the unidimensionality of the PC tasks.  A test of the Wagner et al. (1993) PC:A/PC:S two-factor correlated model produced an extremely high correlation (r = .95), again suggesting a single PC construct.  The most intriguing finding came from the IRT analysis of a combined pool of all the items.  IRT analyses of the PC items revealed a wide range of variation in item difficulty that appeared to be a function of item tasks demands.  Schatschneider et al., (1999) suggested that the different types of PC tasks commonly used in most reading research differ not so much in the measurement of different underlying traits or constructs, but instead, represent different tasks that vary developmentally along a common single latent trait ability continuum.
Are Memory Span (MS) and Working Memory (MW) the same or different?  Ever since Kyllonen and Christal (1990) published “Reasoning Ability is (little more than) working- memory capacity?!” intelligence scholars have been enamored with the construct of working memory (MW; see Table 3).  Before summarizing the glamorous MWàGf or MWàg research (later in this chapter), a more fundamental question is whether MS is different from MW.  Three studies during the past four years suggest that MS and MW are distinct constructs.
In a sample of 133 university students, Engle, Tuholski, Laughlin and Conway (1999) used confirmatory factor analytic methods to test if three simple short-term storage tasks and three tasks requiring complex processing and storage were best represented by a single memory factor or an alternative two-factor (i.e., MS and MW) model.  The two- factor model provided a better fit to the data and also suggested a MS/MW latent factor correlation of .68.  Also using CFA methods in two childhood samples (ages 7-13 years; n = 155, 132), Kail and Hall (2001) found support for separate MS and MW factors, with latent factor correlations of .32 and .36.  Finally, in a sample of 120 young adults who were administered four simple MS storage tests and three complex MW tests, Conway, Cowan, Bunting, Therriault and Minkoff’s (2002) CFA supported the existence of separate, but highly correlated (.82) MS and MW tests.
The wide range of latent factor MS/MW correlations (.32 to .82) reported across these three studies is difficult to interpret given the differences in the study samples and measures used. To minimize the effect of sampling error and measurement differences, I returned to the WJ III three-stratum CFA model studies reported in the WJ III technical manual (McGrew & Woodcock, 2001) and respecified separate MS and MW correlated factors.  MS was operationally defined by the WJ III Memory for Words and Memory for Sentences tests, while MW was defined by the WJ III Auditory Working Memory, Numbers Reversed, Understanding Directions, and Sound Awareness tests. [Note.  Memory for Sentences and Understanding Directions were also specified to have loadings on Gc.  Sound Awareness had a loading on Ga.]  The latent factor correltions, across five large nationally representative samples that differed by age (6-8; 9-13; 14- 19; 20-29; 40- 90+ years of age) were .67, .79, .82, .84, and .80.  These findings mirror the age trend patterns in the other three studies (i.e., children displayed lower MS/MW correlations than adults), but differ in absolute magnitude.  It appears that MS and MW are strongly correlated, yet separate constructs that become more highly correlated with increasing age.
Should working memory be considered a CHC trait/factor?
.According to Baddeley (2001), the construct of working memory (MW) was first proposed in 1960 by Miller, Galanter and Pribram.  The first multiple component conceptualization was provided by Baddeley and Hitch (1974) who proposed that MW consisted of three components: the visuo-spatial sketchpad, phonological loop and central executive.  MW has been referred to as the “mind’s scratchpad” (Jensen, 1998, p. 220) and most models postulate that it consists of a number of subsystems or temporary “buffers.”  The phonological or articulatory loop processes auditory- linguistic information while the visuo-spatial sketch/scratchpad is the temporary buffer for visually processed information.  Most models hypothesize that the central executive mechanism coordinates and manages the activities and processes in working memory.  Baddelely (2000, 2001) has recently proposed the addition of a fourth component, namely, the episodic buffer.  [Note.  See Baddeley (2001) for an overview of the history and evolution of the Baddeley working memory model.]  Space limitations do not allow for a detailed description and definition of the working memory model and its components, nor is such understanding necessary in the current context.The research literature regarding the MW construct is voluminous and attests to the importance of MW as an important psychological construct.
Although Flanagan and I (McGrew & Flanagan, 1998; Flanagan et al. 2000) previously argued for MW’s preliminary “membership” status in the CHC taxonomy, this recommendation was based primarily on logical and rational considerations. Our recommendation was tempered by Carroll’s (1993) skepticism toward the working memory construct.  Carroll (1993) stated that “although some evidence supports such a speculation, one must be cautious in accepting it because as yet there has not been sufficient work on measuring working memory, and the validity and generality of the concept have not yet been well established in the individual differences research” (p. 647). 
Although MW is undeniably a valid and important psychological construct, this does not necessarily mean MW is a factor analytic, latent trait, individual differences type construct similar to the 60+ narrow cognitive abilities that are the cornerstone of the CHC taxonomy (see Table 3).  According to Carroll (1993), “evidence for the existence of a latent trait derives from a demonstration that a number of similar task sets are highly correlated, or in factor- analytic terms, have weights on the same factor.  A factor, if it is well established in a number of empirical investigations, is in essence a latent trait reflecting differences over individuals in ability characteristics or potentials” (p. 22).  According to Carroll’s definition, the trait-factor evidence for MW is still questionable.
First, the three studies (Conway et al., 2002; Engle et al., 1999; Kail & Hall; 2001) cited in support of separate MS and MW factors either restricted their variable pool to only MS and MW test indicators or used confirmatory methods that specified apriori MS and MW factors.  In a variety of unpublished exploratory factor analyses of the variables described for the WJ III CFA studies (McGrew & Woodcock, 2001), as well as an exploratory analyses using Carroll’s EFA software, the current author never found the two primary WJ III MW tests (Numbers Reversed and Auditory Working Memory) to form a factor distinct from the MS tests (Memory for Words and Memory for Sentences).  Instead, in all analyses across all ages, a clear MS factor is defined primarily by high loadings by the MS tests.  The MW tests were consistently factorial complex.  For example, in a Carroll EFA of 50 WJ III tests and subtests, at the first-order level this author found an MS factor defined primarily by Memory for Words (.80) and Memory for Sentences (.47; also .35 on Gc).  Numbers Reversed loaded on two factors (MS = .13; Quantitative Reasoning-RQ = .21).  The best WJ III operational measure of MW, Auditory Working Memory, also loaded on RQ (defined primarily by Number Series and Number Matrices tests) as well as MS (.26) and Ga (.27).  When a complete set of CHC indicators are present in an EFA study, it appears that MW measures do not represent a distinct trait-like MW factor construct, but instead are factorially complex mixtures of abilities.  This should not be unexpected given the multicomponent conceptualizatioin of MW.  In the case of the WJ III Auditory Working Memory test, one could speculate that the RQ component reflects the manipulation of stimuli (numbers) in the visuo-spatial sketchpad (or use of part of the executive function component that is typically associated with Gf abilities), MS the memory span component, and Ga the use of the phonological loop to facilitate performance. 
Based on the theoretical, logical, and empirical evidence, this author concludes that working memory (MW) is indeed a multicomponent cognitive construct of significant importance, but, it should not be considered to be similar to the other 60+ narrow factor-based trait-like individual difference CHC constructs identified in the psychometric literature.  This conclusion is consistent with Kyllonen (1996) who stated that “the working memory capacity construct does not depend on factor analysis for its identification.  The working memory system was developed theoretically not as a label for an individual-differences factor, but rather as a constuct to explain experimental results in the memory literature” (p.73),  This conclusion does not negate the practical and theoretical importance of measures of working memory.  Obviously, how amalgam constructs like working memory are integrated in the CHC taxonomy needs further deliberation and discussion.  In order to decompose and measure the various processes underlying working memory, additional research focused on the subcomponents of working memory is needed (e.g., see the research of Süß, Oberauer, Wittmann, Wilhelm & Schulze, 2002; Oberauer, Süß, Schulze, Wilhelm & Wittmann, 2000).
One of the most frequent methods used to assess Gc is to ask individuals to define or solve problems (e.g., antonyms) that require the use and understanding of words that vary in frequency in the general culture. Vocabulary, general information, and concepts associated with specialized occupations/professions and knowledge domains are typically avoided in Gc assessment or research.  High performance in one or more of the narrow specialized knowledge domains is instead associated with the constructs of wisdom or expertise (Hunt, 2000).  Typically a dark and deep line is drawn in the psychometric sand between the measurement of generalized (general cultural) and specialized domain-specific knowledge. 
Research regarding the nature and structure of the Gc domain has languished as researchers have focused on “romancing the domains” with more desirable appeal, such as Gf and Gv.  According to Hunt (2000):
Gc is the wallflower of the intellectual trio. Researchers want to go dancing (or to be less lyrical) to understand Gf and Gv. After all, is it not more important to study things that are fluid and dynamic than to study something that is crystallized and just sits there in memory? Besides, if Gf and g are identical, studying Gf kills two birds with one stone. Studies of Gv can be justified by dramatic examples of its importance in glamorous situations (e.g., aviation) or because of its fairly close ties to biology, and especially male-female differences. Like the wallflower it is, Gc languishes in the corner. How can you start a controversy about who acquires and uses culturally defined problem-solving methods? Who, but a few educators, are interested in such nearsighted, bookish behavior? (p. 124)
Anticipating Hunt’s (2000) admonition to researchers “to ask Gc to put away the horn-rimmed glasses, put on a party dress, and take turn on the dance floor” (p.124), Rolfhus and Ackerman (1999) investigated the relations between traditional measures of Gc, a large collection (n = 20) of specialized knowledge tests, and traditional cognitive measures of spatial and numerical abilities.  [Note.  The Rolfhus and Ackerman (1999) knowledge tests were in the domains of American government, history, and literature and art, astronomy, biology, business/management, chemistry, economics, electronics, geography, law, music, physics, psychology, statistics, technology, tools/shop, western civilization, and world literature.]  In a university sample, these researchers first factored the 20 knowledge tests with the software and procedures employed by Carroll (1993).  Four stratum I knowledge ability factors were found (Humanities, Science, Civics and Mechanical) which were, in turn, subsumed by a broad second- order General Knowledge (Gkn) factor.   The Rolfhus and Ackerman narrow knowledge factors are very similar to the Information about Culture (K2), Science (K1), and Mechanical and Technical Knowledge (MK) narrow abilities reported in Chapter 12 (Abilities in the Domain of Knowledge and Achievement) of Carroll (1993).
Of particular interest was the finding that the broad verbal (Gc) and knowledge (Gkn) factors correlated at a moderate level, a level which indicated that Gc, as typically assessed, was related to, but was independent of Gkn.  It is doubtful that a separate broad Gkn ability would be present at younger developmental levels given the large source of common educational variance shared by children vis-à-vis the cultural homogenizing mechanism of schooling. However, at least by young adulthood, and possibly during high school, a Gc/Gkn distinction appears viable.  The Gc/Gkn distinction is consistent with Cattell’s (1971/1987) notions regarding Gc where he wrote that crystallized intelligence (Rolfus & Ackerman, 1999):
must become different for different people.  If [individuals’ learning experiences] are sufficiently varied and lack any common core, the very concept of general intelligence begins to disappear.  An effort to measure Gc in practice might amount to producing as many tests as there are occupations. (p. 144)
Collectively, the knowledge abilities catalogued by Carroll (1993), the research of Rolfhus and Ackerman (1999), and Hunt’s (2000) wisdom (i.e., domain- specific knowledge in intelligence theory and research), argues for the inclusion of a broad Gkn domain that emerges and “breaks off” from Gc during adulthood.
[Note.  Although prior to the time frame for the current review, Kyllonen and Christal (1990), in four separate samples, previously established the validity of a general knowledge domain with confirmatory factor analysis methods.  Both Kyllonen and Christal (1990) and the Ackerman research group have used Gk as the abbreviation for broad general knowledge.  Given that Gk has also been used to designate a broad general kinesthetic ability (discussed later in this chapter), one of the two abbreviations needed further specification.  Gkn was choosen to replace Gk for general knowledge.  Gk was selected to remain “as is” for general kinesthetic ability]
General Knowledge (Gkn) can be defined as an individual’s breadth and depth of acquired knowledge in specialized domains that do not represent the general universal experiences of individuals in a culture.  In our highly specialized society, knowledge is not a unitary entity, especially at the higher levels of functioning and mature adulthood (Hunt, 2000).  Gkn abilities result from domain-specific experiences and training and typically “depend on regular, frequent, and systematic practice and training over at least a decade” (Gilhooly, 1994, p. 638).  The primary distinction between Gc and Gkn is the extent to which acquired knowledge is a function of degree of general cultural universality. Gc primarily reflects general knowledge accumulated via the experience of cultural universals.  Gkn reflects deep specialized domain- specific knowledge developed through intensive practice (over an extended period of time) and the maintenance of the knowledge base through regular practice and motivated effort (Horn, 1998; Horn & Masunaga (2000). 
Similar to Gc, Gkn abilities can be categorized as both declarative (static) and procedural (dynamic) knowledge.  Declarative or explicit knowledge refers to knowledge "that something is the case, whereas procedural or implicit knowledge is knowledge of how to do something" (Gagne, 1985, p. 48). Declarative knowledge is consciously known and can typically be communicated by the “knower” (via spoken or written language, or, a specialized code, such as music notation). Although procedural knowledge can be demonstrabled in behavior, it is often difficult to explictly communicate (is not at a conscious level of awareness) (Gilhooly, 1994, p. 637).  One manner in which procedural knowledge is conceptualized is in the form of schemas, which can be thought of as well “organized methods of problem solving” (Hunt, 1999, p. 21) that emerge from cumulative experience.  A psychologist’s knowledge of the definitions of the broad CHC abilties (see Table 3) would reflect declarative knowledge, while the psychologist’s ability to instantly recognize and interpret the meaning of a specific pattern of CHC ability scores from an intellectual assessment would require procedural knowledge (i.e., CHC intelligence interpretation schema).  The empirically identified narrow Gkn abilities are listed in Table 3.  [Note.  The current author took the liberty, based on a review of Carroll (1993) and the recent Gkn research literature, to add certain narrow abilities previously reported by Carroll (but which have not been included in most contemporary publications), and to move some that have previously been listed under Gc.] The degree of correlation between Gkn narrow abilities will likely be a function of the extent to which expertise within one domain overlaps with expertise in another. 
The positing of a broad Gkn ability separate from Gc (during adulthood) may facilitate the bridge between CHC and information processing theories vis-à-vis a common focus on the development of expertise.  Expertise involves the acquisition, storage, and utilization of both the implicit (tacit) and explicit knowledge in a field “where domain refers to a knowledge base and field to the social organization of that knowledge base” (Sternberg, 1998).   For example, a psychologist with expertise in psychometrics would likely have a well developed explicit knowledge of the facts, formulas, principles, statistics, and major ideas of the domain of psychometrics (e.g., SEM and IRT theory and methods). The person’s implicit or tacit knowledge might constitute unspoken information regarding whom to consult for a specific technical question, which federal agency is likely to have the most relevant grant monies, and which professional conferences provide the best networking for acquiring new project contracts.
Horn and Masunaga (2000) have recently studied the construct of expertise from the perspective of CHC theory.  For example, Horn and Masunaga (2000) hypothesized that the “reasoning involved in exercise of expertise is largely knowledge based and deductive, in contrast to reasoning that characterizes Gf, which is inductive” (p. 145).  Furthermore, reflecting a new CHC-based perspective from which to conceptualize expert “performance,” Horn and Masunaga (2000) concluded that:
The superior performance of experts is characterized by a form of long-term working memory (LTWM).  Within a circumscribed domain of knowledge, LTWM provides the expert with much more information in the immediate situation than is available in the system for short-term retention that has been found to decline with age in adulthoood.  LTWM appears to sublimate a form of deductive reasoning that utilizes a complex store of information to effectively anticipate, predict, evaluate, check, analyse, and monitor in problem- solving within the knowledge domain.  These abilities appear to characterize mature expressions of intelligence ( p. 152).
Speed abilities (Gs, Gt, Gps)
Mental quickness as an indicator of a bright or intelligent person has stood front- and-center in the study of human cognitive abilities for decades (Nettelbeck, 1992, 1994; Nyborg, 2003; Stankov & Roberts, 1997).  According to Nettelbeck, two different perspectives have dominated the study of mental processing speed.  The “speediness” perspective is that most associated with applied intelligence batteries and is defined by the quickness in performing tasks of trivial difficulty or tasks that have been over-learned.  Broad cognitive processing speed (Gs) can be defined as the ability to automatically and fluently perform relatively easy or over-learned cognitive tasks, especially when high mental efficiency (i.e., attention and focused concentration) is required (McGrew, 1993).  Woodcock (1993) has likened Gs to the opening or closing of a valve in a water pipe.  When the valve is wide open, the rate of flow increases (high cognitive processing speed).  When the valve is only partially open, the rate of flow is lessened (lower Gs). The narrow (stratum I) abilities subsumed by Gs, which reflect the integration of recent factor analytic research (discussed below), are listed in Table 3.
The second mental speed perspective is associated with experimental paradigms that employ chronometric measures of reaction and inspection time (Deary, 2003; Nettelbeck, 1994, 2003).  The chronometric approach is based on the idea that “progress can be made in understanding differences in human intelligence if it can be shown that there are individual differences in basic cognitive processes that are correlated with higher level abilities as measured by mental tests” (Deary & Stough, 1996, p. 599).  Carroll and Horn both recognized this second aspect of mental quickness in their respective models. Carroll (1993) included reaction and decision time abilities under a broad Decision/Reaction Time or Speed (Gt) ability.   Horn’s (Horn & Masunaga, 2000) analogous ability is called Correct Decision Speed (CDS), and is typically measured by recording the time an individual needs to provide an answer (either correct or incorrect) to a variety of tasks.  Conceptually, Horn’s CDS appears to represent a narrower ability than Carroll’s more encompassing Gt. Conceptually, CDS, as defined by Horn, could easily fit under Carroll’s Gt. The narrow (stratum I) abilities subsumed by Gt, which reflect the integration of recent factor analytic research (discussed below), are listed in Table 3.
More recently, both Gs and Gt have been investigated as key variables in explaining higher-level complex cognitive processing (e.g., Gf, g) (Kail, 1991; Lohman, 1989).  A pivotal concept in information processing models is that human cognition is constrained by a limited amount of processing resources, particulary in working memory.  "Many cognitive activities require a person's deliberate efforts and that people are limited in the amount of effort they can allocate.  In the face of limited processing resources, the speed of processing is critical because it determines in part how rapidly limited resources can be reallocated to other cognitive tasks" (Kail, 1991, p. 152).  In other words, faster processing of information permits reasoning to reach completion before the requisite information is lost. 
 Although a plethora of research studies have studied mental speed during the past decade, “factor analytic evidence concerning the status of a range of time-dependent constructs has been either piecemeal or nonexistant” (Roberts et al., 2000, p. 346).  Unanswered questions remain such as  "how many different speed abilities exist...what is their position in the hierarchy-that is, are they at the same stratum as broad organizations of the Gf/Gc theory or should they be placed at different strata?" (Stankov, 2000, p. 39).  Attempts to answer these questions have been the focus of the largest number of in-depth CHC- related factor analysis investigations during the last decade.  This focus is appropriate given the "general lack of clarity regarding different aspects of speeded processing" (Ackerman, Beier, & Boyle, 2002, p. 569).  Also contributing to this lack of clarity has been the nearly universal omission (by most authors since 1993) of one of the three different broad speed factors presented in Carroll’s seminal treatise.
In addition to Gs and Gt, Carroll (1993) reported "a third category of second- order speed factors is what will henceforth be symbolized as Gp or 2P, interpreted as General Psychomotor Speed, in that it is primarily concerned with the speed of finger, hand, and arm movements, relatively independent of cognitive control" (p. 618).  The influence of psychomotor speed in speeded tests in intelligence batteries (e.g., Wechsler Coding/Digit Symbol; WJ III Visual Matching; Flanagan et al., 2000) and the importance of sensory-motor functions in neuropsychological assessment (see Lezak, 1995 and Dean & Woodcock, 2003) dictates the need to recognize the complete speed trilogy (Gs, Gt, Gps), as well as to include the broad domain of psychomotor abilities (Psychomotor Ability; Gp).  All speed and psychomotor abilities summarized by Carroll are represented in Figure 2.
[Note.  Gps is used to designate the Broad Psychomotor Speed domain instead of Gp as used by Carroll (1993).  This modification is due to the addition of a broad Psychomotor Ability domain (presented in a special chapter by Carroll) in the current chapter.  Gps (General psychomotor speed) and Gp (General psychomotor ability) are more logical factor codes.
It is important to note that the psychometric abilities presented by Carroll, which are included in Figure 2, most likely represent only a small portion of the complete domain of psychomotor abilities.  Carroll’s review did not deliberately attempt to review the extant psychomotor ability literature.  See Carroll (1993) for his discussion and references to other sources.]
In 1979, Ekstrom, et al., (1979), as part of the historical factor reference kit research, questioned whether more than one perceptual speed factor existed. Approximately 20 years later, a series of studies by Ackerman and colleagues (Ackerman et al., 2002; Ackerman & Cianciolo, 2000; Ackerman & Kanfer, 1993) suggest that Ekstrom et al. (1979) were correct.  The Ackerman group has demonstrated that the traditional Perceptual (clerical) Speed (P) ability may rest at the apex of hierarchy that includes a number of lower-order perceptual speed abilities. The Ackerman group has presented evidence for four different P factors, including the ability to: (a) quickly recognize simple visual patterns (Pattern Recognition; Ppr), (b) scan, compare, and lookup stimuli (Scanning; Ps), (c) perform tasks that place significant demands on immediate short-term memory (Memory; Pm), and (d) perform pattern recognition tasks that impose additional cognitive demands such as spatial visualization, estimating and interpolating, and heightened memory span loads (Complex; Pc).   [Note.  The abbreviations used for the Ackerman Perceptual Speed factors were developed for this document by the current author]
Although using different factor names than the Ackerman group, O'Connor and Burns (2003) presented factorial evidence for Perceptual Speed and Visualization (the time needed to complete tasks that included complex visualization of stimuli) factors that bear resemblance to Ackerman's Pattern Recognition (Ppr) and Complex (Pc) factors, respectively.  Additionally, Stankov and colleagues (Stankov, 2000; Stankov & Roberts, 1997) reported an ability to perform speeded visual or auditory perceptual tasks (Tv/a) that resembles components of the Ackerman Pattern Recognition (Ppr) and Complex (Pc) Perceptual Speed abilities.  In the model presented in Figure 2, these findings are reflected vis-à-vis the reclassification of Perceptual Speed (P) as an intermediate ability lying between the broad (stratum II) and narrow (stratum I) abilities.  The four lower-order perceptual speed abilities (Ppr, Pm, Ps, Pc) are placed at the narrow ability level.
An additional proposed revision to the CHC speed hierarchy is the movement of the Rate-of-test Taking (R9) narrow ability to an intermediate level between stratum I and II.  The rational for this reclassification (see Figure 2) is twofold. First, when attempting to classify the speeded psychometric tests in most intelligence batteries, McGrew and colleagues (McGrew, 1997; McGrew & Flanagan, 1998; Flanagan et al., 2000) found it difficult not to classify all speeded tests as measures of R9.  Second, a closer reading of Carroll (1993) suggests that R9 is an ability that cuts across speeded tasks in multiple domains.   Carroll (1993) stated that the R9 factor did "not appear to be associated with any type of test content" (p. 475) and "the speed factors associated with the major dimensions of level abilities may be thought of as factors of 'rate of test taking' " (p. 508).  Furthermore, Stankov and colleagues (Stankov, 2000) identified a similarly described higher-order factor (Psychometric Time; PT) that subsumed a number of lower-order factors that varied across other broad CHC ability domains (e.g.,  time spent in working on inductive reasoning tasks; time spent in working on visual and auditory perceptual tasks).  In their empirically-based speed hierarchy, Roberts and Stankov (1998) located the PT factor, a factor which has also been interpreted by others (O’Connor & Burns, 2003) as a test-taking speed ability, between the broad and narrow strata.  Support for the general Stankov speed hierarchy has been provided by O’Connor and Burns (2003) who, based on the factor analysis of 18 speeded variables, concluded that  the “data presented here are highly supportive of the model of mental speed proposed by Roberts and Stankov (1999) (p. 722).  The similarity of Carroll's R9 and Stankov’s higher- order PT factors argues for the placement of R9 as an intermediate ability between broad and narrow stratum (see Figure 2).
An additional proposed modification to Carroll's 1993 model is the listing of the Speed of Reasoning (RE) narrow ability under both Gf and Gs.  The finding of a "time spent on inductive reasoning tasks" (Ti) factor under the Roberts and Stankov (1998) higher-order PT factor suggests that RE may tap more Gs than originally suggested.   Evidence supporting the influence of speeded variables during complex task performance (e.g., Gf) has been provided by a diverse array of intelligence researchers (Sternberg, 1977;  Jensen, 1987; Reed & Jensen, 1991, 1992; Vernon, 1987). A recent example is represented by Verguts, De Boeck and Maris’ (1999) experimental investigation of performance on the Ravens Advanced Progressive Matrices (APM).  Verguts et al. (1999) presented evidence in support of rule generation speed in solving complex reasoning tasks.
Rule generation process plays a crucial role in solving the APM items. If (APM) rules are compared with balls in an urn, this means that people sample balls from an urn. Individual differences in the generation process can be thought of as sampling from different urns (qualitative differences) or at different rates (quantitative differences)…Given a limited time to solve the test, and given that the ‘different urns effect’ is cancelled out, this implies that fast persons (fast in the sense of generating many possible rules in a limited time) have a higher probability to solve a particular item correctly (p. 330).

The similarity between Carroll’s RE ability, Stankov and Roberts Ti ability, and Verguts et al. (1999) rule generation speed ability, collectively suggest that Speed of Reasoning (RE) should play a more prominent role in contemporary CHC research and practice.  Findings parallel to the Gf/RE pairing are also present in the domain of Grw.  Carroll (1993), who categorized most all reading and writing abilities as Gc, placed Writing Speed (WS) under Gps due to the obvious speeded motor component.  In well designed confirmatory studies conducted on large nationally representative samples (McGrew & Woodcock, 2001), tests requiring simple speeded writing (WJ III Writing Fluency) and reading (WJ III Reading Fluency) demonstrate dual factor loadings on both broad Grw and Gs factors.   These findings are consistent with Carroll’s (2003) subsequent interpretation of a combined exploratory and confirmatory factor analysis of the WJ-R norm data where Carroll reports that the WJ-R Writing Fluency test demonstrated salient loadings on Gs and a “Language” factor (similar to Grw).  As a result, both Reading Speed (RS) and Writing Speed (WS) are included in the speed hierarchy presented in Figure 2.
The above proposed revisions to the CHC model are echoed by O’Connors and Burns (2003) who stated that “the inference drawn is that if a diverse battery was administered, there may be speed factors associated with each of the second order factors defined in Gf–Gc theory” (p.  722). Stankov and Roberts (1997) suggested the same hypothesis when they concluded that “the possibility cannot be ruled out that there may be as many disparate mental speed factors as there are factors among measures based on accuracy scores” (p. 73). Bates and Shieles (2003) arrived at the same conclusion when they stated:
just as general effects on computational speed underping g, these additional group factors are also explained by variance in speed, but that the particular groups factors such as verbal and visuo-spatial reflect parcelated speed effects: speed variance reflected not across the whole brain but in a restricted set of processing modules. Some support for this notion is found in the already demonstrated finding that most or all of the abilities identified by Carroll (1993) are correlated with speed measures. Thus, for instance,‘‘fluid’’ ability is related to speed of reasoning, ‘‘crystallized’’ intelligence to reading speed, visual perception/spatial ability to perceptual speed, ideational fluency with retrieval ability, test-taking speed with cognitive speed, and, of course, reaction time with processing speed. The two abilities without a named speed correlate are memory and learning, and auditory perception. But of course working memory is associated with speed of rehearsal…and a growing literature supports a direct auditory analogue of IT for auditory stimuli (p. 284). [Note. See Parker, Crawford,  & Stephen (1999) for an example of research regarding auditory inspection time.]
There is little doubt that intelligence scholars have been enamored with the measurement of speed of basic information processing as measured by Reaction Time (RT) and Inspection Time (IT) paradigms (Roberts & Stankov, 1997; Nyborg, 2003).  [Note.  The reaction and inspection time literature is too voluminous to treat in this chapter. See Deary, (2003) and Nettelbeck, (2003) for recent summaries.]  Literature reviews (Grudnik & Kranzler, 2001; Kranzler & Jensen, 1989; Nettelbeck, 1987) have established the relationship between IT and psychometric g in a range for .30 to .50 (Stankov & Roberts, 1997). Despite this wide interest, researchers have been unable to reach a consensus on what RT and IT are measuring (Deary, 2000) and what implications these measures have for intelligence theory (Stankov & Roberts, 1997) and for applied practice (e.g., education) (Ackerman & Lohman, 2003). 
When traditional speeded psychometric measures are factored together with measures of reaction and inspection time (RT/IT), relatively robust and separate reaction time (RT) and movement time (MT) factors emerge (O'Connor & Burns, 2003; Roberts & Stankov, 1998; Stankov, 2000; Stankov & Roberts, 1997).  The RT/MT dichotomy reflects the two phases of reaction time as measured by various elementary cognitive tasks (ECTs) (see summaries by Deary, 2003; Nettelbeck, 2003). 
Given the robust finding of separate RT and MT components across different reaction time paradigms, and the emergence of distinct higher-order RT and MT factors that subsume lower- order reaction time factors in empirical studies (see Roberts & Stankov, 1999; Stankov, 2000), a logical, theoretical, and operational decision was made to classify the RT and MT factors as intermediate factors between the broad and narrow ability strata (see Figure 2).  An intriguing set of findings warranting future research are the reported significant correlations between DT and broad memory (Gy as per Carroll, 1993) and reasoning (Gf),  and MT with Ga (Roberts et al., 2000).  The Ga/MT correlation “is most interesting because it suggests possible links among natural tempo, psychomotor performance, and audition” (Roberts et al., 2000, p. 351).
In a study designed specifically to evaluate the role of IT in structural models of intelligence, Burns and Nettelbeck (2003) conducted a Carroll-type exploratory factor analyses of chronometric IT measures together with select tests of Gsm, Gs, Gv, and Gf from the WJ-R and WAIS-R.  These exploratory analyses were followed by confirmatory factor methods.  The results unambiguously found that IT loaded on the psychometric broad Gs processing speed factor. IT did not load on any other first-order CHC factors.  Burns and Nettelbeck (2003) concluded that “IT, to be sure, somehow taps the same processes as those that contribute to performance on tests of clerical speed” (p. 249).
Finally, although using different terminology, the research of Stankov and colleagues (Roberts & Stankov, 1998; Stankov & Roberts, 1997; Stankov, 2000) suggests that a model of human cognitive abilities that includes a general speed ability (g-speed; see Figure 2) at the same level as g is plausible. According to Stankov (2000), “the structure of mental speed may be as complex as the structure of all other cognitive abilities and the Gt factor may analogous to a putative general factor based on accuracy scores (i.e., psychometric g)” (p. 41).