2.2 B. 1st Generation Gf-Gc Assessment
The integration of the Cattell-Horn Gf-Gc and Carroll three-stratum theories under the common CHC framework, and more importantly, the subsequent impact of CHC theory on the applied field of intellectual test development and assessment, was due to a number of “bridging” events that occurred between 1985 and today.  Only the major developments that resulted in the “cross- fertilization” of knowledge from the leading scholars in intelligence with that of applied test developers, or events that accelerated and/or changed the direction of the theory-to-practice fertilization, will be highlighted next..
Cattell-Horn Gf-Gc theory "discovered"
By the mid to late 1980’s, John Horn, a student of Cattell’s, had concluded that the available research supported the presence of at least six to seven additional broad “G” abilities beyond Gf and Gc (see section B in Table 1).  According the Horn and Noll (1997), the Cattell-Horn Gf-Gc theory evolved from a lengthy and systematic program of structural (factor analytic) research by Cattell and Horn (Catell & Horn, 1978; Hakistian & Catell, 1978; Horn, 1968, 1976, 1988, 1989; Horn & Catell, 1966, 1967; Horn & Bramble, 1967; Horn & Stankov, 1982; Rossman & Horn, 1972).  The contribution of the Cattell-Horn Gf-Gc program of research to the development of psychometric theories of intelligence is impressive.  During this same time period, Jan-Eric Gustafsson (1984, 1988) was similarly evaluating Gf-Gc models that included, in addition to a higher- order general intelligence (g) factor, a variety of Gf-Gc flavored broad abilities.  John Carroll was also publishing glimpses of his eventual three-stratum model of intelligence (Carroll & Maxwell, 1979; Carroll, 1983, 1985).  Yet, at a time when the leading intelligence scholars were being drawn faster and faster toward the center of a psychometric vortex that would reveal a more-or-less common taxonomic structure of human cognitive abilities, the field of applied intelligence testing was largely ignorant of these developments. The eight-to-nine broad Gf-Gc ability model had yet to hit the radar screen of practicing psychologists.
The seed that eventually blossomed and  introduced CHC theory in the field of applied intelligence testing, was planted, in 1985, in the mind of one applied psychoeducational test developer of the times (viz., Richard Woodcock).  The seed was planted during a presentation on Gf-Gc theory by John Horn at a 1985 conference honoring Lloyd Humpreys (Schrank, Flanagan, Woodcock & Mascolo, 2002).   Hearing Horn’s Gf- Gc presentation resulted in Woodcock’s decision to consider the multiple ability Gf-Gc theory as the model for a revision of the 1977 Woodcock-Johnson Psychoeducational Battery (WJPEB; Woodcock & Johnson, 1978; see sections C1-C2 in Table 1). The psychometric intelligence theory-to-practice bridge was now under construction.
Cattell-Horn Gf-Gc theory overview
By the late 1980’s and early 1990’s, scholars who routinely published in the rarified air of the journal Intelligence had generally recognized the Horn–Cattell Gf-Gc model as the best approximation of a taxonomic structure of human cognitive abilities. For example, Carroll (1993) stated, after his seminal review of the extant factor analytic literature, that the Horn–Cattell Gf- Gc model “appears to offer the most well- founded and reasonable approach to an acceptable theory of the structure of cognitive abilities” (Carroll, 1993, p. 62).
Gf-Gc theory received its original name because early versions (Cattell, 1943, 1963) of the theory only proposed two abilities; fluid (Gf) and crystallized (Gc) intelligence.  By 1991, Horn (1991) had already extended the Gf-Gc model of Cattell to the identification of 9 to 10 broad Gf-Gc abilities: Fluid Intelligence (Gf), Crystallized Intelligence (Gc), Short-Term Acquisition and Retrieval (SAR or Gsm), Visual Intelligence (Gv), Auditory Intelligence (Ga), Long-Term Storage and Retrieval (TSR or Glr), Cognitive Processing Speed (Gs), Correct Decision Speed (CDS), and Quantitative Knowledge (Gq).  The relative “newcomer” ability associated with the comprehension and expression of reading and writing skills (Grw) was added during this time period (Horn, 1988; McGrew, Werder, & Woodcock, 1991; Woodcock, 1994; see section E1 in Table 1). [Note - these broad and narrow abilities are defined later in this document in Table 3]
As illustrated in Figure 1, the Cattell-Horn Gf-Gc theory has its roots in Thurstone’s (1938; 1947) theory of Primary Mental Abilities (PMA’s).  In fact, according to Horn and Noll (1997), “to a considerable extent, modern hierarchical theories derive from this theory” (p. 62).  At the time, Thurstone’s PMA theory was at variance from the prevailing view that a higher-order g- factor existed, and instead posited between seven to nine independent (orthogonal) primary abilities:  induction (I), deduction (D), verbal comprehension (V), associative memory (Ma), spatial relations (S), perceptual speed (P), numerical facility (N), and word fluency (Fw).  [Different sources (Carroll, 1993; Horn & Noll, 1997; Jensen, 1998) list between 7-9 abilities and also provide slightly different names for the Thurstone PMA’s.] A large number of replication and extension studies confirmed Thurstone’s PMA’s and led to the eventual identification of over 60 abilities (Carroll, 1993; Horn & Noll, 1997; Jensen, 1998).  Early pre-Carroll (1993) factor analyses syntheses and summaries were published (Eckstrom, French & Harmon, 1979; French, 1951; French, Eckstrom & Price, 1963; Guilford, 1967; Hakstian & Cattell, 1974; Horn, 1972) with the patterns of intercorrelations of the PMA’s providing the rational for the specification of the higher-order broad G-abilities in the Cattell-Horn Gf-Gc model (Horn & Noll, 1997; Horn & Masunaga, 2000).  A thorough treatment of the contemporary Horn–Cattell Gf-Gc model can be found in Horn and Noll (1997).
The Horn-Carroll-Woodcock "fortuitous" tripartite
In the fall of 1985, the current author was engaged as a consultant and revision team member for the Woodcock-Johnson-- Revised (WJ-R; 1989).  The first order of business was to attend a March, 1986 “kickoff” revision meeting in Dallas, Texas.  Woodcock invited a number of consultants, the two most noteworthy being John Horn and Carl Haywood.  [The 1977 WJ was, at the time, the only individually administered intelligence test battery to include miniature “learning” tasks.  The possibility of revising these tests, or developing new tests, that reflected the dynamic assessments methods rooted in Vygotsky’s (1978) zone of proximal development (Sternberg & Kaufman, 1998) resulted in the inclusion of Dr. Carl Haywood, an recognized expert on the test-teach-test dynamic testing paradigm.]  Revision team members were notified that it was important to hear Horn describe Gf- Gc theory, and also to determine if “dynamic” testing concepts could be incorporated in the WJ- R.   At the last minute, the president of the publisher of the WJ (DLM: Developmental Learning Materials), Andy Bingham, made a fortuitous unilateral decision to invite (to the March, 1986 WJ- R revision meeting) an educational psychologist he had worked with on the American Heritage Word Frequency Book and Dictionary (Carroll, Davies & Richmond, 1971).   This educational psychologist, whom most of the WJ-R revision team or DLM staff did not know, was John B. Carroll. 
The first portion of the meeting was largely devoted to a presentation of the broad strokes of Gf- Gc theory by Horn.  With the exception of Carroll and Woodcock, most individuals present (myself included) were confused and struggling to grapple with the new language of  “Gf this…Gc that…SAR (short term acquisition and retrieval)…TSR (tertiary storage and recall)…etc.”  During most of this time John Carroll sat quietly to my immediate left.
When asked for his input, Carroll pulled an old and battered square-cornered brown leather briefcase from his side, placed it on the table, and proceeded to remove a thick computer printout (of the old green and white barred tractor-feed variety associated with mainframe printers). Carroll proceeded to present the results of a just completed exploratory Schmid-Leiman factor analysis of the correlation matrices from the 1977 WJ technical manual.   A collective “ah ha” engulfed the room as Carroll’s WJ factor interpretation provided a meaningful link between the theoretical terminology of Horn and the concrete world of WJ tests.
It is this author’s personal opinion, that this moment, a moment where the interests and wisdom of a leading applied test developer (Woodcock), the leading proponent of Cattell-Horn Gf-Gc theory (Horn), and one of the preeminent educational psychologists and scholars of the factor analysis of human abilities (Carroll) intersected (see section C in Table 1), was the flash point that resulted in all subsequent theoryto--practice bridging events that led to today’s CHC theory and related assessment developments.  A fortuitous set of events had resulted in the psychometric stars aligning themselves in perfect position to lead the way for most all subsequent CHC assessment related developments.

[Note. This was the first of a number of exhilarating meetings with Horn and Carroll and primary WJ-R revision team members.  These sessions also extended into the revision of the subsequent edition (WJ III).  Horn and Carroll were generally in agreement regarding most aspects of the human cognitive ability taxonomy, with one exception—the existence of g.   Suffice it to say, Horn (g does not exist) and Carroll (g exists) held strong and opposite views on the existence of g, and neither convinced the other during exchanges that often were quite “spirited.” Their positions are described later in this chapter.]
Publication of the Horn-Cattell Gf-Gc based WJ-R Battery
With a Cattell-Horn Gf-Gc map in hand, McGrew was directed to organize the available WJ factor and cluster analytic research studies (Kaufman & O’Neal, 1988; McGrew, 1986, 1987; McGue, Shinn & Ysseldyke, 1979, 1982; Rosso & Phelps, 1988; Woodcock, 1978).  Pivotal to this “search for WJ Gf-Gc structure” were factor analyses of the WJ correlaltion matrices by Carroll (personal communication, March 1986) and a WJ-based doctoral dissertation (Butler, 1987) directed by Horn. Woodcock and McGrew, both freshly armed with rudimentary confirmatory factor analyses skills and software, threw themselves into reanalyses of the WJ correlation matrices.  The result of this synthesis was the development of the WJ-R test development blueprint table (McGrew et al., 1991; Schrank et al., 2002) that identified existing WJ tests that were good measures of specific Gf-Gc abilities, as well as suggesting Gf-Gc “holes” that needed to be filled by creating new tests.  The goal was for the WJ-R to have at least two or more cognitive tests measuring aspects of each of seven (Gf, Gc, Gv, Ga, Gsm, Glr, Gs) Cattell-Horn Gf-Gc broad abilities.
The publication of the WJ-R Tests of Cognitive Abilities (COG) represented the official “crossing over” of Gf-Gc theory from the domain of intelligence scholars and theoreticians to applied practitioners, particularly those conducting assessments in educational settings (see C2 in Table 1).  The WJ-R represented the first individually administered, nationally normed, clincial battery to close the gap between contemporary psychometric theory (i.e., Cattell-Horn Gf-Gc theory) and applied practice. According to Daniel, (1997), the WJ-R was “the most thorough implementation of the multifactor model” (p. 1039) of intelligence.  An important WJ-R component was the inclusion of a chapter by Horn in an appendix of the WJ-R technical manual (McGrew et al., 1991).  Horn’s chapter represented the first up-to-date comprehensive description of the Horn-Cattell Gf-Gc theory in a publication readily accessible to assessment practitioners.  As a direct result of the publication of the WJ-R, “Gf-Gc-as-a-second- language” emerged vigorously in educational and school psychology training programs, journal articles and books, psychological reports, and become a frequent topic on certain professional and assessment related electronic listservs.
Gf-Gc battery "free" assessment concept born
In 1990, Woodcock published an article that, in a sense, provided a “battery-free” approach to Gf- Gc theoretical interpretation of all intelligence test batteries.  In a seminal article summarizing his analysis of a series of joint confirmatory factor studies of the major intelligence batteries (i.e., K- ABC, SB-IV, Wechslers, WJ, WJ-R; see C3 in Table 1), Woodcock (1990), using empirical criteria,  classified the individual tests of all the major batteries as per the Cattell-Horn Gf-Gc model.  For example, the WJ-R Visual–Auditory Learning test was classified by Woodcock (1990) as a strong measure of Glr based on a median factor loading of .697 across 14 different analyses. Another example of a clear classification was the SB-IV Vocabulary test as a strong measure of Gc, based on a median factor loading of .810 across four analyses.  
In the discussion of his results, Woodcock demonstrated how each individual test from each intelligence battery mapped onto the Cattell-Horn Gf-Gc taxonomy.   The resulting tables demonstrated how each battery adequately measured certain Gf- Gc domains, but failed to measure, or measured poorly, other Gf- Gc domains.  More importantly, Woodcock (1990) suggested that in order to measure a greater breadth of Gf-Gc abilities, users of other instruments should use “cross-battery” methods to fill their respective Gf-Gc measurement voids.  The concept of Gf-Gc cross-battery assessment was born, as well as a means to evaluate the cross- battery equivalence of scores from different batteries (Daniel, 1997).
In a sense, Woodcock had hatched the idea of Gf-Gc “battery- free” assessment where a common Gf-Gc assessment and interpretive taxonomy was deployed across intelligence batteries. Practitioners were no longer constrained to the interpetive structure provided by a specific intelligence battery.  Practitioners were given permission and a rational to “think outside their test kits” in order to conduct more valid assessments.  Based on Woodcock’s (1990) findings, McGrew (1993) subsequently described a Kaufman-like Gf-Gc supplemental testing approach for use with the WJ-R.  Unwittingly, this was a clinical attempt to implement an informal cross-battery approach to assessment (see section C5 in Table 1).  The development of the formal CHC cross-battery assessment approach was waiting in the wings, and blossomed during the next set of major CHC theory-practice bridging events. 

[ Note.  The reader is encouraged to read Woodcock’s original 1990 article to gain an appreciation for the significance of the work and why it has played such a significant role in the infusion of CHC theory into the practice he concept of applying a theoretical model not originally associated with a published battery to that battery was not a new idea (see Kaufman, 1976).  Woodcock’s unique contribution was the extension of this concept beyond application to the Wechsler scales to all available intelligence batteries, basing this “battery-free” interpretive philosophy on the most validated model of the structure of human cognitive abilities and, more importantly, superimposing the Gf-Gc structure on batteries based on empirical evidence.]
Carroll's 1993 Principia Cognitive Abilities
Carroll’s (1993) book, Human cognitive abilities: A survey of factor-analytic studies, may represent in the field of applied psychometrics, a work similar in stature to other noted “principia” publications in other fields (e.g., Newton’s three volume, The Mathematical Principles of Natural Philosophy, or Principia as it became known; Whitehead & Russell’s, Principia Mathematica; see section D in table 1).  Briefly, Carroll summarized a review and reanalysis of more than 460 different data sets that included nearly all the more important and classic factor analytic studies of human cognitive abilities.
The current author is not alone in the elevation of Carroll’s work to such a high stature.  On the book cover, Richard Snow states that “John Carroll has done a magnificent thing. He has reviewed and reanalyzed the world’s literature on individual differences in cognitive abilities…no one else could have done it… it defines the taxonomy of cognitive differential psychology for many years to come.” Burns (1994) was similarly impressed when he stated that Carroll’s book “is simply the finest work of research and scholarship I have read and is destined to be the classic study and reference work on human abilities for decades to come” (p. 35).  Horn (1998) describes Carroll’s (1993) work as a “tour de force summary and integration” that is the “definitive foundation for current theory” (p. 58).  Horn compared Carroll’s summary to “Mendelyev’s first presentation of a periodic table of elements in chemistry” (p. 58).  Jensen (2004) stated that “on my first reading this tome, in 1993, I was reminded of the conductor Hans von Bülow’s exclamation on first reading the full orchestral score of Wagner’s Die Meistersinger, ‘‘It’s impossible, but there it is!’’ Finally, according to Jensen (2004):
Carroll’s magnum opus thus distills and synthesizes the results of a century of factor analyses of mental tests. It is virtually the grand finale of the era of psychometric description and taxonomy of human cognitive abilities. It is unlikely that his monumental feat will ever be attempted again by anyone, or that it could be much improved on. It will long be the key reference point and a solid foundation for the explanatory era of differential psychology that we now see burgeoning in genetics and the brain sciences (p. 5).
The raw material reviewed and analyzed by Carroll was drawn from decades of tireless research by a diverse array of dedicated scholars (e.g., Spearman, Burt, Cattell, Gustaffson, Horn, Thurstone, Guilford, etc.).   Carroll (1993) recognized that his theoretical model built on the research of others, particularly Cattell and Horn.  According to Carroll (1993), the Horn-Catell Gf-Gc model “appears to offer the most well-founded and reasonable approach to an acceptable theory of the structure of cognitive abilities” (p. 62).
The beauty of Carroll’s book was that, for the first time ever, an empirically-based taxonomy of human cognitive ability elements, based on the analysis (with a common method) of the extant literature since Spearman, was presented in a single, coherent, organized, systematic framework.  Lubinski (2000) put a similar spin on the nature and importance of Carroll’s Principia when he stated that “Carroll’s (1993) three-stratum theory is, in many respects, not new.  Embryonic outlines are seen in earlier psychometric work (Burt, Cattell, Guttman, Humphreys, and Vernon, among others). But the empirical bases for Carroll’s (1993) conclusions are unparalleled; readers should consult this source for a systematic detailing of more molecular abilities” (p. 412).
Carroll proposed a three-tier model of human cognitive abilities that differentiated abilities as a function of breadth. At the broadest level (stratum III) is a general intelligence factor conceptually similar to Spearman’s and Vernon’s g. Next in breadth are eight broad abilities that represent “basic constitutional and long-standing characteristics of individuals that can govern or influence a great variety of behaviors in a given domain” (Carroll, 1993, p. 634). Stratum level II includes the abilities of Fluid Intelligence (Gf), Crystallized Intelligence (Gc), General Memory and Learning (Gy), Broad Visual Perception (Gv), Broad Auditory Perception (Ga), Broad Retrieval Ability (Glr), Broad Cognitive Speediness (Gs), and Reaction Time/Decision Speed (Gt). Finally, stratum level I includes over 69 narrow abilities that are subsumed by the stratum II abilities, which in turn are subsumed by the single stratum III g factor. The posthumous publication of Carroll’s work in this volume (see Chapter ____) provides a more detailed summary of his model.
It is important to note that the typical schematic representation of Carroll’s three-stratum model does not precisely mirror the operational structure generated by his exploratory factor analysis with the Schmid- Leiman orthoganolization (EFA-SL) procedure. The typical depiction of Carroll’s model looks much like the CHC theory model (Figure 1e).  In reality, assuming a three- order (stratum) factor solution, Carroll’s analyses looked more like Figure 1d where the following elements are presented: (1) all tests load on the third-order g-factor (arrows from g to T1-T12; omitted from Figure); (2) salient loadings for tests on their respective first-order factor(s) (e.g., arrows from PMA1 to T1- T3), (3) salient loadings for tests on their respective second-order factor(s) (e.g., arrows from G1 to T1-T6), (4) first-order factors loading on their respective second-order factor(s) (e.g., arrows from G1 to PMA1 and PMA2), and (5) second-order factors loading on third-order g-factor (e.g., arrows from G1 and G2 to g). 
In a sense, Carroll provided the field of intelligence the much needed Rosetta stone that would serve as a key for deciphering and organizing the enormous mass of human cognitive abilities structural literature that had accumulated since the days of Spearman.  Carroll’s work was also influential in creating the awareness among intelligence scholars, applied psychometricians, and assessment professionals, that understanding human cognitive abilities required 3-Stratum (3-S) vision.  As a practical benefit, Carroll’s work provided a common nomenclature for professional communication.  Historically the clinical intelligence testing literature is replete (including my own book on the WJ-R; McGrew, 1994) with a myriad of test interpretation terms such as “fund of information,” “verbal concept formation,” “visual perception of meaningful stimuli,” and the “ability to distinguish essential from nonessential details,” to list but a few. The origin of many of these terms would be difficult to trace, with most being passed down through the clinical literature, often without empirical support.  Carroll’s model provided a standard nomenclature that would go “far in helping us all better understand what we are measuring, facilitate better communication between and among professionals and scholars, and increase our ability to compare individual tests across and within intelligence batteries” (McGrew, 1997, p.171).
The importance of the convergence on a provisional cognitive ability structural framework should not be minimized.  Such a structure, grounded in a large body of convergent and discriminant validity research, is the first of at least a dozen conditions required for the building of an aptitude theory that can, in turn, produce a theory of aptitude-treatment interactions (ATIs; Snow, 1998, p. 99).

[Note. The interested reader should review Table 3.5 on pages 110-111 of Carroll (1993) for an example of a Carroll EFA-SL with three-orders of factors.  During his later years, Carroll recognized the advantages of CFA and encouraged others to use CFA methods to check his 1993 EFA-based results (Carroll, 1994).  I had the fortunate opportunity to visit and work with Carroll in Fairbanks, Alaska four weeks prior to his passing away.  It was clear, as illustrated in his combined EFA+CFA WJ-R analyses (2003), that he had blended the two methodologies.  His computer disks were full of unpublished EFA+CFA analyses that he had graciously completed for other researchers or, that represented his analysis of correlation matrices that had been included in manuscripts he had been asked to review for a number of journals.  His approach had clearly evolved to one of first obtaining results from his EFA Schmid/Leiman approach (as described in Chapter 3 of his 1993 book; see Figure 1d) and then using those results as the starting point for CFA refinement and model testing (as described in Carroll, 2003; see Figure 1e]