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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.. |
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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. |
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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). |
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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.] |
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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. |
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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.] |
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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] |
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1. 1. Introduction
