CHC model presented in Figure 1e reveals a quandary (i.e., g?) for users of CHC theory.
Namely, to g (Carroll) or not to g (Horn)? To properly evaluate the relative
merits of the g vs.
no-g positions would require extensive reading of the voluminous g literature. No
less than three
books (Brand, 1996; Jensen, 1998; Nyborg, 2003) have been devoted exclusively to the topic of g
during the past decade. The existence and nature of g has been debated by the giants in
of intelligence (since the days of Spearman) with no universal resolution. The essence of the
Cattell-Horn versus Carrol g conundrum is best summarized by Hunt (1999) who stated:
Carroll notes that abilities in the second-order stratum (e.g.,
Gc and Gf) are positively
correlated. This led Carroll to conclude that there is a third, highest-level stratum with a
single ability in it: general intelligence. Here Carroll differs with the interpretations of
Cattell and Horn. Cattell and Horn acknowledge the correlation, but regard it as a
statistical regularity produced because it is hard to define a human action that depends
on just one of the second- order abilities. Carroll sees the same correlation as due to the
causal influence of general intelligence. It is not clear to me how this controversy could
be resolved (p.2).
if no such thing as g exists, applied psychologists need to be cognizant of the reality
positive manifold among the individual tests in intelligence batteries which is practically
operationalized in the form of the global composite IQ score (Daniel, 2000). Also, the positive
manifold among cognitive measures often must be included in research designs to test and
evaluate certain hypotheses. Researchers using the CHC model must make a decision whether
g should be included in the application of the model in research. Brief summaries of the
respective Horn and Carroll positions are presented below
See Daniel (2000) for a discussion of the various issues involved in calculating practical composite
IQ scores from intelligence batteries comprised of different measures.]
(Horn & Masunaga, 2000) typically presents two lines of evidence against the g as a
unitary process position. Structurally, Horn and Masunaga (2000) argue that batteries
well selected to provide reliable measures of the various processes thought to be indicative of
general intelligence do not fit the one common factor (i.e., Spearman g) model. This has
demonstrated time and time again
(p. 139). The statement also challenges Jensens
1993) g argument in the form of the indifference of the indicator (see Horn, 1998).
(Horn & Noll, 1997; Horn & Masunaga, 2000) further argues that Carrolls (1993) research
reveals no fewer than eight different general factors, with the general factor from one battery
dataset not necessarily being the same as the general factor in other batteries or datasets. More
specifically, Horn and Noll (1997) argue that the probem for theory of general intelligences is
that the factors are not the same from one study to another
the different general factors do not
meet the requirements for the weakest form of invariance (Horn & McArdle, 1992) or satisfy the
conditions of the Spearman model. The general factors represent different mixture measures, not
one general intelligence (p. 68). That is, the general factors fail to meet the same
requirement (Horn, 1998).
and what is probably the most convincing portion of Horns argument, is the fact that
research reveals that the relationships that putative indicators of general intelligence have
variables of development, neurological functioning, education, achievement, and genetic structure
are varied (Horn & Masunaga, 2000, p.139). That is, the broad CHC abilities demonstrate
differential relations with: (1) different outcome criteria (e.g., in the area of academic
achievement see McGrew, 1993; McGrew & Hessler, 1995, McGrew & Knopik, 1993; Evans,
Floyd. McGrew & Leforgee, 2002; Floyd, Evans & McGrew, 2003), (2) developmental growth
curves, (3) neurological functions, and (4) degree of heritability. The many relationships
the construct validities of the different broad factors do not indicate a single unitary principle
(Horn & Masunaga, 2000, p. 139). See Horn and Noll (1997) for additional information.
presented earlier in this chapter, Carroll (2003), in his final publication, tested the g
vs. g- is-Gf models in the WJ-R norm data. Carroll (2003) concluded that researchers who are
concerned with this structure in one way or another
.can be assured that a general factor g
exists, along with a series of second-order factors that measure broad special abilities (p. 19).
Carroll (2003) further stated that doubt is cast on the view that emphasizes the importance of
.these data tend to discredit the limited structural analysis view and the second-
stratum multiplicity view (p. 17).
primary basis for Carrolls belief in g stems not necessarily from the positive correlations
among dissimilar tasks, but rather from the three-stratum model that, for a well-designed dataset,
yields factors at different strata, including a general factor (Carroll, 1996; p. 12-13).
(1996) believed that for each factor in his three-stratum theory, there was a specific state or
substate (e.g., structured patterns of potentialities latent in neurons; Carroll,
1998, p. 10) that
exists within an individual that accounts for the performance on tasks that require a specific latent
abilitywe can infer that something is there (Carroll, 1998, p. 10). By
emergence of a g-factor in his EFA-SL analyses must reflect some form of specific state or
subtrate within an individual.
(2003) further argued that the different g factors he reported (Carroll, 1993) do represent
the same construct given the underlying assumptions and procedures of Schmid-Leiman factor
analysis. In response to Horn's arguments, Carroll (2003) stated that Horn conveniently
a fundamental principle on which factor analysis is based (a principle of which he is undoubtedly
aware)--that the nature of a single factor discovered to account for a table of intercorrelations
does not necessarily relate to special characteristics of the variables involved in the correlation
matrix; it relates only to characteristics or underlying measurements (latent variables) that
common to those variables. I cannot regard Horn's comment as a sound basis for denying the
existence of a factor g, yet he succeeded in persuading himself and many others to do exactly
this for an extended period of years (p. 19).
in a personnel communication received just prior to his passed away, Carroll provided
the following comments regarding the "proof of g (Carroll, personal communication,
It is important to recognize that in my paper published in
the Nyborg book occurs the
first modern, real, scientific proof of g - in contrast to the many unacceptable "proofs"
claimed by Spearman, Burt, Pearson, and others. It used the features of a complete
proof advanced by LISREL technologies. Jöreskog
has discussed these features in his
of particular interest are the proofs of the status of g, Gc, and Gf,
provided in the Nyborg chapter
in the sense g, Gc and Gf could be independently
established, plus several other factors, (e.g. Gv, Ga). It was truly marvelous that
enough data from these factors had accumulated to make their independence
The "general factor" appears to pertain only to
very general items of general knowledge-
- e.g., items of knowledge that are common to most people, present only as specified by
parameters of "item difficulty." g thus appears not to pertain to the many items
knowledge incorporated in Gf or Gc. These items of knowledge are in some way
special- classified under Gf or Gc (or some combination of these). It appears that
human being becomes a "member of society" only by acquring apsects of special
knowledge (either fluid or crystallized, or some combination of them).