Meta-Analysis of g Loadings According to the Cattell-Horn-Carroll Theory of Intelligence

1
Meta-Analysis of g Loadings According to the
Cattell-Horn-Carroll Theory of Intelligence
James Arnett and Randy G. Floyd The
University of Memphis
Results
Background Information
Analyses
Mean subtest g loadings were computed for all
subtest g loadings (n 3,149 M .65, SD
.13), and across each of the broad ability
domains (Figure 1). Quantitative Knowledge (M
.75, SD .08), Comprehension- Knowledge (Gc M
.74, SD .09) , and Fluid Reasoning ( Gf M
.68, SD .10) had mean subtest g loadings above
the grand mean. Long-Term Retrieval (Glr M
.60, SD .14), Visual-Spatial Thinking (Gv M
.60, SD .12), Short-Term Memory (Gsm M .57,
SD .10), Auditory Processing (Ga M .55, SD
.09), and Processing Speed (Gs M .53, SD
.13) had mean subtest g loadings below the grand
mean. Criteria for high, medium, and low g
loadings are outlined in Floyd et al (2009).
Mean subtest g loadings for Gc and Gq are high (g
loadings .70, and mean subtest g loadings for
Glr, Gv, Ga, Gsm, and Gs are medium (.50
g-loadings .69). A one-way analysis of
variance (ANOVA) was done, and a significant main
effect was found F(7, 3139) 207.882, plt.001.
Tukeys HSD) post-hoc tests revealed that Gc and
Gq were significantly higher than Glr, Gv, Ga,
Gsm, and Gs (p lt .001), but Gc and Gq were not
significantly different from each other (p gt
.10). Gf was significantly higher than Glr, Gv,
Ga, Gsm, and Gs (p lt .001). Gv was significantly
higher than Gsm and Gs (p lt .001), as well as Ga
(p lt .01). Glr was significantly higher than Gs
and Ga (p lt .001), as well as Gsm (p lt .01)). Gv
and Glr were not significantly different from
each other (p gt .10). Gsm was significantly
higher than Gs (p lt.001), but not Ga (p gt.10).
Finally, Ga and Gs were not significantly
different from each other.
Each subtest from the 10 batteries included in
Figure 1 was labeled as a measure of one or more
of the broad abilities as classified by Flanagan
et al. (2007) and related books. Because subtests
from the Cattell Culture Fair Intelligence Test,
the Pictorial Test of Intelligence, and the
McCarthy Scales of Children Abilities had not
been categorized according to the broad
abilities, their subtest g loadings were excluded
from the analyses. Subtests that were labeled as
measuring more than one broad ability were
excluded from the analysis. Because there were so
few subtests that measures reading and writing
ability (Grw n 6), these g loadings were also
excluded.
In recent years, many theories have emerged
attempting to create a comprehensive model of
intelligence. For example, Carroll (1993)
re-analyzed 460 data sets and found a general
factor as well as several broad ability factors,
which he organized into 3 levels. Stratum I
represented narrow abilities, Stratum II
represented broad abilities that each narrow
ability would fall under, and Stratum III
represented the general factor. Broad ability
factors identified by Carroll (1993) were said to
be dominated by what he labeled as factor g, or
the general factor. Carroll theorized that the
more cognitively complex a factor seemed to
represent, the higher the correlation with g.
Carrolls broad abilities are, from most highly
correlated with the g factor to least highly
correlated, as follows Fluid Intelligence,
Crystallized Intelligence, General Memory and
Learning, Broad Visual Perception, Broad Auditory
Perception, Broad Retrieval Ability, Broad
Cognitive Speediness, and Processing Speed.
Carrolls three-stratum model was consistent with
the truncated model of the extended Gf-Gc theory
of Horn and Cattell, so McGrew (1997, 2005)
suggested combining these models in the
Cattell-Horn-Carroll (CHC) theory (Woodcock,
McGrew, Mather, 2001). Due to apparent
ambivalence about the validity of the general
factor stemming, at least partially from
arguments made by Horn and colleagues (e.g.,
Horn Noll, 1997) McGrew and a group of other
scholars focused attention on the broad abilities
of CHC theory in a variety of publications (e.g.,
McGrew Flanagan, 1998 Flanagan, McGrew,
Ortiz, 2000), and revisions to the most prominent
intelligence tests batteries were explicitly or
implicitly constructed to measure the general
factor and the broad abilities of CHC theory. As
a result, based on factor-analytic evidence and
judgments based on content reviews, most
intelligence subtests have been labeled according
to the broad abilities they measure (see
(Flanagan, Ortiz, Alfonso, 2007 McGrew
Flanagan, 1998). However, less is known about the
extent to which these subtests measure the
higher-order general factor relative to broad
abilities and how the relations between the
subtest scores and the general factor
(represented in a g loading) vary across the
CHC broad ability domains.
Figure 1
Highest and Lowest g-loading by Broad Ability
___________High ______________
____________Low______________

Table 1
g loading Subtest Test Battery Author(Year) g loading Subtest Test Battery Author(Year)
Gc .91 Riddles KABC Keith(1984) .24 Double Meanings KAIT McGrew(1996)
Glr .84 Rebus Learning KAIT McGrew (1996) .26 Recall of Objects DAS Sattler(2001)
Gv .87 Verb Vis-Spat SB 5 Roid(2003) .24 Attention Divided Leiter-R Roid(1997)
Ga .72 Sound Blending WJ-R McGrew(1995) .33 Incomplete Words WJ-R McGrew(1995)
Gsm .82 Word Order KABC Kaufman(1984) .25 Digit Span WISC-III Roid(1993)
Gf .88 Verb Qn Reas SB 5 Roid(2003) .23 Matrix Reasoning WAIS-III Gignac(2006)
Gs .78 Symbol Search WAIS-III Gignac(2006) .23 Coding WISC-R Naglieri(1987)
Gq .91 Quantitative SB 4 Reynolds(1988) .46 Quantitative SB 4 Reynolds(1988)
Purpose
It is an opportune time to conduct a
meta-analysis examining the g-loadings of
subtests from individually administered
intelligence test batteries. A meta-analysis can
help to determine (a) which intelligence tests
contain subtests that are the best measures of
the general factor on average, (b) if there are
differences across g loadings according to the
broad ability domains, and (c) if there are
differences across g loadings on subtests that
fall under the same broad ability domain.
Figure 2
Mean g loadings by Intelligence Test Battery
Wechsler Intelligence Scale for Children (WISC n 637) M .62, SD .15 Wechsler Adult Intelligence Scale (WAIS n 761) M .70, SD .11
Wechsler Preschool and Primary Scale of Intelligence (WPPSI n 166) M .60, SD .12 Kaufman Assessment Battery for Children (KABC n 152) M .58, SD .12
Woodcock- Johnson Tests of Cognitive Abilities (WJ n 594) M .61, SD .13 Stanford-Binet Intelligence Scales (SB n 470) M .70, SD .09
Differential Ability Scales (DAS n 163) M .57, SD .15 Kaufman Adult Intelligence Scale (KAIT n 150) M .71, SD .12
Leiter International Performance Scale, Revised (Leiter-R n 133) M .51, SD .12 Universal Nonverbal Intelligence Test (UNIT n 10) M .72, SD .10
Method
Discussion
Source Collection

• Results support the hypothesis that the greater
  number of mental processes required to complete a
  cognitive task, the more highly g loaded they are
  (Marshalek, Lohman, Snow, 1983 McGrew , 2002).
• Medium to high mean subtest g loadings across
  all broad abilities, and the variability across
  broad abilities, supports the inclusion of both a
  general factor and more specific cognitive
  domains in models of intelligence. These findings
  also support use of factor analysis specifying at
  least two orders of factors.
• Subtests with high g loadings, regardless of the
  broad ability they may also measure, should be
  expected to be the best predictors of academic
  success and job performance (Jensen 1998
  Schmidt, 2002).
• Intelligence test batteries vary somewhat in the
  amount of general intelligence they measure. The
  UNIT includes subtests with the highest mean g
  loading (although n 10), whereas the Leiter-R
  includes subtests with the lowest mean g loading.
  Both test batteries are nonverbally administered.

First, Floyd, McGrew, Barry, Rafael, and Rogers
(2009) was consulted to obtain the articles
identified in their review that produced subtest
g loadings. Second, a literature search was
conducted to identify journal articles that had
been published in a peer-reviewed journal between
1975-2007. This scanning was done through
electronic journal data bases, such as ERIC,
PsycInfo, JSTOR, and Google Scholar. Third,
manuals for each edition of the intelligence test
batteries listed in McGrew and Flanagan (1998)
and Flanagan et al. (2007) were reviewed to
identify g loadings. Major instructional texts
(e.g., Sattler, 2001, 2004) were also reviewed.
From this list, 63 sources and 3,748 g loadings
were identified. Inclusion criteria for these
sources included (a) empirically derived g
loadings for subtests on intelligence test
batteries, (b) published between 1975 and 2007.