3.1 A. Large sample studies
Studies with CHC designed batteries
The most thorough evaluations of the structure of CHC theory are factor analysis studies of variables from standardized test batteries administered to large nationally representative samples.  The most comprehensive evaluation of Carroll’s three-stratum CHC model is the hierarchical cross-age (ages 6 through 90 years) multiple-group confirmatory factor analysis of the WJ-R norm data by Bickley, Keith and Wolfe (1995).  Consistent with Carroll’s (1993) conclusion that the structure of cognitive abilities is largely the same across ages, Bickley et al. found that the structure of cognitive abilities, as defined by eight broad abilities (Gf, Gv, Gs, Glr, Gc, Ga, Gsm, Gq) and a higher-order g ability, was invariant from childhood to late adulthood.  Bickley et al. concluded that “this study provides compelling evidence that the three-stratum theory may form a parsimonious model of intelligence.  The fact that it is also grounded in a strong foundation of vast, previous research also lends strong support for the acceptance of the model.” (p. 323).  
More recently, in the large nationally representative WJ III standardization sample, McGrew and Woodcock (2001) reported a CHC-based confirmatory factor analysis of 50 test variables from ages six through late adulthood.  Support was found for a model consisting of a higher-order g- factor that subsumed the broad abilities of Gf, Gc, Gv, Ga, Gsm, Glr, Gs, Grw, and Gq.  A comparison with four alternative models found the CHC model to be the most plausible representation of the structure in the data.
Subsequently, Taub and McGrew (in press) used multiple-group confirmatory factor analyses to evaluate the factorial cross-age invariance of the WJ III Cognitive (COG) Battery from ages 6 through 90+.  In addition to supporting the construct validity of a higher-order g and seven lower- order broad CHC factors (Gf, Gc, Gv, Ga, Gsm, Glr, Gs), Taub and McGrew’s analyses supported the invariance of the WJ COG measurement and CHC theoretical frameworks.  These findings are consistent with Bickely et al. (1995) and provide additional support for the validity of the broad and general stratum abilities of CHC theory (from childhood through adulthood).
Of particular interest to the current chapter, and representing his last formal publication, Carroll (2003) applied his factor analytic procedures and skills to an investigation of the structure of the 1989 WJ-R norm data.  The purpose of Carroll’s analyses was to compare the viability of three different views of the structure of human cognitive abilities.  According to Carroll (2003), these views can be characterized as:
(1)  Standard multifactorial model:  This is the classic view of Spearman (Spearman, 1927, Spearman & Wynn Jones, 1950) and others (e.g., Carroll, 1993; Thurstone & Thurstone; 1941; Jensen; 1998) that a general (g) intelligence factor exists as well as a variety of less general “broad” abilities. 
(2) Limited structural analysis model. This model also posits the presence of higher- order g ability, as well as lower-order broad abilities, but suggests that fluid intelligence (Gf) is highly correlated with, and may be identical with g.  This model is primarily associated with Gustafsson and others (Gustafsson, 1984, 1989, 200l; Gustafsson & Balke, 1993; Gustafsson & Undheim, 1996)
(3)  Second-stratum multiplicity model. This is a g-less model that also includes broad abilities, but suggests that the non-zero intercorrelations among lower-stratum factors do not support the existence of g.   This is largely the view of Horn and Cattell (Cattell, 1971, Horn, 1998; Horn & Noll, 1997)

Carroll (2003) judged the WJ-R norm data to be a “sufficient” dataset for “drawing conclusions about the higher-stratum structure of cognitive abilities” (p. 8).  Carroll submitted the 16- and 29- variable WJ-R correlation matrices reported by McGrew, et al. (1991) to the same exploratory factor analysis Schmid-Leiman procedures used in his 1993 survey.  These EFA-based results, in turn, served as the starting point for a confirmatory analyses intended to compare the three different structural model views of intelligence vis-à-vis the model comparison statistics provided by SEM methods. 
Briefly, 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 a Gf factor….these data tend to discredit the limited structural analysis view and the second-stratum multiplicity view” (p. 17).   Interestingly, in these analyses Carroll used the broad ability nomenclature of CHC theory when reporting support for the broad abilities of Gf, Gc, Gv, Ga, Gsm, Glr, Gs, Gq and Language (comprised of reading and writing tests; aka., Grw). 
     The most recent morphing of the long line of Stanford-Binet Intelligence scales (Stanford Binet Intelligence Scales—Fifth Edition, SB5; Roid, 2003) was guided extensively by the work of both Carroll and Horn (see Roid, 2003, p.7-11), consultation from authors of the CHC-designed WJ-III (see Roid, Woodcock, McGrew, 1997 in Roid, 2003; also see Roid, 2003, p. v,) and a review of the CHC-organized cross-battery research literature of Flanagan, McGrew and colleagues (see Roid, 2003, p. 8-9).  The result is a CHC-organized battery designed to measure the broad cognitive abilities of Fluid Reasoning (Gf), Quantitative Reasoning (Gq), Crystallized Knowledge (Gc), Short-term Memory (Gsm), and Visual Processing (Gv). Not measured are the broad abilities of Grw, Ga, Glr, and Gs. Confirmatory factor analysis reported in the SB5 manual indicates that the five-factor model (Gf, Gq, Gc, Gsm, Gv) was the most plausible model when compared to four alternativs models (one, two, three, and four-factor models).
Studies with other batteries
Recently, Roberts, Goff, Anjoul, Kyllonen, Pallier and Stankov (2000) examined the factor structure of the Armed Services Vocational Aptitude Battery (ASVAB) as per fluid and crystallized intelligence theory and Carroll's (1993) three-stratum model. In two samples (n = 349, n = 6751), adult subjects were administered both the ASVAB and marker tests from the ETS Kit of Factor-Referenced Cognitive Tests (Ekstrom, French, Harmon, & Derman, 1976).  Exploratory and confirmatory factor analyses supported a model that included the broad abilities of Gf, Gc, Gsm (SAR), Gv, Glr (TSR), and Gs. [Note.  Unless otherwise indicated, throughout this document the factor names as reported by the original investigators are in parenthesis.  The factor names/CHC abbreviations preceding the names in parentheses reflect the current authors reinterpretation of the factors as per CHC theory.]
Although not using the language of CHC theory, Tulsky and Price’s (2003) recent confirmatory factor analysis of the WAIS-III/WMS-III national standardization co-norming sample also supports the CHC model.  Of the six factors retained in their final cross-validated model, three factors can clearly be interpreted as broad CHC factors--Gs (Processing Speed), Gc (Verbal Comprehension), and Gv (Perceptual Organization).  Tulsky and Price’s Visual Memory factor could be classified as Gv (MV).  The factor Tulsky and Price interpreted as Auditory Memory was defined by salient loadings from the WMS-III Logical Memory I and II, Verbal-Paired Associates I and II, and the Word List I and II tests, tests that have previously been classified as per CHC theory (see Flanagan et al., 2000) as measures of Glr (i.e., MM, MA, M6).  Finally, the factor defined by the WMS-III Spatial Span and WAIS-III Digit Span, Letter-Number Sequencing, and Arithmetic tests was interpreted by Tulsky and Price as Working Memory (Gsm- MW). [Note. In this particular instance, the factor codes in parenthesis reflect the current  author’s interpretation and or factor labeling An alternative interpretation of the Working Memory factor could be Numerical Fluency (Gs-N) due to of the common use of numerals in all tasks (e.g., Digit Span, Letter- Number Sequencing, and Arithmetic all require the manipulation of numbers;  Spatial Span performance might be aided via the subvocal counting of the shapes to be recalled). 
Finally, Tirre and Field’s (2002) systematic investigation of the structure of the Ball Aptitude Battery (BAB), when cast within a CHC lens, provides additional support for the broad strokes of the CHC model.  These investigators reported the results of three separate cross- battery confirmatory factor analysis (BAB and Comprehensive Ability Battery, CAB; BAB and Armed Services Vocational Aptitude Battery, ASVAB; BAB and General Aptitude Test Battery, GATB) and their reanalysis of Neuman, Bolin, and Briggs (2000) BAB study. Although Tirre and Field reported 15 different types of factors across all studies, only those factors replicated in at least two of the samples are discussed here.  These included g (General Cognitive Ability), Gps (Perceptual Motor Speed), Gs-P (Clerical Speed), Gf (Reasoning), Gc (Verbal), and Gq (Numerical Ability).   Two additional Glr-type factors emerged and were defined by slightly different combinations of tests in the different analyses.   What Tirre and Field (2002) labeled “Episodic Memory” appears to be a Glr “level” factor defined primarily by the combination of Associative Memory (MA) and Meaningful Memory (MM) measures.  In contrast, their “Creativity” factor was defined by Glr “rate” measures requiring rapid or fluent generation of ideas (FI – Ideational Fluency).  Tirre and Field (2002) interpreted an additional factor as representing “Broad Retrieval Ability.”  However, in two of the three investigations where this factor emerged, the strongest factor loading(s) were for Gf tests (BAB Inductive Reasoning, BAB Analytical Reasoning).