3.2 B. Small sample studies
A number of small sample studies, many which analyzed joint (cross battery) datasets, provide additional support for the broad strokes of CHC theory.
In a study of 179 adults, Pallier and Stankov (1996) used exploratory factor analysis with a collection of 25 cognitive measures that have been used for decades in many intelligence research studies (i.e., not a single nationally normed battery).  Six CHC factors were identified.  The broad factors reported included Gf, Gc, Gsm (SAR), Gv, Ga, and Gs.  With the exception of a seventh separate Induction (I) factor that was correlated with Gf, the six- factor structure is consistent with CHC theory.  In a study that used some of the same measures, as well as measures of tactile and kinesthetic abilities, Roberts, Stankov, Pallier & Dolph (1997) used a combination of exploratory and confirmatory factor analysis on a set of 35 variables adminstered to 195 college and adult subjects.  In addition to the possibility of a broad tactile- kinesthic ability (discussed later in this chapter), this study provided support for the CHC abilities of Gc, Gf, Gv, Gsm (SAR), and a blended Gs/Gt.
Li, Jordanova and Lindenberger (1998) also included three measures of tactile abilities together with 14 research tests of cognitive abilities in a study designed to explore the relations between perceptual abilities and g in a sample of 179 adults.  Embedded in the causal model, to operationally represent g, were five first-order factors consistent with the CHC model—Gs (Perceptual Speed), Gf (Reasoning) and Gc (Knowledge).  Two additional factors, labeled Memory and Fluency, when viewed through a CHC lens appear to represent the “level” (MA/MM) and “rate” (FI) components of Glr
Reed and McCallum (1995) presented the results of an exploratory factor analysis for 104 elementary school subjects who had been administered 18 tests from the Gf-Gc designed WJ-  R and 6 tests from the Universal Nonverbal Intelligence Test (UNIT; Bracken & McCallum, 1998).   The original WJ- R/UNIT correlation matrix was subsequently submitted to a CHC- designed confirmatory factor analysis (McGrew, 1997) and the results supported a model consisting of  Gf, Gv, Gs(P), Glr (MA), Gc, Ga (PC), and Gsm (MS). [Note.  The CHC classifications derived from this 4-26-97 analyses are presented in McGrew and Flanagan (1998).]   McGhee and Lieberman (1994) also used exploratory factor methods to investigate the dimensionality of 18 measures selected from a variety of psychoeducational batteries.  In a small sample of 50 second grade students, six distinct CHC cognitive factors were identified; Gv (MV), Gsm (MS), Gv (SR), Gc, Ga (PA), and Gq (KM).   [Note.  The factor interpretations presented here are based on McGrew’s interpretation of the McGhee and Lieberman results.  They used similar Gf-Gc terminology to provide slightly different, but very similar, factor interpretations.]  In addition, two tests requiring the drawing of designs represented a visual-motor factor that corresponds to abilities within Carroll’s (1993) Broad Psychomotor Ability domain.  Fifteen of the WJ-R tests were also subjected to an exploratory factor analysis together with 12 tests from the Detroit Test of Learning Aptitude—Adult in a sample (n = 50) of elderly adults (Buckhalt, McGhee & Ehrler, 2001). Buckhalt et al. (2001) reported evidence in support of eight CHC broad abilities (Glr, Gc, Gsm, Ga, Gq, Gf, Gv and Gs[Note.  The Buckhalt et al. (2001) Glr factor was defined primarily by measures of Glr, but also had a number of significant loadings from tests that measure Gv abilities.  This author has repeatedly seen the same type of factor in exploratory factor analysis of the WJ-R and WJ III norm data.]
Cross-battery studies including tests from the Kaufman Adolescent and Adult Intelligence Test (KAIT; Kaufman & Kaufman, 1993) have also supported portions of the CHC model. In a sample of 255 normal adolescent and adult subjects, Kaufman, Ishikuma and Kaufman (1994) completed an exploratory factor analysis of 11 tests from the WAIS-R, 8 tests from the KAIT, 2 tests from the Kaufman Functional Academic Skills Test (K-FAST; Kaufman & Kaufman, 1994a), and 3 tests from the Kaufman Short Neuropsychological Assessment Procedure (K- SNAP; Kaufman & Kaufman, 1994b).  Referring to their interpretation as a “Horn analysis,” Kaufman et al (1994) provided support for four CHC domains.  Distinct Gc and Gf factors were identified.  In addition, a Gsm (MS) factor was evident, which the authors labeled, as per Horn,  Short-term Acquisition and Recall (SAR).  Kaufman et al. also presented what they termed a blended Gv/Gf factor.  Inspection of the most salient tests on this blended factor (viz., WAIS-R Object Assembly, .84; Block Design, .75; Picture Completion, .61; Picture Arrangement, .61) suggests that broad Gv is a more defensible interpretation of the factor (see McGrew & Flanagan, 1998; Woodcock, 1990).
Two additional studies using the KAIT tests deserve comment.  Although using a mixture of Cattell- Horn and Luria-Das terminology to interpret the factors, Kaufman’s (1993) exploratory factor analysis of 8 KAIT and 13 K-ABC tests in a sample of 124 11-to-12 year olds supplied evidence for six CHC domains.  Kaufman’s KAIT/K-ABC factor results supported the validity of the Gc and Gf abilities.  Kaufman’s “Achievement” factor could be interpreted as a blend of Grw and Gq.  Two different visual factors were identified and were labeled “Simultaneous” and “Broad Visualization” by Kaufman.   Post hoc CHC reinterpretation (see McGrew, 1997; McGrew & Flanagan, 1998) suggest that these two factors could be interpreted as broad Gv (salient loadings for K-ABC Photo Series, .80; Matrix Analogies, .61; Triangles, .61; Spatial Memory, .58; KAIT Memory for Block Designs, .32) and narrow Visual Memory (Gv-MV; KAIT Memory for Block Designs-.44, K- ABC Gestalt Closure-.42, K-ABC Hand Movements- .40) factors.  Finally, the factor defined by K-ABC Number Recall and Word Order could be interpreted as Memory Span (Gsm- MS) rather than “Sequential.” 
Flanagan and McGrew (1998) conducted a CHC-designed cross-battery confirmatory factor study of the KAIT tests together with select WJ-R and WISC-III tests in a non-white sample of 114 students in 6th, 7th, and 8th grade.  Although a variety of specific hypotheses were tested at the stratum I (narrow) ability level, at the broad factor level support was found for the CHC abilities of Gf, Gc, Gv (MV & CS), Ga (PC), Gsm (MS), Glr (MA), Gs (P) and Grw.  The Flanagan and McGrew study is notable in that it represented the first CHC- designed cross- battery study to attempt to evaluate, where possible in the model, all three strata of the CHC theory (see Table 1).
Finally, a number of recent studies have extended the CHC cross-battery research via the use of WJ III tests as CHC factor markers.  In a sample of 155 elementary aged subjects who had been administered 18 WJ III tests and 12 tests from the Das Naglieri Cognitive Assessment System (CAS; Naglieri & Das, 1996), Keith, Kranzler and Flanagan’s (2001) confirmatory factor analysis provided support for the CHC abilities of Gf, Gc, Gv, Ga (PC), Gsm, Glr (MA), and Gs.  In what may be the most comprehensive CHC-organized cross- battery investigation to date, McGrew, Gregg, Hoy, Stennett, Davis, Knight and Coleman (2001; reported in Kaufman & Lichtenberger, 2002) analyzed 53 different tests (26 WJ III; 6 KAIT; 11 WAIS-III; 10 WMS-III) in a mixed normal and learning disabled university sample (n = 200).  Confirmatory factor analyses provided support for the broad CHC abilities of Gf, Gc, Gv, Ga, Gsm, Glr, Grw, Gq, and Gs.  Finally, in a more recent attempt to specify a three-stratum CHC cross-battery model, Phelps, McGrew, Knopik, and Ford (2003) analyzed the performance of 148 elementary aged students on 12 WISC-III tests and 29 WJ III tests. The best fitting confirmatory model provided support for a CHC framework that included the broad abilities of Gf, Gc, Gv, Ga, Gsm, Glr, and Gs.

The Buckhalt et al. (2001) Glr factor was defined primarily by measures of Glr, but also had a number of significant loadings from tests that measure Gv abilities.  This author has repeatedly seen the same type of factor in exploratory factor analysis of the WJ-R and WJ III norm data.