5.3 C. Beyond g: CHC Lower-Stratum Abilities are Important
“The g factor (and highly g-loaded test scores, such as the IQ) shows a more far-reaching and universal practical validity than any other coherent psychological construct yet discovered” (Jensen, 1998, p. 270).   The strength of g’s prediction, together with past attempts to move “beyond g” (i.e., the addition of specific abilities to g in the prediction and explanation of educational and occupational outcomes), historically have not met with consistent success. In his APA presidential address, McNemar (1964) concluded “the worth of the multi-test batteries as differential predictors of achievement in school has not been demonstrated” (p. 875).   Cronbach and Snow’s (1977) review of the aptitude-treatment interaction (ATI) research similarly demonstrated that beyond general level of intelligence (g), few, if any, meaningful specific ability- treatment interactions existed.  Jensen also reinforced the preeminent status of g when he stated that “g accounts for all of the significantly predicted variance; other testable ability factors, independently of g, add practically nothing to the predictive validity” (Jensen, 1984, p. 101). 
In applied assessment settings, attempts to establish the importance of specific abilities above and beyond the full scale IQ (research largely based on the Wechsler batteries) score have typically meet with failure.  As a result, assessment practitioners have been admonished to “just say no” to the practice of interpreting subtest scores in individual intelligence batteries (McDermott, Fantuzzo, & Glutting, 1990; McDermott & Glutting, 1997).  The inability to move beyond g has provided little optimism for venturing beyond an individual’s full scale IQ score in the applied practice of intelligence test interpretation.  However, Daniel, (2000) believes these critics have probably “overstated” their case given some of the techniques they have used in their research.
Despite the “hail to the g” mantra, a number of giants in the field of intelligence continue to question the “conventional wisdom” of complete deference to g (Carroll, 1996).   Carroll (1993) concluded that “there is no reason to cease efforts to search for special abilities that may be relevant for predicting learning” (p. 676).  In a subsequent publication, Carroll (1996) stated that “I believe that the conventional wisdom is to some extent incorrect, however, because there are many types of learning or performance that can be shown to depend not only on the general factor but also on lower-stratum factors…I would point out that although Spearman attached great importance to the general factor, he regarded some lower-stratum factors as being of educational and occupational significance” (p. 8).  Snow (1998) struck a similar chord when he stated that
certainly it is often the case that many ability-learning correlations can be accounted for by an underlying general ability factor.  Yet, there are clearly situations, such as spatial- mechanical, auditory, or language learning conditions, in which special abilities play a role aside from G (p. 99).
In the school psychology literature, Flanagan (1999), McGrew, Flanagan, Keith and Vanderwood (1997) and Keith (1999) have suggested that advances in theories of intelligence (viz., CHC theory), the development of CHC theory- driven intelligence batteries (viz., WJ-R, WJ III) , and the use of more contemporary research methods (e.g., structural equation modeling, SEM) argue for continued efforts to investigate the effects of g and specific abilities on general and specific achievements.  A brief summary of CHC-based g+specificàachievement abilities research follows.
CHC g+Specific-to- Achievement SEM Studies
Using a Gf-Gc framework, Gustafsson and Balke (1993) reported that some specific cognitive abilities may be important in explaining school performance beyond the influence of g when: (1) a Gf-Gc intelligence framework is used, (2)  cognitive predictor and academic criterion measures are both operationalized in multidimensional hierarchical frameworks, and (3) cognitiveàachievement relations are investigated with research methods (viz., SEM) particularly suited to understanding and explaining (versus simply predicting).  The key advantage of the SEM method is that it allows for the simultaneous inclusion of casual paths (effects) from a latent g factor, plus specific paths for latent factors subsumed by the g factor, to a common dependent variable factor (e.g., reading).  This is not possible when using multiple regression methods.
Drawing on the research approach outlined by Gustafsson and Balke (1993), a series of CHC designed studies completed during the past decade have identified significant CHC narrow or broad effects on academic achievement, above and beyond the effect of g.  Using the Cattell- Horn Gf-Gc based WJ-R norm data, McGrew, Flanagan, Keith, and Vanderwood (1997) and Vanderwood, McGrew, Flanagan, and Keith (2002) found, depending on the age level (five grade- differentiated samples from grades 1-12), that the CHC abilities of Ga, Gc, and Gs had significant cross-validated effects on reading achievement above and beyond the large effect of g.  In the 1st-2nd grade cross- validation sample (n = 232), McGrew et al. (1997) reported a strong direct effect of g on reading which was accompanied by significant specific effects for Ga (.49) on word attack skills and Gc (.47) on reading comprehension.  In math, specific effects beyond the high direct g effect were reported at moderate levels (generally .20 to .30 range) for Gs and Gf, while Gc demonstrated high specific effects (generally .31 to .50 range). Using the same WJ-R norm data, Keith (1999) employed the same g+specificàachievement SEM methods in an investigation of general (g) and specific effects on reading and math as a function of ethnic group status.  Keith’s (1999) findings largely replicated those of McGrew et al. (1997) and suggested that CHC g+specificàachievement relations are largely invariant across ethnic group status.
In a sample of 166 elementary aged students, Flanagan (2000) applied the same methodology used by McGrew et al. (1997), Keith et al. (1999) and Vanderwood et al. (2002) to a WISC- R+WJ-R “cross-battery” dataset.  A strong .71 direct effect for g on reading was found, together with significant specific effects for Ga (.28) on word attack and Gs (.15) and Gc (.42) on reading comprehension.  More recently, McGrew (2000) reported the results of similar modeling studies with the CHC-based WJ III.  In three age- differentiated samples (ages 6-8, 9-13, 14-19), in addition to the ubiquitous large effect for g on reading decoding (.81 to .85), significant specific effects were reported for Gs (.10 to .35) and Ga (.42 to .47). 
Beyond g: Summary
Collectively, the CHC-based g+specificàachievement SEM studies reported during the last decade suggest that even when g (if it does exist) is included in causal modeling studies, certain specific lower-stratum CHC abilities display significant causal effects on reading and math achievement.  Critics could argue that the trivial increases in model fit and the amount of additional achievement variance explained (vis-à-vis the introduction of specific lower-order CHC paths) is not statistically significant (which is the case), and thus, Occam’s Razor would argue for the simpler models that only include g.  Alternatively, knee-jerk acceptance of Occam’s Razor can inhibit scientifically meaningful discoveries. As best stated by Stankov, Boyle and Cattell (1995) in the context of research on human intelligence, “while we acknowledge the principle of parsimony and endorse it whenever applicable, the evidence points to relative complexity rather than simplicity.  Insistence on parsimony at all costs can lead to bad science” (1995, p. 16). 
In sum, even when a Carroll g-model of the structure of human cognitive abilities is adopted, research indicates that a number of lower-stratum CHC abilities make important contributions to understanding academic achievement, above and beyond g. Reschly (1997) reached the same conclusion when he stated, in response to the first McGrew et al. (1997) paper, that “the arguments were fairly convincing regarding the need to reconsider the specific versus general abilities conclusions.   Clearly, some specific abilities appear to have potential for improving individual diagnoses.  Note, however, that it is potential that has been demonstrated...” (p. 238).

[Note. The g+specificà achievement studies could be considered to represent the Carroll position on how cognitive abilities predict/explain academic achievement.  The Horn position could similarly be operational defined in research studies that use either SEM or multiple regression of the lower-order CHC variables on achievement (no g included in the models).  The results of such Horn CHCàachievement models, completed in either the WJ-R or WJ III norm data, can be found in McGrew (1993), McGrew and Hessler (1995), McGrew and Knopik (1993), Evans, Floyd. McGrew and Leforgee (2002), Floyd, Evans and McGrew (2003).  With the exception of Gv, all broad CHC abilities (Gf, Gc, Ga, Glr, Gsm, Gs) are reported to be significantly associated (at different levels that often vary within each ability domain by age) with reading, math, and writing achievement in the Horn CHCàachievement model. ]