Selection and description of studies
A research investigation had to meet all of the following criteria to be included in the current review. First, the study had to be explicitly designed as per the CHC (or Gf-Gc) cognitive abilities framework. Second, the study must have empirically investigated the relations between the primary CHC cognitive variables (independent variables; IVs) and achievement variables in reading and math (dependent variables; DVs). Third, the research report had to report quantitative information (e.g., reporting of statistical difference tests; regression weights; effect sizes) regarding the relevant strength of each CHC IV and the respective achievement DV domain. Finally, the study had to include markers from 5 or more of the 7 primary CHC cognitive domains.    
Nineteen investigations met all criteria. Each investigation was described (see Table 1) according to: type of sample, age or grade range of samples , size of sample(s), number of samples analyzed, cognitive assessment batteries providing the IVs , CHC strata of IVs, achievementDVs , type of achievement DV, and type of analyses (see Table 1 notes for additional information). Inspection of the 19 investigations reflected a division between studies that analyzed observable or manifestIVs (and no full scale or g score) and those that analyzed latentIVs (with or without a latent g factor).
Insert Table 1 about here  (click here to view)
The majority of investigations reported results for more than one sample. For example, in Study 1 (McGrew, 1993), 15 subsamples (sample n range of 59-325) of the WJ-R norm data were analyzed separately with multiple regression methods across the ages of 5 to 19 years. However, from this point forward we refer to the number of analyses and not the number of samples. This is an important distinction given that many analyses used the same norm subjects (e.g., WJ-R or WJ III standardization data) but divided the same subject pool into different age groups, analyzed the same set of subject data but employed different analysis methods, or analyzed test vs. cluster scores with the same subject pool (see second note in Table 1). Thus, many of the samples were not independent—but the analyses were. There were a total of 134 analyses—54.5 % were manifest variable (MV; n=73) and 45.5 % were latent variable (LV; n=61). 
Of the 134 analyses, 126 (94 %) were exclusive to the WJ-R or WJ III norm data. Given the preponderance of WJ-R and WJ III studies, the coded age-ranges were driven, in large part, by the age- ranges reported in these investigations. The result was the division of the analyses into the age groups of 6-8, 9-13, and 14-19 years of age.  For investigations that analyzed a finer gradation of development (e.g., McGrew, 1993, reported regression results for each year from ages 5 thru 19), the appropriate subsamples (e.g., results for ages 5, 6, 7 and 8) were treated as a single age group (ages 6-8). Certain studies (studies 7-10) were based on a single wide-range sample (e.g., Ganci, 2004, samples of elementary reading disabled (RD) and non-reading disabled (NRD) across ages 6-12) and thus, these single sets of results were included in each of the broad three age groups for which the single sample included subjects. This resulted in some single wide-age samples being reported in 2 or 3 of the three major age-grouped analyses.
19 studies included in review (Table 1)
As reported in Table 1, studies were categorized as analyzing either manifest or latent variables.  Most studies also used one of four types of research analysis methods.  A summary description and pictorial representation of the four types of research models can be accessed byclicking here.
Below are references and links to the 19 research studies included in Table 1.
Benson, N. (2009).  Integrating psychometric and information processing perspectives to clarify the process of mathematical reasoning.  Manuscript in preparation.
Benson, N. (2008). Cattell-horn-carroll cognitive abilities and reading achievement. Journal of Psychoeducational Assessment, 26(1), 27-41.
Evans, J. J., Floyd, R. G., McGrew, K. S., & Leforgee, M. H. (2002). The relations between measures of Cattell-Horn-Carroll (CHC) cognitive abilities and reading achievement during childhood and adolescence. School Psychology Review, 31(2), 246-262.
Flanagan, D. P. (2000). Wechsler-based CHC cross-battery assessment and reading achievement: Strengthening the validity of interpretations drawn from Wechsler test scores. School Psychology Quarterly, 15(3), 295-329.
Floyd, R. G., Bergeron, R., & Alfonso, V. C. (2006). Cattell-Horn-Carroll cognitive ability profiles of poor comprehenders. Reading and Writing, 19(5), 427- 456.
Floyd, R. G., Evans, J. J., & McGrew, K. S. (2003). Relations between measures of Cattell- Horn-Carroll (CHC) cognitive abilities and mathematics achievement across the school- age years. Psychology in the Schools, 40(2), 155-171.
Floyd, R. G., Keith, T. Z., Taub, G. E., & McGrew, K. S. (2007). Cattell-Horn-Carroll cognitive abilities and their effects on reading decoding skills: g has indirect effects, more specific abilities have direct effects. School Psychology Quarterly, 22(2), 200-233.
Ganci, M. (2004). The diagnostic validity of a developmental neuropsychological assessment (NEPSY) - Wechsler Intelligence Scale for Children-third edition (WISC-III) based cross battery assessment. Retrieved from ProQuest UMI Dissertation Publishing (UMI Microform 3150999).
Hale, J. B., Fiorello, C. A., Dumont, R., Willis, J. O., Rackley, C., & Elliott, C. (2008). Differential Ability Scales-Second Edition (Neuro) psychological predictor of math performance for typical children and children with math disabilities. Psychology in the Schools, 45(9), 838-858.
Keith, T. Z. (1999). Effects of general and specific abilities on student achievement: Similarities and differences across ethnic groups. School Psychology Quarterly, 14(3), 239-262.
McGrew, K. (2007)Prediction of WJ III reading and math achievement by WJ III cognitive and language tests.  Unpublished data analysis available at IQs Corner Blog.
McGrew, K. (2008)Cattell-Horn-Carroll g and specific ability effects on reading and math: Reanalysis of Phelps et al. (2007).  Unpublished data analysis available at IQs Corner Blog.
McGrew, K. S. (1993). The relationship between the WJ-R Gf-Gc cognitive clusters and reading achievement across the lifespan. Journal of Psychoeducational Assessment, Monograph Series: WJ R Monograph,  39-53.
McGrew, K. S., Flanagan, D. P., Keith, T. Z., & Vanderwood, M. (1997). Beyond g:  The impact of Gf-Gc specific cognitive abilities research on the future use and interpretation of intelligence tests in the schools . School Psychology Review, 26(2), 189-210.
McGrew, K. S., & Hessler, G. L. (1995). The relationship between the WJ-R Gf-Gc cognitive clusters and mathematics acheivement across the life-span. Journal of Psychoeducational Assessment, 13, 21-38.
Miller, B. D. (2001). Using Cattell-Horn-Carroll cross-battery assessment to predict reading achievement in learning disabled middle school students. Retrieved from ProQuest UMI Dissertation Publishing (UMI Microform 9997281).
Proctor, B. E., Floyd, R. G., & Shaver, R. B. (2005). Cattell-Horn-Carroll broad cognitive ability profiles of low math achievers. Psychology in the Schools, 42(1), 1-12.
Taub, G. E., Floyd, R. G., Keith, T. Z., & McGrew, K. S. (2008). Effects of general and broad cognitive abilities on mathematics achievement. School Psychology Quarterly, 23(2), 187-198.
Vanderwood, M. L., McGrew, K. S., Flanagan, D. P., & Keith, T. Z. (2002). The contribution of general and specific cognitive abilities to reading achievement. Learning and Individual Differences, 13, 159-188.