We examined the degree to which the conventional notion of g associated with IQ tests and general cognitive ability tests ("COG-g") relate to the general ability that underlies tests of reading, math, and writing achievement ("ACH-g"). Two large, nationally representative data sets and two independent individually-administered set of test batteries were analyzed using confirmatory factor analysis procedures: (a) the Kaufman-II sample (N=2520), organized into six age groups between 4-5 and 16-19 years, tested on both the Kaufman Assessment Battery for Children-2nd ed. (KABC-II) and the Kaufman Test of Educational Achievement-2nd ed. (KTEA-II) Comprehensive Form; and (b) the WJ III sample (N=4969), organized into four age groups between 5-6 and 14-19 years, tested on both the Cognitive and Achievement batteries of the Woodcock-Johnson-3rd ed. (WJ III). Second-order latent factor models were used to model the test scores. Multi-group confirmatory factor analysis was used to investigate factor loading invariance across the age groups. In general, invariance was tenable, which allowed for valid comparisons of second-order "COG-g" and "ACH-g" factor variance/covariances and correlations across age. Although "COG-g" and "ACH-g" were not isomorphic, they correlated substantially, with an overall mean correlation coefficient of 0.83, and with the correlations generally increasing with age (ranging from 0.77 to 0.94). The nature of the relation between "COG-g" and "ACH-g" was explored and the best measures of "COG-g" were examined. (Contains 9 tables and 2 figures.)