Diverse tests of cognitive abilities correlate about 0.30 phenotypically and about 0.60 genetically. Their phenotypic overlap defines general cognitive ability (g), driven largely by genetic overlap. Consequently, much of our understanding of the genetic landscape of specific cognitive tests likely reflects g rather than the tests themselves. Removing this g-associated genetic variance will sharpen research on cognitive tests. Here, we use Genomic Structural Equation Modelling (Genomic SEM) to remove shared genetic variance among 12 diverse cognitive tests that capture verbal and nonverbal cognitive domains. We applied Genomic SEM to summary statistics from the largest genome-wide association studies of verbal tests (GenLang Consortium, five tests) and largely nonverbal tests (UK Biobank, seven tests) to chart the genetic landscape of the 12 tests independent of g as compared to uncorrected cognitive tests. We found that SNP heritabilities were nearly as high for the tests corrected for g as uncorrected: the average SNP heritability was 0.16 (SE = 0.02) for the uncorrected tests and 0.13 (SE = 0.02) for the tests corrected for g. Despite this, the genetic landscape of the cognitive tests transformed after controlling for genomic g. The matrix of positive genetic correlations for the cognitive tests (average 0.45) disappeared after g-correction, and some strong negative correlations emerged
for instance, Memory and Word (-0.72), Fluid and Symbol (-0.72), and Tower and Spelling (-0.79). The summary statistics for these g-corrected cognitive tests can be used by researchers to create polygenic scores that focus on the specificity of the tests.