We carried out a genome-wide association study (GWAS) for general cognitive ability (GCA) plus three other analyses of GWAS data that aggregate the effects of multiple single-nucleotide polymorphisms (SNPs) in various ways. Our multigenerational sample comprised 7,100 Caucasian participants, drawn from two longitudinal family studies, who had been assessed with an age-appropriate IQ test and had provided DNA samples passing quality screens. We conducted the GWAS across ∼ 2.5 million SNPs (both typed and imputed), using a generalized least-squares method appropriate for the different family structures present in our sample, and subsequently conducted gene-based association tests. We also conducted polygenic prediction analyses under five-fold cross-validation, using two different schemes of weighting SNPs. Using parametric bootstrapping, we assessed the performance of this prediction procedure under the null. Finally, we estimated the proportion of variance attributable to all genotyped SNPs as random effects with software GCTA. The study is limited chiefly by its power to detect realistic single-SNP or single-gene effects, none of which reached genome-wide significance, though some genomic inflation was evident from the GWAS. Unit SNP weights performed about as well as least-squares regression weights under cross-validation, but the performance of both increased as more SNPs were included in calculating the polygenic score. Estimates from GCTA were 35% of phenotypic variance at the recommended biological-relatedness ceiling. Taken together, our results concur with other recent studies: they support a substantial heritability of GCA, arising from a very large number of causal SNPs, each of very small effect. We place our study in the context of the literature-both contemporary and historical-and provide accessible explication of our statistical methods.