There is increasing use of dense single nucleotide polymorphisms (SNPs) for whole-genome association studies (WGAS) in livestock to map and identify quantitative trait loci (QTL). These studies rely on linkage disequilibrium (LD) to detect an association between SNP genotypes and phenotypes. The power and precision of these WGAS are unknown, and will depend on the extent of LD in the experimental population. One complication for WGAS in livestock populations is that they typically consist of many paternal half-sib families, and in some cases full-sib families; unless this subtle population stratification is accounted for, many spurious associations may be reported. Our aim was to investigate the power, precision and false discovery rates of WGAS for QTL discovery, with a commercial SNP array, given existing patterns of LD in cattle. We also tested the efficiency of selective genotyping animals. A total of 365 cattle were genotyped for 9232 SNPs. We simulated a QTL effect as well as polygenic and environmental effects for all animals. One QTL was simulated on a randomly chosen SNP and accounted for 5%, 10% or 18% of the total variance. The power to detect a moderate-sized additive QTL (5% of the phenotypic variance) with 365 animals genotyped was 37% (p < 0.001). Most importantly, if pedigree structure was not accounted for, the number of false positives significantly increased above those expected by chance alone. Selective genotyping also resulted in a significant increase in false positives, even when pedigree structure was accounted for.