In our approach, we tried to eliminate possible causes of sample structure (for example, hidden relatedness, population stratification) that may lead to spurious association.56 Consequently, phenotypic correlations between individuals are due to genetic similarities so that the estimated genetic variance component entirely reflects LD between the genotyped SNPs and the unknown causal variants. Our estimates are unbiased estimates of the variance in neuroticism and extraversion explained by common SNPs, so that the estimates are not expected to change (within bounds implied by the s.e. and assuming the same genomic coverage by SNPs) as sample sizes increase. These results imply that with larger sample sizes, common associated variants could be detected in single SNP analysis, depending on effect sizes of single variants.