of the second-stage GWAS compared to what would be expected by chance (H0 = 0.5); (2) a binomial test of whether a greater proportion of the SNPs were nominally significant (two-sided P < 0.05) in the second-stage GWAS compared to the empirical null distribution; (3) a test of joint enrichment, using a non-parametric (one-sided) Mann-Whitney test of the null hypothesis that the P values of the SNPs are derived from the empirical null distribution. We strongly rejected the null hypotheses in all quasi-replication tests, suggesting that the externalizing GWAS is not spurious overall and that it was more enriched for association with the second-stage phenotypes than their respective polygenic background GWAS signal.
