identifying the true variances for these values). Of course, we would expect to see clustering of nominally-positive SNPs in each sample in regions in which there was either a) linkage disequilibrium between the SNPs studied and between these SNPs and functional variants that influenced addiction vulnerability or b) linkage disequilibrium between these SNPs and stochastic differences in haplotype frequencies in individual samples of cases vs those in a single sample of controls that are unrelated to the phenotype. The second way in which we seek replication identifies, in independent samples, many of the same chromosomal regions based on their content of clustered, nominally positive SNPs. This comparison addresses the null hypothesis that the clustering observed in each sample derives from stochastic case vs control differences in haplotype frequencies rather than case vs control differences that are truly related to differences in phenotypes. This comparison also provides additional support for our ability to reject the null and alternative hypotheses relating to assay noise. We thus identify more chromosomal regions and genes based on the overlap between the chromosomal regions identified by data from each sample than we would expect if the only reason for clustering of nominally positive SNPs in each
