We adopt the second perspective throughout this paper, and our power calculations are for the probability that for each of the genotyping chips considered, there will be SNPs reaching a prespecified, low, p-value, under specific assumptions about the underlying genetic effects. Given current practice, we believe the right quantity to calculate would be the probability, for the respective chips, effect sizes, and sample sizes, that the experiment would give rise to SNPs showing enough signal to be taken forward for replication. This is (inevitably) ill-posed, so we focus instead on a surrogate for it, namely the probability that at least one SNP will have a p-value below a very stringent threshold. In this context there is nothing special about the choice of p-value threshold, and it is now well understood, for example from meta-analyses, that SNPs well down any ranked list of hits from the GWAS associations can still be genuine associations. For definiteness, we focus throughout on the threshold of p<5×10−7). This is deliberately set so that false positive rates will be low – for example, most SNPs with
