We do not pursue this approach here, principally because it does not reflect the way GWAS experiments are typically used in practice: regardless of the genotyping chip used, whether or not genotype imputation is employed, and the population studied, researchers tend to focus on the most significant SNPs after the GWAS and try to confirm that they are real in replication studies. In addition, as noted above, overall GWAS false positive rates are low, for any of the commercial chips, at the very low per-SNP significance level we consider. Nonetheless, in what follows, readers should be aware that we are comparing power, defined here as the probability that at least one SNP reaches a fixed p-value threshold under specific assumptions about design and effect sizes, across settings in which these very low false positive rates will differ between chips (and across populations).
