Empirical Type I error results. Two sub-populations of 500 individuals each, Fst = 0.01. K1 and p1 are the population prevalence of disease and risk allele frequency, respectively, in sub-population 1. K2 and p2 are the population prevalence of disease and risk allele frequency, respectively, in sub-population 2. The x-axis is the various methods of selecting PCs for inclusion in the model of association and the symbols in the plot represent the phenotypic structure. The y-axis is the proportion of logistic regression models adjusting for the selected PCs for which the SNP p-values are significant at a significance level of 0.05.