Although we see evidence of at least three axes with large genetic variations in each of the four combinations of cases and controls considered here, confounding by PS would occur only when cases and controls distribute differently along one or more main axes of variations. To assess confounding by PS in each study, we compared the distribution of the cases and controls for each of the top 5 PC directions by using the Wilcoxon rank-sum test (Table 3). The analysis was restricted to the first 5 PC directions in each study since all other directions were not significant by the Tracy-Widom test.
