The conventional statistic here is an ANOVA F-statistic. (See for instance [29]). We have here a “one-way layout,” where we want to test if the group means significantly differ. This amounts to a check on our Tracy–Widom statistic, which we compute ignoring the labels. We also routinely compute an F-statistic for every pair of populations, and each eigenvector (unpublished data). We give three examples of ANOVA analysis on real data. In the first, we look at population data from sub-Saharan Africa, genotyped with 783 microsatellites and 210 biallelic indels in the CEPH–HGDP dataset [30,31]. We group the West African and Bantu speaking populations (Yoruba, Bantu South Africa, and Bantu Kenya) as “Bantu” and also examine samples from San and Mandenka. We show plots of the first two eigenvectors in Figure 4. Table 1 shows the key statistics for this dataset. In Table 1, the ANOVA p-value is obtained from the usual F-statistic, and we apply ANOVA to each of the first three eigenvectors.
