The bottom panel of Table 1 evaluates the performance of competing methods under the situation that the strength of association between the SNP and phenotypic traits varies from 0.1 to 0.5. Similar to the previous situation, the three Fisher combination tests had almost identical performance and their power decreased as the correlation ϱ increased. Furthermore, the Fisher combination tests had higher power than the other three methods (MANOVA, PCA, and TATES) in most conditions. MANOVA only beat the Fisher when ϱ=0.75; TATES had higher power than the Fisher when ϱ≥0.5.