Bonferroni correction hides significant motif combinations

Three or more motifs often work together, and the effects are essential in cellular machinery. However, the scanning of the associations of motifs is limited to single motifs or pairs, as the result of scanning for combinations of three or more motifs often includes no significant results. Even if we find a combination with a very small raw P-value in the scan, the combination is not significant because the adjusted P-value by a multiple testing correction, such as the Bonferroni correction, is larger than the given significance level. While it is known that the Bonferroni correction is a very conservative correction, a few biological experiments have used more sensitive random permutation based multiple testing correction such as Westfall-Young procedure (WY procedure). In this paper, we show that the Bonferroni correction and its modified procedure are too conservative to find statistically significant combinations consisting of three or more motifs, while the WY procedure can detect them. These results suggest that the statistically significant epistatic effects have been overlooked and motivate us to reanalyze the publicly available datasets.