The TATES test is a modification of the Simes (Simes 1986) and GATES (Li et al. 2011) corrections for multiple testing. The Simes test is a modification of the Bonferroni correction intended to adjust for multiple testing. Assume that p1, p2,…, pm are p-values corresponding to test statistics Z1, Z2,…, Zm of multiple tests H1, H2,…, Hm, respectively. It is assumed that the test statistics are continuous. Then, under the null hypothesis the distribution of the p-values is uniform on [0,1]. For any given significance level α the test is defined as follows: with p(1) ≤ p(1) ≤ … ≤ p(m) ordered, reject H0={H1, H2,…, Hm] if p(j) ≤ α j / m for any j = 1,2,…, m and is based on the inequality: Pr{∪j=1m(p(j)≤αj/m)}≤αThe resulting Simes p-value is: pSimes=minj{mjp(j)}.
