When a set of k independent statistical tests is performed we must adapt the significance level in order to obtain a global desired level, alpha= 0.05 or 0.01. One must set, with alpha´ the significance level of each individual test: ____alpha = 1 - (1-alpha´)^k _alpha is the probability to get at least one significant test among k. From which we find alpha´ = 1 - (1- alpha)^(1/k) __ 1 minus the k root of (1-alpha). Therefore setting all k individual tests at alpha´ level we are sure that alpha is the probability to observe at least one of them significant. For k=2: ___________alpha________alpha´_____ ___________0.05________0.02532____ ___________0.01________0.00501____
Bonferroni´s correction, alpha´ = alpha/2, leads to similar values: 0.025 and 0.005 respectively.