Date: Jan 3, 2013 1:38 PM
Author: Luis A. Afonso
Subject: Sidak correction
Sidak correction

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.

Luis A. Afonso