Bonferroni procedure, multiple testing

A number of procedures for controlling error rates have been developed to solve the multiple-testing problem (Dudoit et al., 2003). The Bonferroni procedure for controlling the FWER at level a rejects any hypothesis Hj with unadjusted p-value... 

Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika, 75(4) ... 

Hommel, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. 

The primary statistical tests used in the studies described in this text are based on the chi-square tests which are in turn derived from the chi-square distribution which is based on the chi distribution. These tests include the chi-square test for goodness of fit, the chi-square test of independence, and Fisher s Exact Test. There are also corrections to some of the tests that account for small number deviations, Yates Correction for Continuity, and for multiple studies attempting to verify the same procedures or processes, Bonferroni s correction. 

There is a knotty issue in multiple regression with using the Student s t-test for >1 independent predictors. That is, because more than one test was conducted, for example, 0.95 = 0.857 confidence. To adjust for this, the user can undertake a correction process, such as the Bonferroni joint confidence procedure. In our example, there are parameters, if one includes bo. Not all of them need to be tested, but whatever that test number is, we call it as g, where g Bonferroni method is /8i =bi <(a/2g n-i-i>S6- This is the same formula as the previous one, using the t-table, except that a is divided by 2g, where g is the number of contrasts. 

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