Bonferroni correction
bonferroni(pValues, alpha, silent=FALSE)A list containing:
A numeric vector containing the new adjusted pValues
(if alpha is given) A logical vector indicating which hypotheses are rejected
A Mutoss S4 class of type errorControl, containing the type of error controlled by the function.
A numeric vector containing the unadjusted pValues. No assumption is made on the dependence structure.
The overall type I error at which the FWER shall be controlled (optional).
logical scalar. If TRUE no output is generated.
MuToss-Coding Team
The classical Bonferroni correction outputs adjusted p-values, ensuring strong FWER control under arbitrary dependence of the input p-values. It simply multiplies each input p-value by the total number of hypotheses (and ceils at value 1).
It is recommended to use Holm's step-down instead, which is valid under the exact same assumptions and more powerful.
Bonferroni, C. E. (1935) Il calcolo delle assicurazioni su gruppi di teste. 'In Studi in Onore del Professore Salvatore Ortu Carboni. Rome: Italy, pp. 13-60.
Bonferroni, C. E. (1936) Teoria statistica delle classi e calcolo delle probabilita. Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze 8, 3-62, 1936.