mutoss (version 0.1-10)

holm: Holm's (1979) step-down-procedure

Description

Holm's step-down-procedure is applied to pValues. It controls the FWER in the strong sense under arbitrary dependency.

Usage

holm(pValues, alpha, silent=FALSE)

Arguments

pValues

pValues to be used. They can have arbitrary dependency structure.

alpha

The level at which the FWER shall be controlled

silent

If true any output on the console will be suppressed.

Value

adjPValues

A numeric vector containing the adjusted pValues

rejected

A logical vector indicating which hypotheses are rejected

criticalValues

A numeric vector containing critical values used in the step-down test

errorControl

A Mutoss S4 class of type errorControl, containing the type of error controlled by the function and the level alpha.

Details

Holm's procedure uses the same critical values as Hochberg's procedure, namely c(i)=alpha/(m-i+1), but is a step-down version while Hochberg's method is a step-up version of the Bonferroni test. Holm's method is based on the Bonferroni inequality and is valid regardless of the joint distribution of the test statistics, whereas Hochberg's method relies on the assumption that Simes' inequality holds for the joint null distribution of the test statistics. If this assumption is met, Hochberg's step-up procedure is more powerful than Holm's step-down procedure.

References

S. Holm (1979). A simple sequentially rejective multiple test procedure. Scand. J. Statist. Vol. 6, 65-70. $n$

Huang, Y. and Hsu, J. (2007). Hochberg's step-up method: cutting corners off Holm's step-down method. Biometrika, 94(4):965-975.

Examples

result 	<- holm(r, 0.05)
result 	<- holm(r, 0.05, silent = TRUE)