sidak {mutoss}

Sidak correction

Description

The classical Sidak correction returns adjusted p-values, ensuring strong FWER control under the assumption of independence of the input p-values. It only uses the fact that the probability of no incorrect rejection is the product over true nulls of those marginal probabilities (using the assumed independence of p-values).

Usage

sidak(pValues, alpha, silent=FALSE)

Arguments

pValues

pValues to be used.

alpha

The level at which the FWER shall be controlled (optional).

silent

logical scalar. If TRUE no output is generated.

Details

The procedure is more generally valid for positive orthant dependent test statistics.

It is recommended to use the step-down version of the Sidak correction instead (see SidakSD), which is valid under the exact same assumptions but is more powerful.

Value

A list containing:

adjPValues

A numeric vector containing the adjusted pValues

rejected

(if alpha is given) A logical vector indicating which hypotheses are rejected

errorControl

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

Author(s)

MuToss-Coding Team

References

Sidak, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association, 62:626-633.

Examples

alpha <- 0.05
p <-c(runif(10, min=0, max=0.01), runif(10, min=0.9, max=1))
result <- sidak(p)
result <- sidak(p, alpha)
result <- sidak(p, alpha, silent=TRUE)