# BL: Benjamini-Liu (1999) step-down procedure In mutoss: Unified Multiple Testing Procedures

## Description

Benjamini-Liu's step-down procedure is applied to pValues. The procedure controls the FDR if the corresponding test statistics are stochastically independent.

## Usage

 `1` ```BL(pValues, alpha, silent=FALSE) ```

## Arguments

 `pValues` Numeric vector of p-values `alpha` The level at which the FDR is to be controlled. `silent` If true any output on the console will be suppressed.

## Details

The Benjamini-Liu (BL) step-down procedure neither dominates nor is dominated by the Benjamini-Hochberg (BH) step-up procedure. However, in Benjamini and Liu (1999) a large simulation study concerning the power of the two procedures reveals that the BL step-down procedure is more suitable when the number of hypotheses is small. Moreover, if most hypotheses are far from the null then the BL step-down procedure is more powerful than the BH step-up method. The BL step-down method calculates critical values according to Benjamin and Liu (1999), i.e., c_i = 1 - (1 - min(1, (m*alpha)/(m-i+1)))^(1/(m-i+1)) for i = 1,...,m, where m is the number of hypotheses tested. Then, let k be the smallest i for which P_(i) > c_i and reject the associated hypotheses H_(1),...,H_(k-1).

## Value

A list containing:

 `adjPValues` A numeric vector containing the adjusted pValues. `criticalValues` A numeric vector containing critical values used in the step-up-down test. `rejected` 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 and the level `alpha`.

Werft Wiebke

## References

Bejamini, Y. and Liu, W. (1999). A step-down multiple hypotheses testing procedure that controls the false discovery rate under independence. Journal of Statistical Planning and Inference Vol. 82(1-2): 163-170.

## Examples

 ```1 2 3 4``` ```alpha <- 0.05 p <-c(runif(10, min=0, max=0.01), runif(10, min=0.9, max=1)) result <- BL(p, alpha) result <- BL(p, alpha, silent=TRUE) ```

mutoss documentation built on May 2, 2019, 2:38 a.m.