# BY: Benjamini-Yekutieli (2001) step-up procedure In mutoss: Unified Multiple Testing Procedures

 BY R Documentation

## Benjamini-Yekutieli (2001) step-up procedure

### Description

The Benjamini-Yekutieli step-up procedure is applied to pValues. The procedure ensures FDR control for any dependency structure.

### Usage

``BY(pValues, alpha, silent=FALSE)``

### Arguments

 `pValues` The used unadjusted pValues. `alpha` The level at which the FDR shall be controlled. `silent` If true any output on the console will be suppressed.

### Details

The critical values of the Benjamini-Yekutieli (BY) procedure are calculated by replacing the alpha of the Benjamini-Hochberg procedure by alpha/sum(1/1:m)), i.e., c(i)=i*alpha/(m*(sum(1/1:m))) for i=1,...,m. For large number m of hypotheses the critical values of the BY procedure and the BH procedure differ by a factor log(m). Benjamini and Yekutieli (2001) showed that this step-up procedure controls the FDR at level alpha*m/m0 for any dependency structure among the test statistics.

### 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`.

WerftWiebke

### References

Benjamini, Y. and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics, 29(4):1165-1188.

### Examples

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

mutoss documentation built on March 31, 2023, 8:46 p.m.