Statistics and Its Interface

Volume 6 (2013)

Number 1

On permutation procedures for strong control in multiple testing with gene expression data

Pages: 79 – 89



Grzegorz A. Rempala (Department of Biostatistics and Cancer Research Center, Georgia Health Sciences University, U.S.A.)

Yuhong Yang (School of Statistics, University of Minnesota, U.S.A.)


We consider two popular, permutation-based, step-down procedures of $p$-values adjustment in multiple testing problems known as min $P$ and max $T$ and intended for strong control of the family-wise error rate, under the so-called subset pivotality property (SPP). We examine key but subtle issues involved in ascertaining validity of these methods, and also introduce a new, slightly narrower notion of strong control which ensures proper bounds on the family-wise error rate in min $P$ and max $T$ without SPP.


multiple testing, strong control of family-wise error rate, step down p-value adjustment methods, subset pivotality property, permutation test

2010 Mathematics Subject Classification

Primary 62H15, 62J15. Secondary 92D10.

Published 18 March 2013