\HeaderA{mt.rawp2adjp}{Adjusted p-values for simple multiple testing procedures}{mt.rawp2adjp}
\keyword{htest}{mt.rawp2adjp}
\begin{Description}\relax
This function computes adjusted \eqn{p}{}-values for simple
multiple testing procedures from a vector of raw (unadjusted)
\eqn{p}{}-values. The procedures include the Bonferroni, Holm (1979),
Hochberg (1988), and Sidak procedures for strong control of the
family-wise Type I error rate (FWER), and the Benjamini \& Hochberg
(1995) and Benjamini \& Yekutieli (2001) procedures for (strong)
control of the false discovery rate (FDR).
\end{Description}
\begin{Usage}
\begin{verbatim}
mt.rawp2adjp(rawp, proc=c("Bonferroni", "Holm", "Hochberg", "SidakSS", "SidakSD", "BH", "BY"))
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{rawp}] A vector of raw (unadjusted) \eqn{p}{}-values for each
hypothesis under consideration. These could be nominal
\eqn{p}{}-values, for example, from t-tables, or permutation
\eqn{p}{}-values as given in \code{mt.maxT} and \code{mt.minP}. If the
\code{mt.maxT} or \code{mt.minP} functions are used, raw
\eqn{p}{}-values should be given in the original data order,
\code{rawp[order(index)]}.
\item[\code{proc}] A vector of character strings containing the names of the
multiple testing procedures for which adjusted \eqn{p}{}-values are to
be computed. This vector should include any of the following:
\code{"Bonferroni"}, \code{"Holm"}, \code{"Hochberg"},
\code{"SidakSS"}, \code{"SidakSD"}, \code{"BH"}, \code{"BY"}. 

\end{ldescription}
\end{Arguments}
\begin{Details}\relax
Adjusted \eqn{p}{}-values are computed for simple FWER and FDR
controlling procedures based on a vector of raw (unadjusted)
\eqn{p}{}-values.
\item[Bonferroni] Bonferroni single-step adjusted \eqn{p}{}-values
for strong control of the FWER. 
\item[Holm] Holm (1979) step-down adjusted \eqn{p}{}-values for
strong control of the FWER.
\item[Hochberg] Hochberg (1988) step-up adjusted \eqn{p}{}-values
for 
strong control of the FWER (for raw (unadjusted) \eqn{p}{}-values
satisfying the Simes inequality). 
\item[SidakSS] Sidak single-step adjusted \eqn{p}{}-values for
strong control of the FWER (for positive orthant dependent test
statistics). 
\item[SidakSD] Sidak step-down adjusted \eqn{p}{}-values for
strong control of the FWER (for positive orthant dependent test
statistics). 
\item[BH] adjusted \eqn{p}{}-values for the Benjamini \& Hochberg
(1995) step-up FDR controlling procedure (independent and positive
regression dependent test statistics).
\item[BY] adjusted \eqn{p}{}-values for the Benjamini \& Yekutieli
(2001) step-up FDR controlling procedure (general dependency
structures).
\end{Details}
\begin{Value}
A list with components
\begin{ldescription}
\item[\code{adjp}] A matrix of adjusted \eqn{p}{}-values, with rows
corresponding to hypotheses and columns to multiple testing
procedures. Hypotheses are sorted in increasing order of their raw
(unadjusted) \eqn{p}{}-values.
\item[\code{index}] A vector of row indices, between 1 and
\code{length(rawp)}, where rows are sorted according to 
their raw (unadjusted) \eqn{p}{}-values. To obtain the adjusted
\eqn{p}{}-values in the original data order, use
\code{adjp[order(index),]}. 

\end{ldescription}
\end{Value}
\begin{Author}\relax
Sandrine Dudoit, \url{http://www.stat.berkeley.edu/~sandrine},\\
Yongchao Ge, \email{yongchao.ge@mssm.edu}.
\end{Author}
\begin{References}\relax
Y. Benjamini and Y. Hochberg (1995). Controlling the false discovery
rate: a practical and powerful approach to multiple
testing. \emph{J. R. Statist. Soc. B}. Vol. 57: 289-300.\\ 

Y. Benjamini and D. Yekutieli (2001). The control of the false discovery
rate in multiple hypothesis testing under dependency. \emph{Annals of
Statistics}. Accepted.\\ 

S. Dudoit, J. P. Shaffer, and J. C. Boldrick (Submitted). Multiple
hypothesis testing in microarray experiments.\\ 

Y. Ge, S. Dudoit, and T. P. Speed. Resampling-based multiple testing for microarray data hypothesis, Technical Report \#633 of UCB Stat. \url{http://www.stat.berkeley.edu/~gyc}\\

Y. Hochberg (1988). A sharper Bonferroni procedure for multiple tests of
significance, \emph{Biometrika}. Vol. 75: 800-802.\\ 

S. Holm (1979). A simple sequentially rejective multiple test
procedure. \emph{Scand. J. Statist.}. Vol. 6: 65-70.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{mt.maxT}{mt.maxT}}, \code{\LinkA{mt.minP}{mt.minP}},
\code{\LinkA{mt.plot}{mt.plot}}, \code{\LinkA{mt.reject}{mt.reject}}, \code{\LinkA{golub}{golub}}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
# Gene expression data from Golub et al. (1999)
# To reduce computation time and for illustrative purposes, we condider only
# the first 100 genes and use the default of B=10,000 permutations.
# In general, one would need a much larger number of permutations
# for microarray data.

data(golub)
smallgd<-golub[1:100,] 
classlabel<-golub.cl

# Permutation unadjusted p-values and adjusted p-values for maxT procedure
res1<-mt.maxT(smallgd,classlabel)
rawp<-res1$rawp[order(res1$index)]

# Permutation adjusted p-values for simple multiple testing procedures
procs<-c("Bonferroni","Holm","Hochberg","SidakSS","SidakSD","BH","BY")
res2<-mt.rawp2adjp(rawp,procs)

\end{ExampleCode}
\end{Examples}