\name{power.randomized}
\alias{power.randomized}
\title{
  Power Calculation for Completely Randomized Treatment-Control Designs in Microarray studies
}
\description{
  This routine computes the individual power value for a completely randomized design with \code{n} treatment units and \code{n} control units (\code{2n} units in total). This power value is the expected fraction of truly differentially expressed genes that will be correctly declared as differentially expressed by the tests.
}
\usage{
  power.randomized(ER0, G0, absMu1, sigmad, n)
}
\arguments{
  \item{ER0}{
mean number of false positives.
  }
  \item{G0}{
  anticipated number of genes in the experiment that are not differentially 
expressed.
}
  \item{absMu1}{
  absolute mean difference in log-expression between treatment and control conditions as postulated under the alternative hypothesis H1.
  }
  \item{sigmad}{
  anticipated standard deviation of the difference in log-expression between treatment and control conditions. The relation between the standard deviation of the difference (\code{sigmad}) and the experimental error standard deviation (\code{sigma}) is \code{sigmad=sqrt(2)/sigma}.}
  \item{n}{the sample size for each group.}
}
\value{
  \item{power}{power.} 
  \item{psi1}{non-centrality parameter.}
}
\references{
  Lee, M.-L. T. (2004).
  Analysis of Microarray Gene Expression Data.
  \emph{Kluwer Academic Publishers, ISBN 0-7923-7087-2.}

  Lee, M.-L. T., Whitmore, G. A. (2002).
  Power and sample size for DNA microarray studies.
  \emph{Statistics in Medicine, \bold{21}:3543-3570.}
}
\note{
  Examples and explainations can be found in \url{
http://www.biostat.harvard.edu/people/faculty/mltlee/pdf/Web-power-trt-cont050510.pdf}.
}
\author{
  Weiliang Qiu (\email{weiliang.qiu@gmail.com}),
  Mei-Ling Ting Lee (\email{meilinglee@sph.osu.edu}),
  George Alex Whitmore (\email{george.whitmore@mcgill.ca})
}
\seealso{ \code{\link{power.matched}},
  \code{\link{power.multi}},
  \code{\link{sampleSize.randomized}},
  \code{\link{sampleSize.matched}}
}
\examples{
  power.randomized(ER0=2, G0=5000, absMu1=1, sigmad=0.5657, n=8)
}
\keyword{htest}
\keyword{design}