The R Project SVN R

% copyright (C) 1998 B. D. Ripley
%
\name{aov}
\title{Fit an Analysis of Variance Model}
\usage{
aov(formula, data=NULL, projections=FALSE, contrasts=NULL, ...)
se.aov(object, n, type = "means") 
}
\alias{aov}
\alias{print.aov}
\alias{print.aovlist}
\alias{summary.aov}
\alias{summary.aovlist}
\alias{print.summary.aov}
\alias{print.summary.aovlist}
\arguments{
 \item{formula}{A formula specifying the model.}
 \item{data}{A data frame in which the variables specified in the
   formula will be found. If missing, the variables are searched for in
   the standard way.}
 \item{projections}{Logical flag: should the projections be returned?}
 \item{contrasts}{A list of contrasts to be used for some of the factors
   in the formula. These are not used for any \code{Error} term, and
   supplying contrasts for factors only in the \code{Error} term will give
   a warning.}
 \item{\dots}{Arguments to be passed to \code{lm}, such as \code{subset}
   or \code{na.action}.}
}
\description{
 This provides a wrapper to \code{lm} for fitting linear models to
 balanced or unbalanced experimental designs. The call to \code{lm} sets
 \code{singular.ok} to \code{TRUE} to allow for aliased effects.

 The main difference from \code{lm} is in the way \code{print},
 \code{summary} and so on handle the fit: this is expressed in the
 traditional language of the analysis of variance rather than of linear
 models.

 If the formula contains a single \code{Error} term, this is used to
 specify error strata, and appropriate models are fitted within each
 error stratum.

 The formula can specify multiple responses.
}
\value{
  An object of class \code{c("aov", "lm")} or for multiple responses
  of class \code{c("maov", "aov", "mlm", "lm")} or for multiple error
  strata of class \code{"aovlist"}.  There are
  \code{\link{print}} and \code{\link{summary}} methods available for these.
}
\author{B.D. Ripley}
\seealso{\code{\link{lm}},\code{\link{alias}},\code{\link{proj}},
  \code{\link{model.tables}}
}
\examples{
## From Venables and Ripley (1997) p.210.
N <- c(0,1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,0)
P <- c(1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0)
K <- c(1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0)
yield <- c(49.5,62.8,46.8,57.0,59.8,58.5,55.5,56.0,62.8,55.8,69.5,55.0,
           62.0,48.8,45.5,44.2,52.0,51.5,49.8,48.8,57.2,59.0,53.2,56.0)
npk <- data.frame(block=gl(6,4), N=factor(N), P=factor(P),
                  K=factor(K), yield=yield)

( npk.aov <- aov(yield ~ block + N*P*K, npk) )
summary(npk.aov)
coefficients(npk.aov)

## as a test, not particularly sensible statistically
op <- options(contrasts=c("contr.helmert", "contr.treatment"))
npk.aovE <- aov(yield ~  N*P*K + Error(block), npk)
npk.aovE
summary(npk.aovE)
options(op)# reset to previous
}
\keyword{models}
\keyword{regression}