\HeaderA{summary.manova}{Summary Method for Multivariate Analysis of Variance}{summary.manova}
\aliasA{print.summary.manova}{summary.manova}{print.summary.manova}
\keyword{models}{summary.manova}
\begin{Description}\relax
A \code{summary} method for class \code{"manova"}.
\end{Description}
\begin{Usage}
\begin{verbatim}
## S3 method for class 'manova':
summary(object,
        test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"),
        intercept = FALSE, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{object}] An object of class \code{"manova"} or an \code{aov}
object with multiple responses.
\item[\code{test}] The name of the test statistic to be used.  Partial
matching is used so the name can be abbreviated.
\item[\code{intercept}] logical.  If \code{TRUE}, the intercept term is
included in the table.
\item[\code{...}] further arguments passed to or from other methods.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The \code{summary.manova} method uses a multivariate test statistic
for the summary table.  Wilks' statistic is most popular in the
literature, but the default Pillai--Bartlett statistic is recommended
by Hand and Taylor (1987).

The table gives a transformation of the test statistic which has
approximately an F distribution.  The approximations used follow
S-PLUS and SAS (the latter apart from some cases of the
Hotelling--Lawley statistic), but many other distributional
approximations exist: see Anderson (1984) and Krzanowski and Marriott
(1994) for further references.  All four approximate F statistics are
the same when the term being tested has one degree of freedom, but in
other cases that for the Roy statistic is an upper bound.
\end{Details}
\begin{Value}
A list with components
\begin{ldescription}
\item[\code{SS}] A named list of sums of squares and product matrices.
\item[\code{Eigenvalues}] A matrix of eigenvalues.
\item[\code{stats}] A matrix of the statistics, approximate F value,
degrees of freedom and P value.
\end{ldescription}
\end{Value}
\begin{References}\relax
Anderson, T. W. (1994) \emph{An Introduction to Multivariate
Statistical Analysis.} Wiley.

Hand, D. J. and Taylor, C. C.  (1987)
\emph{Multivariate Analysis of Variance and Repeated Measures.}
Chapman and Hall.

Krzanowski, W. J. (1988) \emph{Principles of Multivariate Analysis. A
User's Perspective.} Oxford.

Krzanowski, W. J. and Marriott, F. H. C. (1994) \emph{Multivariate
Analysis. Part I: Distributions, Ordination and Inference.} Edward Arnold.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{manova}{manova}}, \code{\LinkA{aov}{aov}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
## Example on producing plastic film from Krzanowski (1998, p. 381)
tear <- c(6.5, 6.2, 5.8, 6.5, 6.5, 6.9, 7.2, 6.9, 6.1, 6.3,
          6.7, 6.6, 7.2, 7.1, 6.8, 7.1, 7.0, 7.2, 7.5, 7.6)
gloss <- c(9.5, 9.9, 9.6, 9.6, 9.2, 9.1, 10.0, 9.9, 9.5, 9.4,
           9.1, 9.3, 8.3, 8.4, 8.5, 9.2, 8.8, 9.7, 10.1, 9.2)
opacity <- c(4.4, 6.4, 3.0, 4.1, 0.8, 5.7, 2.0, 3.9, 1.9, 5.7,
             2.8, 4.1, 3.8, 1.6, 3.4, 8.4, 5.2, 6.9, 2.7, 1.9)
Y <- cbind(tear, gloss, opacity)
rate <- factor(gl(2,10), labels=c("Low", "High"))
additive <- factor(gl(2, 5, length=20), labels=c("Low", "High"))

fit <- manova(Y ~ rate * additive)
summary.aov(fit)           # univariate ANOVA tables
summary(fit, test="Wilks") # ANOVA table of Wilks' lambda
summary(fit)               # same F statistics as single-df terms
\end{ExampleCode}
\end{Examples}

