\Header{eff.aovlist}{Compute Efficiencies of Multistratum Analysis of Variance}
\keyword{models}{eff.aovlist}
\begin{Description}\relax
Computes the efficiencies of fixed-effect terms in an analysis of
variance model with multiple strata.\end{Description}
\begin{Usage}
\begin{verbatim}
eff.aovlist(aovlist)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{aovlist}] The result of a call to \code{aov} with a \code{Error} term.

\end{ldescription}
\end{Arguments}
\begin{Details}\relax
Fixed-effect terms in an analysis of variance model with multiple strata
may be estimable in more than one stratum, in which case there is less
than complete information in each. The efficiency is the fraction of
the maximum possible precision (inverse variance) obtainable by
estimating in just that stratum.

This is used to pick strata in which to estimate terms in
\code{model.tables.aovlist} and elsewhere.\end{Details}
\begin{Value}
A matrix giving for each non-pure-error stratum (row) the efficiencies
for each fixed-effect term in the model.\end{Value}
\begin{Author}\relax
B.D. Ripley\end{Author}
\begin{SeeAlso}\relax
\code{\Link{aov}}, \code{\Link{model.tables.aovlist}},
\code{\Link{se.contrast.aovlist}}\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
## for balanced designs all efficiencies are zero or one.
## so as a statistically meaningless test:
options(contrasts=c("contr.helmert", "contr.poly"))
## 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.aovE <- aov(yield ~  N*P*K + Error(block), npk)
eff.aovlist(npk.aovE)
\end{ExampleCode}
\end{Examples}

