\Header{MJ241}{MJ241 Split Plot}
\begin{Format}
MJ241 data frame with 16 observations on 4 variables.
\Tabular{rlll}{
[,1] & block & factor & block identifier \\{}
[,2] & fert & factor & fertilizer level \\{}
[,3] & variety & factor & variety level \\{}
[,4] & yield &  numeric & plot yield
}\end{Format}
\begin{Details}
\end{Details}
\begin{Source}
\end{Source}
\begin{References}
\end{References}
\begin{Examples}
\begin{ExampleCode}

# attach library; get data
#library( pda )
data( MJ241 )

# MJ 24.1 Split Plot
MJ241$plot <- 4 * ( MJ241$block - 1 ) + MJ241$fert
MJ241$fert <- factor( MJ241$fert )
MJ241$block <- factor( MJ241$block )
MJ241$variety <- factor( MJ241$variety )
MJ241$plot <- factor( MJ241$plot )

# split plot with block and block:fert as fixed effects
MJ241.fit <- aov( yield ~ block * fert + variety + variety:fert,
   MJ241 )

# split plot using block:fert as random effect
# see Venables & Ripley (1994, sec. 6.7) or
# Chambers & Hastie (1992, sec. 5.2.1)
MJ241.bfit <- aov( yield ~ fert + variety + variety:fert
   + Error( block + block:fert ), MJ241 )
print( summary( MJ241.bfit ))

# split plot using LME (Splus on ALPHA computers only)
# see Lindstrom & Bates (1988) JASA 83:1014-1022
library( nlme )
MJ241.lme <- lme( yield ~ fert + variety + variety:fert,
   random = ~ block + block:fert,
   cluster = ~ plot, data = MJ241,
   est.method = "RML", re.structure = "identity")
print( summary( MJ241.lme ))
print( fitted.values( MJ241.lme ))

\end{ExampleCode}
\end{Examples}

