Compute Efficiency Factors for aovlist Model Terms
DESCRIPTION:
Computes the relative efficiency of each treatment term in each stratum
USAGE: 
eff.aovlist(aovlist)
REQUIRED ARGUMENTS:
aovlist:
an aovlist object
VALUE:
a matrix of relative efficiencies: the rows correspond to the error strata, the columns to the treatment terms.
DETAILS:
In some multistratum anova, treatment factors are not orthogonal to error strata, and there is partial information for a treatment in more than one strata. Typically, the most efficient strata is the lowest strata in which the treatment occurs. The relative efficiencies measure the proportion of the treatment that projects onto each error stratum. Efficiencies affect the computation of fitted effects, means and their standard errors (see model.tables).

The computation requires the qr component of the aovlist object.

REFERENCES:
Heiberger, R. M. (1989). Computation for the Analysis of Designed Experiments. New York: Wiley.
SEE ALSO:
model.tables , aov .
EXAMPLES: 
facs <- fac.design(c(3,2,3,4), factor.names=c("B","C","Block","Rep"))
A <- factor( c(2, 3, 1, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 2, 3, 1, 3,
        1, 2, 2, 3, 1, 1, 2, 3, 3, 1, 2, 2, 3, 1, 1, 2, 3, 2, 1, 3, 3, 2, 1,
        3, 2, 1, 1, 3, 2, 1, 3, 2, 2, 1, 3, 3, 2, 1, 2, 1, 3, 1, 3, 2, 3, 2,
        1, 2, 1, 3, 1, 3, 2))
Y <- c(80, 86, 70, 74, 82, 86, 78, 55, 82, 67, 67, 57, 38, 73,
        75, 78, 51, 66, 136,
        56, 64, 95, 76, 71, 43, 81, 90, 81, 61, 65, 89, 87, 66, 91, 97, 60,
        86, 79, 73, 97, 79, 113, 73, 76, 97, 116, 86, 81, 66, 85, 101, 117,
        106, 102, 88, 107, 70, 79, 92, 96, 53, 66, 92, 88, 109, 95, 81, 58,
        56, 90, 68, 67)
cox205.df <- data.frame(Y,A,facs)
cox205.aov <- aov(Y ~ A * B * C +Error(Rep/Block), cox205.df, qr=T)
eff.aovlist(cox205.aov)