Compute Efficiencies of Multistratum Analysis of Variance
Computes the efficiencies of fixed-effect terms in an analysis of variance model with multiple strata.
The result of a call to
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 for a term is the fraction of the maximum possible precision (inverse variance) obtainable by estimating in just that stratum. Under the assumption of balance, this is the same for all contrasts involving that term.
In many cases terms will only occur in one stratum, when all the efficiencies will be one: this is detected and no further calculations are done.
The calculation used requires orthogonal contrasts for each term, and will throw an error if non-orthogonal contrasts (e.g., treatment contrasts or an unbalanced design) are detected.
A matrix giving for each non-pure-error stratum (row) the efficiencies
for each fixed-effect term in the model.
Heiberger, R. M. (1989) Computation for the Analysis of Designed Experiments. Wiley.
## An example from Yates (1932), ## a 2^3 design in 2 blocks replicated 4 times Block <- gl(8, 4) A <- factor(c(0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1, 0,1,0,1,0,1,0,1,0,1,0,1)) B <- factor(c(0,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0,1,1, 0,0,1,1,0,0,1,1,0,0,1,1)) C <- factor(c(0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1, 1,0,1,0,0,0,1,1,1,1,0,0)) Yield <- c(101, 373, 398, 291, 312, 106, 265, 450, 106, 306, 324, 449, 272, 89, 407, 338, 87, 324, 279, 471, 323, 128, 423, 334, 131, 103, 445, 437, 324, 361, 302, 272) aovdat <- data.frame(Block, A, B, C, Yield) old <- getOption("contrasts") options(contrasts = c("contr.helmert", "contr.poly")) (fit <- aov(Yield ~ A*B*C + Error(Block), data = aovdat)) eff.aovlist(fit) options(contrasts = old)