agridat (version 1.12)

kempton.barley.uniformity: Uniformity trial of Spring Barley in 1978

Description

Uniformity trial of Spring Barley in 1978

Format

A data frame with 196 observations on the following 3 variables.

row

Row position

col

Column position

yield

Grain yield, kg

Details

A uniformity trial of spring barley planted in 1978. Conducted by the Plant Breeding Institute in Cambridge, England.

Each plot is 5 feet wide, 14 feet long.

References

McCullagh, P. and Clifford, D., (2006). Evidence for conformal invariance of crop yields, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science. 462, 2119--2143.

Examples

# NOT RUN {
data(kempton.barley.uniformity)
dat <- kempton.barley.uniformity

require(lattice)
desplot(yield~col*row, dat, main="kempton.barley.uniformity")
asp <- (28*14)/(7*5) # aspect ratio (rows * ft)/(cols * ft)
desplot(yield~col*row, dat, aspect=asp,
        main="kempton.barley.uniformity (true aspect)") # true view

dat <- transform(dat, xf = factor(col), yf=factor(row))

# }
# NOT RUN {
# Kempton estimated auto-regression coefficients b1=0.10, b2=0.91
require(asreml)
m1 <- asreml(yield ~ 1, data=dat, rcov=~ar1(xf):ar1(yf))

require(lucid)
vc(m1)
##      effect component std.error z.ratio constr
##  R!variance    0.1044   0.022       4.7    pos
##    R!xf.cor    0.2458   0.07484     3.3  uncon
##    R!yf.cor    0.8186   0.03822    21    uncon

# asreml estimates auto-regression correlations of 0.25, 0.82
# Kempton estimated auto-regression coefficients b1=0.10, b2=0.91

# }
# NOT RUN {
# Kempton defines 4 blocks, randomly assigns variety codes 1-49 in each block, fits
# RCB model, computes mean squares for variety and residual.  Repeat 40 times.
# Kempton's estimate: variety = 1032, residual = 1013
# Our estimate: variety = 825, residual = 1080
fitfun <- function(dat){
  dat <- transform(dat, block=factor(ceiling(row/7)),
                   gen=factor(c(sample(1:49),sample(1:49),sample(1:49),sample(1:49))))
  m2 <- lm(yield*100 ~ block + gen, dat)
  anova(m2)[2:3,'Mean Sq']
}
set.seed(251)
out <- replicate(50, fitfun(dat))
rowMeans(out)

# }