agridat (version 1.8.1)

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

Description

Uniformity trial of Spring Barley in 1978

source

R. A. Kempton and C. W. Howes (1981). The use of neighbouring plot values in the analysis of variety trials. Applied Statistics, 30, 59--70.

Details

A uniformity trial of spring barley planted in 1978. Each plot is 5 feet wide, 14 feet long. Conducted by the Plant Breeding Institute in Cambridge, England.

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

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))

# Kempton estimated auto-regression coefficients b1=0.10, b2=0.91
require(asreml)
m1 <- asreml(yield ~ 1, data=dat, rcov=~ar1(xf):ar1(yf))
summary(m1)$varcomp
# asreml estimates auto-regression correlations of 0.25, 0.82
# Kempton estimated auto-regression coefficients b1=0.10, b2=0.91

# 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)