Uniformity trial of barley

Uniformity trial of barley at Cambridge, England, 1978.

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.

Field width: 7 plots * 14 feet = 98 feet

Field length: 28 plots * 5 feet = 140 feet

Format

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

row

row

col

column

yield

grain yield, kg

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. https://doi.org/10.2307/2346657

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. https://doi.org/10.1098/rspa.2006.1667

Examples

# \dontrun{

  library(agridat)
  data(kempton.barley.uniformity)
  dat <- kempton.barley.uniformity

  libs(desplot)
  desplot(dat, yield~col*row,
          aspect=140/98, tick=TRUE, # true aspect
          main="kempton.barley.uniformity")
  
  
  # Kempton estimated auto-regression coefficients b1=0.10, b2=0.91
  
  dat <- transform(dat, xf = factor(col), yf=factor(row))

  # ----------

  libs(asreml,lucid) # asreml4
  
  dat <- transform(dat, xf = factor(col), yf=factor(row))
  m1 <- asreml(yield ~ 1, data=dat, resid = ~ar1(xf):ar1(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:08:48 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1       138.768     0.0880303    195 17:08:48    0.0 (1 restrained)
#>  2       190.210     0.0624855    195 17:08:48    0.0
#>  3       224.660     0.0667102    195 17:08:48    0.0
#>  4       230.382     0.0828740    195 17:08:48    0.0
#>  5       231.397     0.0999127    195 17:08:48    0.0
#>  6       231.425     0.1038940    195 17:08:48    0.0
#>  7       231.425     0.1043644    195 17:08:48    0.0
  
  # vc(m1)
  ##       effect component std.error z.ratio bound 
  ##      xf:yf!R    0.1044   0.02197     4.7     P   0
  ## xf:yf!xf!cor    0.2458   0.07484     3.3     U   0
  ## xf:yf!yf!cor    0.8186   0.03821    21       U   0
  
  # asreml estimates auto-regression correlations of 0.25, 0.82
  # Kempton estimated auto-regression coefficients b1=0.10, b2=0.91

  # ----------

  if(0){
    # 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) # 826 1079
  }


# }