Split-plot experiment of oats

The yield of oats from a split-plot field trial conducted at Rothamsted in 1931.

Varieties were applied to the main plots.

Manurial (nitrogen) treatments were applied to the sub-plots.

Each plot is 1/80 acre = 28.4 links * 44 links.

Field width: 4 plots * 44 links = 176 links.

Field length: 18 rows * 28.4 links = 511 links

The 'block' numbers in this data are as given in the Rothamsted Report. The 'grain' and 'straw' values are the actual pounds per sub-plot as shown in the Rothamsted Report. Each sub-plot is 1/80 acre, and a 'hundredweight (cwt)' is 112 pounds, so converting from sub-plot weight to hundredweight/acre needs a conversion factor of 80/112.

The 'yield' values are the values as they appeared in the paper by Yates, who used 1/4-pounds as the units (i.e. he multiplied the original weight by 4) for simpler calculations.

Format

row

row

col

column

yield

yield in 1/4 pounds per sub-plot, each 1/80 acre

nitro

nitrogen treatment in hundredweight per acre

gen

genotype, 3 levels

block

block, 6 levels

grain

grain weight in pounds per sub-plot

straw

straw weight in pounds per sub-plot

Source

Report for 1931. Rothamsted Experiment Station. Page 143. https://www.era.rothamsted.ac.uk/eradoc/article/ResReport1931-141-159

References

Yates, Frank (1935) Complex experiments, Journal of the Royal Statistical Society Supplement 2, 181-247. Figure 2. https://doi.org/10.2307/2983638

Examples

if (FALSE) { # \dontrun{

  library(agridat)
  data(yates.oats)
  dat <- yates.oats

  ## # Means match Rothamsted report p. 144
  ## libs(dplyr)
  ## dat 
  ##   summarize(grain=mean(grain)*80/112,
  ##             straw=mean(straw)*80/112)

  libs(desplot)
  # Experiment design & yield heatmap
  desplot(dat, block ~ col*row, col.regions=c("black","yellow"),
          out1=block, num=nitro, col=gen,
          cex=1, aspect=511/176, # true aspect
          main="yates.oats")


  # Roughly linear gradient across the field.  The right-half of each
  # block has lower yield.  The blocking is inadequate!
  libs("lattice")
  xyplot(yield ~ col|factor(nitro), dat,
         type = c('p', 'r'), xlab='col', as.table = TRUE,
         main="yates.oats")

  libs(lme4)
  # Typical split-plot analysis. Non-significant gen differences
  m3 <- lmer(yield ~ factor(nitro) * gen + (1|block/gen), data=dat)
  # Residuals still show structure
  xyplot(resid(m3) ~ dat$col, xlab='col', type=c('p','smooth'),
         main="yates.oats")

  # Add a linear trend for column
  m4 <- lmer(yield ~ col + factor(nitro) * gen + (1|block/gen), data=dat)
  # xyplot(resid(m4) ~ dat$col, type=c('p','smooth'), xlab='col')

  ## Compare fits
  AIC(m3,m4)
  ##    df      AIC
  ## m3  9 581.2372
  ## m4 10 557.9424 # Substantially better


  # ----------

  # Marginal predictions

  # --- nlme ---
  libs(nlme)
  libs(emmeans)
  # create unbalance
  dat2 <- yates.oats[-c(1,2,3,5,8,13,21,34,55),]
  m5l <- lme(yield ~ factor(nitro) + gen, random = ~1 | block/gen,
             data = dat2)

  # asreml r 4 has a bug with asreml( factor(nitro))
  dat2$nitrof <- factor(dat2$nitro)

  # --- asreml  ---
  if(require("asreml", quietly=TRUE)){
    libs(asreml,lucid)
    m5a <- asreml(yield ~ nitrof + gen,
                  random = ~ block + block:gen, data=dat2)
    lucid::vc(m5l)
    lucid::vc(m5a)

  emmeans::emmeans(m5l, "gen")
  predict(m5a, data=dat2, classify="gen")$pvals
  }
  

} # }