agridat (version 1.16)

bliss.borers: Corn borer infestation under four treatments

Description

Corn borer infestation under four treatments

Format

A data frame with 48 observations on the following 3 variables.

borers

number of borers per hill

treat

treatment factor

freq

frequency of the borer count

Details

Four treatments to control corn borers. Treatment 1 is the control.

In 15 blocks, for each treatment, 8 hills of plants were examined, and the number of corn borers present was recorded. The data here are aggregated across blocks.

Bliss mentions that the level of infestation varied significantly between the blocks.

Examples

# NOT RUN {
data(bliss.borers)
dat <- bliss.borers

# Add 0 frequencies
dat0 <- expand.grid(borers=0:26, treat=c('T1','T2','T3','T4'))
dat0 <- merge(dat0,dat, all=TRUE)
dat0$freq[is.na(dat0$freq)] <- 0

# Expand to individual (non-aggregated) counts for each hill
dd <- data.frame(borers = rep(dat0$borers, times=dat0$freq),
                 treat = rep(dat0$treat, times=dat0$freq))

require(lattice)
histogram(~borers|treat, dd, type='count', breaks=0:27-.5,
          layout=c(1,4), main="bliss.borers", xlab="Borers per hill")


if(require(MASS)){
  m1 <- glm.nb(borers~0+treat, data=dd)
  # Bliss, table 3, presents treatment means, which are matched by:
  exp(coef(m1)) # 4.033333 3.166667 1.483333 1.508333
  # Bliss gives treatment values k = c(1.532,1.764,1.333,1.190).
  # The mean of these is 1.45, similar to this across-treatment estimate
  m1$theta # 1.47
}


# Plot observed and expected distributions for treatment 2
if(require(latticeExtra)){
  xx <- 0:26
  yy <- dnbinom(0:26, mu=3.17, size=1.47)*120 # estimates are from glm.nb
  histogram(~borers, dd, type='count', subset=treat=='T2',
            main="bliss.borers - trt T2 observed and expected",
            breaks=0:27-.5) +
              xyplot(yy~xx, col='navy', type='b')
}


# "Poissonness"-type plot
if(require(vcd)) {
  dat2 <- droplevels(subset(dat, treat=='T2'))
  vcd::distplot(dat2$borers, type = "nbinomial",
           main="bliss.borers neg binomialness plot")
  # Better way is a rootogram
  g1 <- vcd::goodfit(dat2$borers, "nbinomial")
  plot(g1, main="bliss.borers - Treatment 2")
}

# }