5. Suppose I have an agricultural experiment with a field which I can divide into 5
×
5 plots. I have
5 treatments, each a different density of mielie plants (I am interested in how close together I
should plant them for maximum yield). What design should I use? What are the experimental
units? Use R to randomly assign treatments to experimental units.
6.
Categorical vs continuous variables:
Suppose, for an experiment I have a treatment factor
temperature with levels 50, 100, 150 and 200 C . Using the R code shown below, explain carefully
how the parameter estimates and their meaning will differ when the following two linear models
are fitted in R: a) temperature as a continuous variable, and b) temperature as a categorical
variable.
We first generate/simulate some data for the above fictional example:
ob1 <- rnorm(5, mean = 5, sd = 2)
ob2 <- rnorm(5, mean = 10, sd = 2)
ob3 <- rnorm(5, mean = 15, sd = 2)
ob4 <- rnorm(5, mean = 10, sd = 2)
# the above code generates response values
# for the 4 treatment groups, 5 values for each group
# note all of the observations come from a normal distribution
# with the same standard deviation
# only the group means differ
# -- to keep these data (or any data) in a spreadsheet or a data file
#
we need a column for each variable
4

response <- c(ob1, ob2, ob3, ob4)
# response
treat <- rep(c(50, 100, 150, 200), each = 5)
# treatment factor
Make some plots of the data:
boxplot(response ~ treat, xlab = "temperature", ylab = "response")
plot(response ~ treat, xlab = "temperature", ylab = "response")
Fit as a continuous variable:
m1 <- lm(response ~ treat)
summary(m1)
abline(m1)
Temperature as a categorical variable:
temp <- as.factor(treat)
m2 <- lm(response ~ temp)
summary(m2)
Compare the two models with respect to parameter estimates, degrees of freedom, residual
standard deviation, estimate for response when temperature = 100
C. Are these two estimates
the same? If not, why not? When would you use the one model, when the other?
Most of the explanatory variables (treatment or blocking factors) in experiments will be cate-
gorical. But every now and then we will come across a continuous variable, such as temperature,
where we might want to fit a line, rather than get separate estimates for each level.
5

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- Randomness, researcher