Consider the fisher. barley data frame from Example 5.3.

a. Use $\mathrm{R}$ to compute $S S_{E}$. What are the degrees of freedom for $S S_{E}$ ?

b. A statistician analyzing fisher.barley forgot to account for blocking. Estimate the treatment effects without accounting for blocking and compare these estimates when blocking is taken into account.

c. Compute the ANOVA table for fisher . barley with and without blocking. Which columns change? Why?

Data from Example 5.3

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Example 5.3. Randomized block designs were first discussed by Fisher [1937]. The "practical example" he gave was an experiment carried out in the state of Minnesota in 1930 and 1931 reported by Immer, Hayes, and Le Roy [Wright, 2013]. The experiment compared the yield of five different varities of barley. The blocks in this example are twelve separate experiments carried out at six locations in the state. The data are shown in Table 5.4.