Consider a randomized block design with $k$ treatments and $b$ blocks.a. Derive the least squares estimators of the treatment effects using i) dummy coding and ii) deviation coding.

b. Verify the estimators with the fisher.barley data frame from Example 5.3.

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.