If, in a two-way classification, the entire experiment is repeated \(r\) times, the model becomes

\[Y_{i j k}=\mu+\alpha_{i}+\beta_{j}+\varepsilon_{i j k}\]

Data From Theorem 12.2

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for i = 1, 2,..., a, j = 1, 2, ..., b, and k = 1, 2,..., r, where the sum of the a's the sum and the 's are equal to zero. The ijk are independent normally distributed random variables with zero means and the common variance o. (a) Write down (but do not prove) an identity analo- gous to the one of Theorem 12.2, subdividing the total sum of squares into components attributable to treatments, blocks, and error. (b) Give the corresponding degrees of freedom.