Question: For the balanced two-way r c layout with n observations {yijk} in each cell, denote the sample means by {yij. } in the cells,

For the balanced two-way r × c layout with n observations {yijk} in each cell, denote the sample means by {ȳij.

} in the cells, ȳi.. in level i of A, ȳ.j. in level j of B, and ȳ overall for all N = nrc observations. Consider the model that assumes a lack of interaction.

a. Construct the ANOVA table, including SS and df values, showing how to construct F statistics for testing the main effects.

b. Show that the expected value of the numerator mean square for the test of the A factor effect is ????2 +

( cn r−1

) ∑r i=1(????i.. − ̄????)

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