Table 4.6 is a table with two rows and three columns, similar to the interaction effect term in the two-way factorial diagram in Figure 4.4. However, for this question we will assume that only two effects are known: () 11 = 2 and () 12 = €“5.
Table 4.6 Interaction effects.

a. Equation (4.8) states that all the AB effects within Brand C add up to zero [()11 + ()12 + ()13 = 0]. Use this rule to calculate ()13.
b. Equation (4.8) also states that all the AB effects within 0 water amount add up to zero (the same for 5 and 15 drops of water). Use this rule to calculate ()21, ()22, and ()23.
c. Consider a different interaction table with two rows and three columns. Explain why it is not possible to have effects of ()11 = 4, ()13 = €“4, and ()22 = 6 and still follow the restrictions in Equation (4.8).
d. What are the degrees of freedom corresponding to any interaction term (in a balanced completely randomized design) with two levels of factor A and three levels of factor B? In other words, under the restrictions in Equation (4.8), what is the number of free pieces of information (the number of cells in Table 4.6 that are not fixed)?

5 15 2 Brand C Brand D 5