Question

3. Consider a two-factor factorial design with three levels in factor A, four levels in factor B, and four replicates in each of the 12 cells. Complete parts (a) through (d). a. How many degrees of freedom are there in determining the factor A variation and the factor B variation? There is/are degree(s) of freedom in determining the factor A variation. (Simplify your answer.) There is/are degree(s) of freedom in determining the factor B variation. (Simplify your answer.) b. How many degrees of freedom are there in determining the interaction variation? There is/are degree(s) of freedom in determining the interaction variation. (Simplify your answer.) c. How many degrees of freedom are there in determining the random variation? There is/are degree(s) of freedom in determining the random variation. (Simplify your answer.) d. How many degrees of freedom are there in determining the total variation? There is/are degree(s) of freedom in determining the total variation. (Simnlify your answer

Answer 1

a) Factor A degrees of freedom = a - 1 = 3 - 1 = 2

Factor B degrees of freedom = b - 1 = 4 - 1 = 3

b) Interaction degrees of freedom = (a - 1)(b - 1) = 2*3 = 6

d) Random variation degrees of freedom = ab(n - 1) = 2*3*(12 - 1) = 3*4*(4 - 1) = 36

e) Total degrees of freedom = abn - 1 = 3*4*4 - 1 = 47