A factorial design has two levels of factor A and three levels of factor B with six participants in each condition. The F-ratio for the interaction of A x B would have _____ degrees of freedom.
A)2, 35
B)2, 30
C)6, 35
D)6, 30

Question

Quizplus · Accepted Answer

The degrees of freedom for the interaction term in a factorial design is calculated by multiplying the degrees of freedom for factor A by the degrees of freedom for factor B. 
For this design:
Degrees of freedom for factor A = 2-1 = 1
Degrees of freedom for factor B = 3-1 = 2
Interaction df = A(df) * B(df) = 1 * 2 = 2
Total df = (n-1) = (6-1) = 5 participants per condition (6 participants minus 1 for estimating the mean)
Total number of conditions = 2(A) * 3(B) = 6
Total degrees of freedom = (number of conditions - 1) = 6-1 = 5
Therefore, the F-ratio for the interaction of A x B would have 2, 30 degrees of freedom.

A Factorial Design Has Two Levels of Factor a and Three