In a 6 x 7 factorial design with three observations per cell, the df for the interaction F would be
A) 42, 125
B) 42, 60
C) 30, 125
D) 30, 84
E) none of the other alternatives are correct.

Question

Quizplus · Accepted Answer

The degrees of freedom for the interaction F in a factorial design can be calculated as the product of the degrees of freedom for each factor minus 1. For a 6 x 7 factorial design, the degrees of freedom for each factor are 5 (6-1) and 6 (7-1), respectively. Thus, the degrees of freedom for the interaction F would be 5*6 = 30. With three observations per cell and 42 cells (6*7), the total number of observations is 126, leading to total degrees of freedom of 125 (126-1). The degrees of freedom for error would be the total degrees of freedom minus the degrees of freedom for the main effects and the interaction, but since the question specifically asks for the interaction F, the relevant part is 30 for the interaction. The other number (84) does not directly relate to the interaction F's degrees of freedom calculation as described, indicating a misunderstanding in the question's phrasing regarding what the numbers represent. The correct interpretation focuses on the interaction's degrees of freedom, which is 30.

In a 6 X 7 Factorial Design with Three Observations