In a 5 x 6 factorial design with four observations per cell, the df for the interaction F would be
A) 30, 119
B) 30, 90
C) 20, 119
D) 20, 90
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 (number of levels in factor A - 1) * (number of levels in factor B - 1). In this case, with a 5 x 6 factorial design, the df for the interaction would be (5-1)*(6-1) = 4*5 = 20. For the error term, it's calculated as the total number of observations minus the degrees of freedom for the main effects and the interaction. With four observations per cell, there are 5*6*4 = 120 total observations. The df for the main effects are 5-1 = 4 for factor A and 6-1 = 5 for factor B, totaling 9. Adding the 20 df for the interaction gives 29, leaving 120 - 29 - 1 (for the overall mean) = 90 df for error. Hence, the correct answer is 20, 90.

In a 5 X 6 Factorial Design with Four Observations