In the factorial experiment, where a is the number of levels for factor A, b is the number of levels for factor B, and r is the number of replications of each of the ab factor combinations, the degrees of freedom for interaction is given by which of the listed expressions below?
A) (a - 1)(b - 1)
B) (a - 1)(r - 1)
C) (b - 1)(r - 1)
D) ab(r - 1)

Question

In the  factorial experiment, where a is the number of levels for factor A, b is the number of levels for factor B, and r is the number of replications of each of the ab factor combinations, the degrees of freedom for interaction is given by which of the listed expressions below?
A) (a - 1)(b - 1) 
B) (a - 1)(r - 1) 
C) (b - 1)(r - 1) 
D) ab(r - 1)

Quizplus · Accepted Answer

The degrees of freedom for interaction is equal to (a-1)(b-1), as it represents the total number of independent cell means that can be estimated from the data.

In the Factorial Experiment, Where a Is the Number