represents the effect of the interaction of factors A and B and sampling error in the partitioned score of a subject in a two-factor between-subjects analysis of variance.
A) $\bar { X } _ { A B } - \bar { X } _ { G }$
B) $X - \bar { X } _ { A B }$
C) $\bar { X } _ { A B } + \bar { X } _ { A } + \bar { X } _ { B } - \bar { X } _ { G }$
D) $\bar { X } _ { A B } - \bar { X } _ { A } - \bar { X } _ { B } + \bar { X } _ { G }$

Question

represents the effect of the interaction of factors A and B and sampling error in the partitioned score of a subject in a two-factor between-subjects analysis of variance. 
A) $\bar { X } _ { A B } - \bar { X } _ { G }$
B) $X - \bar { X } _ { A B }$
C) $\bar { X } _ { A B } + \bar { X } _ { A } + \bar { X } _ { B } - \bar { X } _ { G }$
D) $\bar { X } _ { A B } - \bar { X } _ { A } - \bar { X } _ { B } + \bar { X } _ { G }$

Quizplus · Accepted Answer

According to the two-factor between-subjects ANOVA, the partitioned score of a subject can be represented by the following formula:

X = Grand mean + main effect of A + main effect of B + interaction effect of A and B + error

Here, the interaction effect of A and B represents the effect of the interaction of factors A and B and sampling error.

To isolate the interaction effect, we need to remove the main effects of A and B from the formula. The formula for the interaction effect can be rearranged as:

Interaction effect = (AB) - (A) - (B) + G

where (AB) represents the mean score of the group that received both Factor A and B, (A) represents the mean score of the group that received only Factor A, (B) represents the mean score of the group that received only Factor B, and G represents the grand mean.

Therefore, the correct choice is D, which represents the formula for interaction effect:

$\bar { X } _ { A B } - \bar { X } _ { A } - \bar { X } _ { B } + \bar { X } _ { G }$

Represents the Effect of the Interaction of Factors a and B