The term $\bar { X } _ { A B } - \bar { X } _ { A } - \bar { X } _ { B } + \bar { X } _ { G }$ in a two-factor between-subjects analysis of variance reflects the.
A)main effect of factor A plus sampling error
B)main effect of factor B plus sampling error
C)effect of the interaction of factors A and B plus sampling error
D)within-cells error variation

Question

The term     $\bar { X } _ { A B } - \bar { X } _ { A } - \bar { X } _ { B } + \bar { X } _ { G }$ in a two-factor between-subjects analysis of variance reflects the.
A)main effect of factor A plus sampling error 
B)main effect of factor B plus sampling error 
C)effect of the interaction of factors A and B plus sampling error 
D)within-cells error variation

Quizplus · Accepted Answer

The term $\bar { X } _ { A B } - \bar { X } _ { A } - \bar { X } _ { B } + \bar { X } _ { G }$ represents the effect of the interaction between factors A and B in a two-factor between-subjects analysis of variance. The presence of sampling error is assumed in all terms of the analysis of variance, so it is included in this term as well. Therefore, the correct answer is C, which reflects the effect of the interaction of factors A and B plus sampling error.

The Term XˉAB−XˉA−XˉB+XˉG\bar { X } _ { A B } - \bar { X } _ { A } - \bar { X } _ { B } + \bar { X } _ { G }XˉAB​−XˉA​−XˉB​+XˉG​

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