The difference . $\bar { X } _ { A } - \bar { X } _ { G }$ 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

Quizplus · Accepted Answer

The difference $\bar { X } _ { A } - \bar { X } _ { G }$ reflects the main effect of factor A plus sampling error. This is because $\bar { X } _ { A }$ represents the mean of a condition under factor A, and $\bar { X } _ { G }$ represents the grand mean across all conditions. The difference between these means isolates the effect of factor A, acknowledging that there is also sampling error present.

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The Difference $\bar { X } _ { A } - \bar { X } _ { G }$