The deviation represented by $$\bar { X } _ { A } - \bar { X } _ { G }$$ reflects the in the partitioned score of a subject in a one-factor between-subjects analysis of variance.
A)effect of factor A alone
B)effect of factor A plus sampling error
C)total variation
D)within-groups error variation

Question

Quizplus · Accepted Answer

The deviation represented by $\bar { X } _ { A } - \bar { X } _ { G }$ reflects the effect of factor A plus sampling error in a one-factor between-subjects analysis of variance. This is because $\bar { X } _ { A }$ is the mean of a specific group under factor A, and $\bar { X } _ { G }$ is the grand mean of all groups. The difference between these means includes both the effect of the factor (how much the specific group deviates from the overall mean due to the factor) and the sampling error (random variation not accounted for by the factor).

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The Deviation Represented By $\bar { X } _ { A } - \bar { X } _ { G }$