The term represents the effect of the independent variable and sampling error in the partitioned score of a subject in a one-factor between-subjects analysis of variance.
A) $X - \bar { X } _ { A }$
B) $X - \bar { X } _ { \mathrm { G } }$
C) $X + \bar { X } _ { A }$
D) $\bar { X } _ { A } - \bar { X } _ { G }$

Question

The term represents the effect of the independent variable and sampling error in the partitioned score of a subject in a one-factor between-subjects analysis of variance. 
A) $X - \bar { X } _ { A }$
B) $X - \bar { X } _ { \mathrm { G } }$
C) $X + \bar { X } _ { A }$
D) $\bar { X } _ { A } - \bar { X } _ { G }$

Quizplus · Accepted Answer

The term $\bar { X } _ { A } - \bar { X } _ { G }$ represents the effect of the independent variable (the difference between the group mean and the grand mean) and implicitly includes the sampling error in the context of a one-factor between-subjects analysis of variance (ANOVA). This term isolates the group effect from the overall mean, highlighting the variance attributable to the independent variable's influence across different groups.

The Term Represents the Effect of the Independent Variable and Sampling