Which of the following equations is correct for partitioning a score in a one-factor between-subjects analysis of variance?
A) $\bar { X } - \bar { X } _ { A } = \left( X - \bar { X } _ { Q } \right) + \left( \bar { X } _ { A } - \bar { X } _ { Q } \right)$
B) $X _ { A } - \bar{X} _ { 0 } = \left( X -\bar{ X} _ { 0 } \right) + \left(\bar{ X} _ { 0 } - \bar{X }_ { A } \right)$
C) $X - \bar { X } _ { G } = \left( \bar { X } _ { A } - \bar { X } _ { G } \right) + \left( X - \bar { X } _ { A } \right)$
D) $X - \bar { X } _ { Q } = \left( \bar { X } _ { A } - \bar { X } _ { \theta } \right) - \left( X - \bar { X } _ { A } \right)$

Question

Which of the following equations is correct for partitioning a score in a one-factor between-subjects analysis of variance? 
A) $\bar { X } - \bar { X } _ { A } = \left( X - \bar { X } _ { Q } \right) + \left( \bar { X } _ { A } - \bar { X } _ { Q } \right)$
B) $X _ { A } - \bar{X} _ { 0 } = \left( X -\bar{ X} _ { 0 } \right) + \left(\bar{ X} _ { 0 } - \bar{X }_ { A } \right)$
C) $X - \bar { X } _ { G } = \left( \bar { X } _ { A } - \bar { X } _ { G } \right) + \left( X - \bar { X } _ { A } \right)$
D) $X - \bar { X } _ { Q } = \left( \bar { X } _ { A } - \bar { X } _ { \theta } \right) - \left( X - \bar { X } _ { A } \right)$

Quizplus · Accepted Answer

The correct equation for partitioning a score in a one-factor between-subjects analysis of variance is $X - \bar { X } _ { G } = \left( \bar { X } _ { A } - \bar { X } _ { G } \right) + \left( X - \bar { X } _ { A } \right)$. This equation breaks down the total deviation of an individual score from the grand mean ($X - \bar { X } _ { G }$) into two components: the deviation of the group mean from the grand mean ($\bar { X } _ { A } - \bar { X } _ { G }$) and the deviation of the individual score from its group mean ($X - \bar { X } _ { A }$).

Which of the Following Equations Is Correct for Partitioning a Score