Complete the formula for the sum of squares between groups: $s _ { B } ^ { 2 } =$
A) $\frac { \left( \bar { X } _ { i } - \bar { X } _ { j } \right) ^ { 2 } } { s _ { w } ^ { 2 } \left( 1 / n _ { \mathrm { i } } + 1 / n _ { j } \right) }$

B) $\frac { \sum \left( n _ { i } - 1 \right) s _ { i } ^ { 2 } } { \sum \left( n _ { i } - 1 \right) }$

C) $\frac { \bar { X } _ { i } - \bar { X } _ { j } } { \sqrt { s _ { w } ^ { 2 } / n } }$

D) $\frac { \sum _ { i } n _ { i } \left( \bar { X } _ { i } - \bar { X } _ { G M } \right) ^ { 2 } } { k - 1 }$

Question

Complete the formula for the sum of squares between groups: $s _ { B } ^ { 2 } =$
A) $\frac { \left( \bar { X } _ { i } - \bar { X } _ { j } \right) ^ { 2 } } { s _ { w } ^ { 2 } \left( 1 / n _ { \mathrm { i } } + 1 / n _ { j } \right) }$

B) $\frac { \sum \left( n _ { i } - 1 \right) s _ { i } ^ { 2 } } { \sum \left( n _ { i } - 1 \right) }$

C) $\frac { \bar { X } _ { i } - \bar { X } _ { j } } { \sqrt { s _ { w } ^ { 2 } / n } }$

D) $\frac { \sum _ { i } n _ { i } \left( \bar { X } _ { i } - \bar { X } _ { G M } \right) ^ { 2 } } { k - 1 }$

Quizplus · Accepted Answer

The correct formula for the sum of squares between groups (SSB) is represented by option D, which calculates the variance between the group means and the grand mean, scaled by the size of each group and normalized by the number of groups minus one.

Complete the Formula for the Sum of Squares Between Groups sB2=s _ { B } ^ { 2 } =sB2​=

Complete the Formula for the Sum of Squares Between Groups $s _ { B } ^ { 2 } =$