The following table shows the results of a two-factor ANOVA.Based on this table,what is the value for ² for factor A?
$$\begin{array} { c c r r l }
\text { Source } & \text { SS } & \text { df } & \text { MS } & \
\text { Between } & 36 & 3 & & \
\text { A } & 12 & 1 & 12 & F = 4.00 \
\text { B } & 3 & 1 & 3 & F = 1.00 \
\text { AxB } & 21 & 1 & 21 & F = 7.00 \
\text { Within } & 84 & 28 & 3 & \
\text { Total } & 120 & 31 & &
\end{array}$$
A)12/36
B)12/96
C)12/99
D)12/120

Question

The following table shows the results of a two-factor ANOVA.Based on this table,what is the value for ² for factor A? 
$$\begin{array} { c c r r l } 
\text { Source } & \text { SS } & \text { df } & \text { MS } & \
 \text { Between } & 36 & 3 & & \
\text { A } & 12 & 1 & 12 & F = 4.00 \
\text { B } & 3 & 1 & 3 & F = 1.00 \
\text { AxB } & 21 & 1 & 21 & F = 7.00 \
\text { Within } & 84 & 28 & 3 & \
\text { Total } & 120 & 31 & &
\end{array}$$
A)12/36 
B)12/96 
C)12/99 
D)12/120

Quizplus · Accepted Answer

The value for $ \eta^2 $ (eta squared) for factor A is calculated as the sum of squares for factor A (SS_A) divided by the total sum of squares (SS_Total). Given SS_A = 12 and SS_Total = 120, the correct calculation is 12/120. However, the correct interpretation for $ \eta^2 $ is the proportion of the variance explained by factor A out of the total variance, which should actually be SS_A divided by the sum of SS_A and SS_Within (SS_A + SS_Within). Since SS_Within is 84, the correct calculation should be 12/(12+84) = 12/96, which is option B. My explanation mistakenly referred to the total sum of squares instead of the correct denominator for $ \eta^2 $, which is the sum of the factor's sum of squares plus the within sum of squares.

The Following Table Shows the Results of a Two-Factor ANOVA