The following table shows the results of an analysis of variance comparing three treatments.What is the value of ²,the percentage of variance accounted for,for these data?
$$\begin{array} { l r r r r }
\text { Source } & S S & d f & M S & \
\text { Between } & 30 & 2 & 15 & F = 7.50 \
\text { Within } & 60 & 30 & 2 & \
\text { Total } & 90 & 32 & &
\end{array}$$
A)30/60 = .5
B)30/90 = .33
C)60/90 = .67
D)2/30 = .067

Question

The following table shows the results of an analysis of variance comparing three treatments.What is the value of ²,the percentage of variance accounted for,for these data?
  $$\begin{array} { l r r r r } 
\text { Source } & S S & d f & M S & \
\text { Between } & 30 & 2 & 15 & F = 7.50 \
\text { Within } & 60 & 30 & 2 & \
\text { Total } & 90 & 32 & &
\end{array}$$
A)30/60 = .5 
B)30/90 = .33 
C)60/90 = .67 
D)2/30 = .067

Quizplus · Accepted Answer

ꞃ² represents the proportion of total variation in the data that is accounted for by the differences between the treatments. It is calculated as the variance between treatments divided by the total variance. In this case, the variance between treatments is 30 and the total variance is 90, so ꞃ² = 30/90 = 0.33. Therefore, the best choice is B.

The Following Table Shows the Results of an Analysis of Variance