Compute the sum of squares.
-A one-way ANOVA is to be performed. Independent random samples are selected from three different populations. The sample data are given in the table below.
$\begin{array} { c | c | c }
\text { Sample 1 } & \text { Sample 2 } & \text { Sample 3 } \
\hline 5 & 3 & 2 \
9 & 7 & 1 \
7 & & 3 \
& & 8
\end{array}$
Compute the treatment sum of squares, SSTR.
A)246.0
B)66.0
C)100.2
D)21.0

Question

Compute the sum of squares.
-A one-way ANOVA is to be performed. Independent random samples are selected from three different populations. The sample data are given in the table below. 
$\begin{array} { c | c | c } 
\text { Sample 1 } & \text { Sample 2 } & \text { Sample 3 } \
\hline 5 & 3 & 2 \
9 & 7 & 1 \
7 & & 3 \
& & 8
\end{array}$ 
Compute the treatment sum of squares, SSTR. 
A)246.0
B)66.0
C)100.2
D)21.0

Quizplus · Accepted Answer

The treatment sum of squares (SSTR) is calculated by comparing the mean of each group to the overall mean, then squaring these differences, multiplying by the group size, and summing these values. Here, the means are: Sample 1: $ \frac{5+9+7}{3} = 7 $, Sample 2: $ \frac{3+7}{2} = 5 $, Sample 3: $ \frac{2+1+3+8}{4} = 3.5 $. The overall mean is $ \frac{5+9+7+3+7+2+1+3+8}{9} = 5.222 $. SSTR = $ 3(7-5.222)^2 + 2(5-5.222)^2 + 4(3.5-5.222)^2 = 21.0 $.

Compute the Sum of Squares Compute the Treatment Sum of Squares, SSTR