Data from a completely randomized design are shown in the following table. $$\begin{array}{l}
\text { Treatment Level }\
\begin{array} { | c | c | c | }
\hline 1 & 2 & 3 \
\hline 27 & 26 & 27 \
\hline 26 & 22 & 29 \
\hline 23 & 21 & 27 \
\hline 24 & 23 & 26 \
\hline
\end{array}
\end{array}$$ For a one-way ANOVA, the Total Sum of Squares (SST)is ________.
A)36.17
B)28.75
C)64.92
D)18.03
E)28.04

Question

Data from a completely randomized design are shown in the following table. $$\begin{array}{l}
\text { Treatment Level }\
\begin{array} { | c | c | c | } 
\hline 1 & 2 & 3 \
\hline 27 & 26 & 27 \
\hline 26 & 22 & 29 \
\hline 23 & 21 & 27 \
\hline 24 & 23 & 26 \
\hline
\end{array}
\end{array}$$ For a one-way ANOVA, the Total Sum of Squares (SST)is ________.
A)36.17
B)28.75
C)64.92
D)18.03
E)28.04

Quizplus · Accepted Answer

The Total Sum of Squares (SST) is calculated by summing the squared differences between each observation and the overall mean of all observations. Given the data, the overall mean is calculated as the sum of all observations divided by the total number of observations. The SST involves calculating the variance of all observations from this overall mean, which in this case results in 64.92. This calculation involves detailed steps including finding the mean of each treatment, the overall mean, and then using these to calculate the sum of squared deviations from the overall mean.

Data from a Completely Randomized Design Are Shown in the Following