7. calculate $ss_{total}$, $ss_{between}$, and $ss_{within}$ for the following set of data:
treatment 1 treatment 2 treatment 3
$n = 10$ $n = 10$ $n = 10$ $n = 30$
$t = 105$ $t = 180$ $t = 110$ $g = 395$
$ss = 350.5$ $ss = 190.0$ $ss = 424$ $sum x^{2}=6,517$

Question

Accepted Answer

# Explanation:
## Step1: Calculate $SS_{total}$
Use the formula $SS_{total}=\sum X^{2}-\frac{G^{2}}{N}$.
Given $\sum X^{2} = 6517$, $G = 395$, $N=30$.
$$
\begin{align*}
SS_{total}&=6517-\frac{395^{2}}{30}\
&=6517-\frac{156025}{30}\
&=6517 - 5200.833\cdots\
&=1316.167
\end{align*}
$$

## Step2: Calculate $SS_{between}$
Use the formula $SS_{between}=\sum\frac{T^{2}}{n}-\frac{G^{2}}{N}$.
For $n = 10$, $T_1 = 105$, $T_2=180$, $T_3 = 110$, $G = 395$, $N = 30$.
$$
\begin{align*}
\sum\frac{T^{2}}{n}&=\frac{105^{2}}{10}+\frac{180^{2}}{10}+\frac{110^{2}}{10}\
&=\frac{11025}{10}+\frac{32400}{10}+\frac{12100}{10}\
&=1102.5+3240+1210\
&=5552.5
\end{align*}
$$
$$
\begin{align*}
SS_{between}&=5552.5-\frac{395^{2}}{30}\
&=5552.5 - 5200.833\cdots\
&=351.667
\end{align*}
$$

## Step3: Calculate $SS_{within}$
Use the formula $SS_{within}=SS_{total}-SS_{between}$ or $SS_{within}=\sum SS_{each\ group}$.
Given $SS_1 = 350.5$, $SS_2=190.0$, $SS_3 = 424$.
$$
\begin{align*}
SS_{within}&=350.5 + 190.0+424\
&=964.5
\end{align*}
$$

# Answer:
$SS_{total}\approx1316.17$, $SS_{between}\approx351.67$, $SS_{within}=964.5$

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Question

Explanation:

Step1: Calculate \(SS_{total}\)

Step2: Calculate \(SS_{between}\)

Step3: Calculate \(SS_{within}\)

Answer: