Question

A one-way analysis of variance was conducted on 5 groups. The total standard devation was calculated to be 2. The total degrees of freedom was found to be 22 and the resulting p-value was found to be 0.25. Use the given information to fill out the rest of the ANOVA table.

Calculate SST [1 pt(s)] Incorrect. Tries 2/3 Submit Answer Calculate SSE [1 pt(s)] Submit Answer Incorrect. Tries 1/3 Calculate SSA [1 pt(s)] Incorrect. Tries 1/3 Submit Answer Calculate the MSE [1 pt(s)] Incorrect. Tries 3/3 Previous Tries Calculate MSA [1 pt(s)] Submit Answer Incorrect. Tries 1/3

Answer 1

1) -

Here, one-way ANOVA conducted on 5 groups.

So, k = number of groups = 5

The total standard devaition calculated is 2 & total degrees of freedom are 22.

$sd = \sqrt{\frac{\sum (y_{i}-\bar{y})^2}{n-1}}$

We know that - $SST = {\sum (y_{i}-\bar{y})^2$

So,

SST sd = > 2= SST 22 = 4 x 22 = SST n-1

Hence, SST = 88

2) -

The p-value is 0.25.

p-value = Pr(F>F_calc) = 0.25 $\Rightarrow$ F_calc = 1.48

Now,

$F = \frac{MSA}{MSE} = \frac{SSA/k-1}{SSE/n-k}$

We have, F = 1.48, k - 1 = 5 - 1 = 4, n - k = 23 - 5 = 18

So, $1.48 = \frac{SSA/4}{SSE/18} \Rightarrow 1.48 = 4.5\frac{SSA}{SSE} \Rightarrow \frac{SSA}{SSE} = 0.3289$

$\Rightarrow$ SSA = 0.3289SSE

We also know that SST = SSA + SSE $\Rightarrow$ SSA + SSE = 88 $\Rightarrow$ 0.3289SSE + SSE = 88

$\Rightarrow$ 1.3289SSE = 88 $\Rightarrow$ SSE = 88/1.3289 $\Rightarrow$ SSE = 66.2202

3) -

SSA = 0.3289SSE = 0.3289(66.2202) = 21.7798

4) -

Now, MSE = SSE/n-k = 66.2202/18 = 3.6789

5) -

MSA = SSA/k-1 = 21.7798/4 = 5.4449