Question

Choose the correct answer below.
A. SST is the third sum of squares. It represents the total variation among all the sample data.
B. SST is the treatment sum of squares. It represents the variation among the sample means.
C. SST is the total sum of squares. It represents the difference between the other sums of squares.
D. SST is the total sum of squares. It represents the total variation among all the sample data.

Answer 1

Answer:

D. SST is the total sum of squares. It represents the total variation among all the sample data.

Explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

If we assume that we have $p$ groups and on each group from $j=1,\dots,p$ we have $n_j$ individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

And we have this property

$SST=SS_{between}+SS_{within}$

If we analyze SST compares the individual values respect the grand mean $\bar x$ in order to find the total variation. so the best option for this case is:

D. SST is the total sum of squares. It represents the total variation among all the sample data.