Question

In a one-way ANOVA, the __________ is calculated by taking the squared difference between each person and their specific groups mean, while the ______________ is calculated by taking the squared difference between each group and the grand mean.

Answer 1

In a one-way ANOVA, the
`SS_(within)` is calculated by taking the squared difference between each person and their specific groups mean, while the
`SS_(between)` is calculated by taking the squared difference between each group and the grand mean.

Explanation:

The one-way analysis of variance (ANOVA) is used "to determine whether there are any statistically significant differences between the means of two or more independent groups".

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 mean.

If we assume that we have p groups and each gtoup have a size
`n_j` then we have different sources of variation, the formulas related to the sum of squares are:

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

A measure of total variation.

`SS_(between)=\sum_(j=1)^(p) n_j (\bar x_(j)-\bar x)^2`

A measure of variation between each group and the grand mean.

`SS_(within)=\sum_(j=1)^(p) \sum_(i=1)^(n_j) (x_(ij)-\bar x_j)^2`

A measure of variation between each person and their specific groups mean.