Exercise

# The unsystematic within-groups variance

To calculate the error term of the repeated measures design, you need the unsystematic within-groups variance: the unsystematic variance or the error term of the between-groups design.

Recall the formula for the *within-groups sum of squares* is given by $$\begin{aligned} ss_{s/a} & = \sum(y_{ij} - y_j)^2 \end{aligned},$$ where \(y_{ij}\) are the individual scores and \(y_j\) are the group means with \(i\) the number of observations and \(j\) the number of groups.

The formula for the *unsystematic variance* of the between-groups design is the given by $$ \begin{aligned} ms_{s/a} & = \frac{ss_{s/a}}{df} \end{aligned},$$ where \(df\) stands for the degrees of freedom.

Instructions

**100 XP**

- You need to subtract each individual score by its corresponding group mean. First you have to make four subsets of the four different groups,
`y_i1`

, ...,`y_i4`

, each subset containing the IQ results of that particular group. Create the subsets using the`subset()`

function, where you first enter the dependent variable and then the independent grouping variable with the condition of the subset. - Now you can then subtract every individual score by its corresponding group mean. Use
`mean()`

. - Put everything together into one vector
`s_t`

, so that it will be easier to do the summation. - Calculate the
*within-groups sum of squares*by squaring the previous result and summing up the elements of the vector. - Calculate the
*unsystematic within-groups variance*`ms_sa`

. You'll want to define the degrees of freedom first.