# Repeated-measures while comparing groups

I've been reading up on related posts, however I'm still confused as to how to choose the appropriate test to analyse a repeated measures variable, while also comparing two groups. The situation is this:

Based on an aptitude test (interval data), students are streamed into two groups (high and low aptitude) at the beginning of secondary school. These two groups receive differentiated instruction throughout the first year (adapted to their aptitude, so to speak). The goal is to research whether belonging to the high or low group has different effects on students' performance (beyond the difference that can be predicted by their high or low aptitude).

Both groups of students are given a performance test at the beginning of the first year of secondary (baseline, T0), and again at the end of the year (T1). This is the only dependent variable. The data from this test are interval. Further data are also collected (independent variables): on students' general academic achievement (ordinal data), teachers' pedagogical practice (nominal), parents' socio-economic status (ordinal), parents' educational status (ordinal).

What I would like to analyse first is the relative difference in performance from T0 to T1, comparing the two groups. Do I use a mixed design for this, because of the between-group and repeated measures variables? Or do I conduct a two-way ANOVA using repeated measures design with Time (two levels, T0 and T1) as the within-subjects factor? But how do I bring Group into this?

A second analysis, would then consist of seeing how each of the other data (aptitude, academic achievement, pedagogical practice, parents' SES and educational status) explain the variation in the dependent performance variable over time? How would I go about doing this?

I would approach this perhaps by taking as my dependent variable the difference between baseline ($T_0$) and $T_1$. So create a new variable called $D_i=y_{it=1}-y_{it=0}$. Then you simply perform a regression on the $D_i$ given the treatment that the student was assigned to (i.e. a binary indicator variable called high aptitude that is coded 1 if the student is in the high aptitude group and zero otherwise), along with the other factors that you might want to control for (i.e. your "otehr" independent variables). By taking the difference between baseline and $T_1$, there are several benefits: you can control for individual aptitude, you remove dependencies between the measurements, and you greatly simplify your analysis.