# Recommended method for analysis of change in two variables over time

I am conducting a pre- and post-test to see if student perceptions change following an treatment. I have two variables that could be treated as continuous, which will be measured both times - motivation and self-efficacy - for a treatment and control group (third variable, I suppose). I'm interested in knowing if there is a higher motivation and self-efficacy combination over time.

1. Chi-square based on expected values

One way I've thought to look at this is reducing it to a 2 x 2 table for "high" and "low" on each variable like this from the pre-test scores: Then I could use a chi-square test for the treatment group's second test with the "expected values" being from the first test. This would show me if there is a change but not necessarily where it is. It also wouldn't tell me the change for specific students - in other words, if every student moved but the totals were still the same I wouldn't know.

2. Multiple t-tests

A second option would be to perform two t-tests. I would first get the change-scores for each student. Then, compare the change in motivation between the control and treatment using an independent t-test, and do the same for self-efficacy. This would tell me whether the treatment had an stronger impact on the variables, but not take into account both at the same time.

What type of analysis could I perform to tell if there is a positive change in these two variables following the experiment?

If you're sure you want to do significance testing, Option 2 is a pretty good choice, although I would replace the $t$-tests with Wilcoxon rank-sum tests, since however you're measuring motivation and self-efficacy, I doubt the scores are normally distributed. I'm not sure if there's an easy way to account for possible dependence between the dependent variables.