Yes, DV is a single. But, How can I measure the statistical difference between the experimental and control group with chi square?( pre test, post test)
Definitely the Chi Square test of independence can estimate differences between 2 groups based on 2 or more conditions. The Phi or Cramers V can show the effect size, like Cohens D for pair wise ttests.
However, you need to tell me your research question and hypothesis!
There are more powerful tests available . There are design of experiments including General Linear Model and logistics regression, but pair wise/repeated measures Friedmans technique is a good choice for preparing v. Post testing if the participants were measured twice on a category or ordinal scale dependent variable.
If you want more help let me know.
See this for more background.
Strang, K.D. (Ed.). (2015). Palgrave handbook of research design in business and management. ISBN: 978-1137379924. NY: Palgrave Macmillan
The RQ/hypotheses and data types/structure guide the methods to use.
Here with pre and post tests, this is a repeated measure, or statistically we use the term probability with replacement. I assume the dependent variables are continuous. A simple pairwise t test can be used, to test both hypotheses separately to see if the 2nd test was higher.
It would not be a 2x2 factorial due to the repeated measures yet I know many researchers do that incorrectly.
If you want to test both groups together, then ANOVA RM is a way but not all software does that easily.
You could do a multivariate check with MANCOVA. putting the two pretest scores as covariates and the post ad the dependent variables.
Alternatively see if you know a local statician to help you out, folleague.