Given a set of data that is not already paired but is known to not be independent, are there any valid methods of statistical analysis one can perform?
The purpose of my analysis is to compare two groups at the college where I am employed - those who took our traditional developmental courses, and those who took courses tailored around Pearson's MyMathLAB system. I am also interested in reporting any statistical significance in performance in transfer-level college math courses the student may have taken after completing either choice of developmental training.
The data set given to me by my employer to analyze is simply a grade report not organized by student, but by class, which means that students who had to repeat our developmental courses are treated as independent cases, instead of paired ones. Because of privacy concerns, getting these data appropriately paired will likely take longer than I need to prepare my report.
Knowing that some of the samples are dependent, and not knowing which, are there any strategies I can use when running regression models and ANCOVA models on these data?
Currently, I'm holding that the data are a no-go for my report, since the presence of dependent samples seem to contaminate any statistical analysis without first having any indication about how those samples are paired. I want to double-check the validity of this conclusion before moving forward with telling my boss, however.
Apologies ahead of time if this question is too general, but I can't figure out how to make anything more specific without explicitly sharing the data set my employer gave me. I would appreciate any suggestions to help clarify my question for anyone willing to help me tackle it.