How can I do better research when the experimental design is lacking?
Though I am not familiar with the specific field you are referring to (neuroscience &amp;c.) one big question presents itself:

Did you actually talk to your adviser/other students about the "problems" you perceive in the experimental setup? Are these actually "problems" or maybe (just maybe) an insufficient understanding on your part?

If it is indeed a problem of experimental design I would propose to contact the ones responsible for the design and try to work something out - i.e., additional experiments or (if possible) looking for external data.