Simpson's paradox should give pause to anyone trying to run statistics on data from poorly selected test subjects. Not only can you get results that are a mirage, you can get results that are the opposite of reality.
When it's well intentioned... A friend went to a statistics-focused master degree, and her first internship made her come back with the comment "well, during class we had one prof tell us exactly what we shouldn't do with the data to analyze it honestly. That's the exact list of tasks I was given for these last few months."
I'm sort of reminded of a comment by an ex who grew up in a poor neighborhood. The cops learn how to fudge their reports so they get past the judges. Replace court judges with peer reviewers.