Quote from harrytrader:
Strange sentence ? sorry this is not an invention from me, this a well known classical flaw that every professional statistician is aware of especially for psychology, sociology and economical fields, and specifically the expression "hidden variable" is the OFFICIAL TERM used in statistical field. These hidden variables rarely appear in physical field since the laws are generally known or at least deterministic enough whereas they are predominant in human activities fields. The rest of what you answered is just the illustration that you ignore the potential existence of these hidden variables. If these hidden variables were evident, be assured that they wouldn't be invented and that so many statistical studies in the human fields although conducted as seriously as they could be as for their data collection and hypothesis tests wouldn't be invalidated as for their conclusion.
It is true that at school, teachers wil rarely learn you about them since they only give the basics and illustrate them in physical field. As for myself I first learn and experience them in food industries where we were accustomed to do psychological tests for assessing (or rather trying to assess) consumers preferences. At that time, for professional reason, I used to read a few books about psychological statistical tests and there were illustrating the difficulty of using statistical tests in such field and give many cases of flaw due to the reason above and warned that any conclusion shouldn't be drawn without multiple checks and wait for possible invalidation by someone. That's why I pretend to say what I said.