My wife is working on a PhD in psychology (she intends to do clinical work) and after hearing about the mathematical "training" they receive in order to do research, I was astonished at the lack of rigour. One personal anecdote stands out. Myself being a professional statistician, she would sometimes come to me for help with her assignments. On one assignment, her professor had misunderstood one particular statistic and had given then a problem that wasn't well defined. I helped her craft a polite email to her professor explaining the ambiguity and asking for a resolution. The professor got extremely defensive and did not answer the question, and none of her colleagues realized that the question was incorrect either. And don't get me started on the conclusions they draw from the smallest of trials... /rant Sorry.