Some thoughts, perhaps not quite half baked:
Scientism has made anecdotal a bad word, but we rely on anecdotal evidence to live successfully. I don’t know where or when this dismissal of anecdote started, but it does us all a disservice. It defies common sense. In the real world, we routinely make evaluation of things based upon successful evaluation of evidence, and report our understanding to our fellows, i.e. anecdotally.
I have studied statistics at the graduate level. Research methods was my favourite class in all of my studies. I have designed a couple of experiments during my studies. I have been paid to run statistical analysis on many more. I do understand experimental design and research methods pretty well. I understand the issue of controls and confounding factors. I understand how we can be fooled by the random events of the world. But, all evidence is subject to interpretation. I know that we can kid ourselves.
I also understand the extreme limitations of the scientific method, as usually defined, and even more so, the way it is horribly flawed in practice. The presentation we get in high school science of how it works is a cartoonish picture of the enterprise.
Science looks to be objective, but subjective-objective is a somewhat flawed distinction in many ways. The first questioning that I heard of the subjective-objective distinction came from the chair of my psychology department. This is in some sense the crux of it all. — Ephetkitoi