What makes statistics/probability easier than other subjects?

Easier?

Probability and statistics are the most devilish, treacherous, subtle, confounding subjects out there, by a wide margin.

They seem easy. To laypersons, to students, to professional scientists. Far too easy, and we’re all paying the price. Probability and statistics are hard, not in some obscure objective sense (arithmetic geometry is harder, by most measures), but hard relative to their ubiquity and relative to how they are perceived.

In no other subject has the main professional society issued a statement – in fucking 2016 – about the proper usage of one of the most basic, fundamental tools, reiterating salient points which should have been obvious to any freshman.

In no other subject did prominent, respected researchers lose their job not because they necessarily deliberately cheated, but because they misunderstood the most basic methodologies. So deeply did they misunderstand them that they were caught because they blogged about it.

No other subject has been dogged by fundamental disagreements on the very meaning of the most profound notions, leading to acrimonious debates, feuds and derision all the way to deep methodological divergence.

In no other subject is it so ridiculously easy to lead people astray – even the most seasoned professionals.

In no other subject do I, little old me, find myself going around telling people to be afraid. Be very afraid. I never do that with anything else. Ever. I never tell people “You think integrals are easy? Ha! Don’t! They’re actually hard!”. That’s never necessary, because people universally fear math more than they ought to…

…except in probability theory. That’s the one and only field which most everyone feels is intuitive and easy, and they are dead wrong.

Seriously. I really do go around teaching this fear. I have a whole lecture/talk/spiel/performance about it which I regularly deliver to data science grad students, to general audiences, to hi-tech companies, to whomever, and the results are always, always the same: people realize something they almost universally hadn’t realized before. I’m not joking and I’m not bragging. That’s a fact.

It’s not a mystery, really. We all use probability. All the time. We make judgment calls, assessments, inferences from partial data, every single moment of our lives (usually smallish ones, occasionally big ones). We’re actually pretty good at it – to a point. We’re not very quantitative, and when things get to low probabilities and high numbers we very quickly run out of power.

But we don’t realize that. We think we get it, but we don’t. We make life-changing decisions on risks and rewards, and when the risks are high and their probabilities are tiny we make profound errors of judgment, because how on earth do we expect our own intuition to tell the difference between 1:100,000 and 1:1,000,000?

People die. Babies die. It’s a human tragedy. Because we don’t appreciate our own ignorance.

No, people, probability and statistics most definitely aren’t easier than other subjects. Everything runs to varying depths, and certainly some pieces of probability and statistics are easier than some pieces of quantum mechanics. I’m aware of that. But relative to how we think about them, as is revealed by this very question, we are way off the mark with them, in the wrong direction.

RESPECT PROBABILITY, dammit. Fucking fear it. Then come back and ask me why it’s easier than other subjects.