- "Polls are useless, they only sampled a few thousand people"
- "Why do we need the crime figures adjusted for the age/income/etc groups? Just gimme the raw truth!"
Have to say, I think stats are the least well taught area in the math curriculum. Most people by far have no clue what Simpson's or Berkson's paradoxes are. Most people do not have the critical sense when presented with stats to ask questions like "how was the data collected" or "does it show what we think it shows".
I just don't see it, tough ironically I don't have stats to back it up.
Something like that would be very useful for political decision, so perhaps we could name it after the latin word for "of the state"…
;P
Civitatis?
> from New Latin statisticum
Also, etymonline makes a pretty convincing case that statisticum refers to the behavior of administrators, not to the concept of the administration, with the -ist- specifically indicating a person.
Much as with reading and writing, I think it takes an active imagination and a long slog of unlearning to trust logic (the "ought to" thinking that shields one from reality) and coming to terms with the race not being to the swift, etc, and that these effects can be quantified.
It's not that some people are incapable of it. Much like literal literacy has reached rates of 99.9 % in parts of the world, I'm convinced statistical literacy can too. But when your teacher is not statistically literate (which I hypothesise they are not, generally speaking), they will not pass that on to you. They will not give you examples where the race is not to the swift. They will not point out when things seem to happen within regular variation and when they seem to be due to assignable causes. They will not observe the battle against entropy in seating choices in the classroom. They will not point out potential confounders in propensity associations. They will not treat student performance as a sample from a hypothetical population. They will not grade multiple-choice questions on KL divergence, although that would be far more useful. I could go on but I think you get the point.
Yet to be clear, I'm not talking about just applying statistical techniques and tools. I'm talking about being able to follow a basic argument that rests on things like "yes I know they are a fantastic founder but startups fail 90 % of the time and so will they" or "if the ordinary variation between bus arrivals is 5–15 minutes and we have waited 20 minutes then there is something specific that put the bus we are waiting for into a different population." These are not obvious things to many people.
This is not a personal failure – it is a lack of role models and teachers. I wouldn't have considered myself statistically literate until recently, and only thanks to accidentally reading the right books. I wouldn't even have known what I was missing were it not for that!
I suspect it will take a few generations to really get it going.
If someone would donate me large amounts of money I would love to actively research this subject, come up with reliable and valid scales to measure statistical literacy, and so on. But in the meantime I can only think in my spare time and sometimes write about it online.
In terms of books: there are a few good ones aimed for the general public, such as The Signal and The Noise. How to Measure Anything: Finding the Value of Intangibles in Business is a good book of applying statistical thinking in a practical setting, though it wouldn't help you wrap your brain around things like the Monty Hall problem.
The one book that really made things click for me was this:
Probability Theory: The Logic of Science by E. T. Jaynes
This book is a bit more math-heavy, but I think anyone with a working background in a science or engineering field (including software engineering) should be able to get the important fundamental idea out of the book.
You don't need to completely comprehend all the details in math (I surely didn't); it is enough to have a high-level understanding of how the formulas are structured at the high level. But you do need enough math (for example, an intuitive understanding of logarithm) for the book to be useful.
I think perhaps the best bang for your buck could be Wheeler's Understanding Variation -- but that is based mainly on vague memory and skimming the table of contents. I plan on writing a proper review of that book in the coming year to make certain it is what I remember it to be.
I think the earlier works by Taleb also touch on this (Fooled by Randomness seems to have it in the title).
But then I strongly recommend branching out to places where these fundamentals are used, to cement them:
- Anything popular by Deming (e.g. The New Economics)
- Anything less popular by Deming (e.g. Some Theory of Sampling)
- Moneyball
- Theory of Probability (de Finetti)
- Causality (Pearl)
- Applied Survival Analysis
- Analysis of Extremal Events
- Regression Modeling with Actuarial and Financial Applications
The more theoretical and applied books are less casual reads, obviously. They also happen to be the directions in which I have gone -- you may have more luck picking your own direction for where to apply and practice your intuition.
Edit: Oh and while I don't have a specific book recommendation because none of the ones I read I have good opinions on, something on combinatorics helps with getting a grasp on the general smell of entropy and simpler problems like Monty Hall.
John Ioannidis has much to say on this topic:
It’s like in chess, I know that the Sicilian is a good opening, that I’m supposed to play a6 in the najdorf, but I absolutely do not “understand” the Najdorf, and I do think it’s fundamentally past the limit of most humans understanding.
> After all, most statisticians thought Marilyn vos Savant was wrong about the goats too...
This is the opposite of the argument that you're making. Here you're saying that probability is so confusing and counterintuitive that even the experts get it wrong.
Even back then most ( almost all? ) statisticians were capable of understanding the monte hall problem. Yet they just assumed that a woman was wrong when she explained something that didn’t match their intuition. Instead of stopping to think, they let their arrogance take over and just assumed they were right.
Most people either don't realize this is necessary or don't have the background to do it even if they did, in my experience.
I might be over reaching but in fact what comes across as arrogance is just an example of statistical illiteracy.
Most (>> 50 percent of) people are very good at detecting patterns. People are very bad at averaging numbers of events, because the detected patterns stand out so much and are implicitly and unconsciously exaggerated.
An example. "in my city people drive like crazy" in fact means: this week i was a lot on the road and i saw 2 out of 500 cars that did not follow the rules and there was even one honking. It 'felt' like crazy traffic but in fact it was not.