What resources would you recommend for someone who wants to improve their statistical literacy? You mention reading the right books, I'd appreciate it if you could give a short list, if you have time.
I am not the person you asked, but I have been on a similar path to improve my statistical literacy. For context, I am fairly good at math generally (used to be a math major in college decades ago; didn't do particularly well though I did graduate) but always managed to get myself extremely confused when it comes to statistics.
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 second both The Signal and the Noise as well as How to Measure Anything. I also mentioned upthread Willful Ignorance.
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.
