This really resonates with me. I've attempted self-study about statistics many times, each time wanting to understand the fundamental assumptions that underlie popular statistical methods. When I read the result of a poll or a a scientific study, how rigorous are the claimed results, and what false assumptions could undermine them?

I want to build intuitions for how these statistical methods even work, at a high level, before getting drowned in math about all the details. And like you say, I want to understand the boundaries: "when statistics will not work; and what it even means when it "works".

I imagine that different methodologies exist on a spectrum, where some give more reliable results, and others are more likely to be noise. I want to understand how to roughly tell the good from the bad, and how to spot common problems.