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I'm teaching one section of an intro-to-stat-for-non-math-folks class this spring as an adjunct. I'm planning to supplement the dry, fire-hose-y textbook with some outside readings (data journalism written by me, where students can reconstruct the analysis; excerpts from The Lady Tasting Tea; and some short posts from the Sequences).

On that last category, I'd love suggestions. I have a few in mind already ("Look into the Dark", the 'Lightness' section of "The 12 Virtues of Rationality", "Making Beliefs Pay Rent").

What would you suggest I pay special attention to? Also, anything you'd suggest as particularly good for pre-reading before the first class?

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Many years ago I was in the situation of having to learn stats for my B.Sc. in Psychology. Up until that point I've always been crap at math and great at everything else in school.

What made stats and to some extent math finally click for me and eventually made me pretty decent at stats was understanding what a formal language actually is by reading Gödel, Escher, Bach: An Eternal Golden Braid.

Now I wouldn't recommend the book itself, because it's extremely dense, I'm just saying assume that people don't understand what a formal language actually is and how it ties into things like axioms and definitions and how it connects to logic. If that fundament isn't in place then I'd assume whatever you try placing on top is built on quicksand.

Unfortunately I don't have good and concise reading suggestions on that point though, I'm afraid. https://en.wikipedia.org/wiki/Formal_language unfortunately gets complex quickly and might cause despair. I think the core insight that needs to be in place is that if a formal language like math is logical, the strict rules of symbol-shuffling are obeyed, and the axoims are actually true, then what falls out the other end is Truth. Moreover, a formal system can be lots of different sets of rules (like different programming languages), but what makes math so special is that its rules are isomorphic to reality, and stats is in essence a subset of that system.

I love GEB! For these kids, it's not going to be a proof-based class. I'm more trying to get them to understand that stat is "a guide to how to update beliefs" rather than "a list of tests with sig/not sig outcomes."

If you can articulate and better define what the actual handful core insights are that you hope to transmit maybe you or someone else here can pinpoint better literature for what you are looking for.

It seems to me Eliezer's "Probability is in the Mind" post may include at least in part of what you are looking for. Maybe you can slightly edit and streamline it for the purpose of making it more approachable to your audience.

Highlights from that post:

Quote #1

Jaynes was of the opinion that probabilities were in the mind, not in the environment—that probabilities express ignorance, states of partial information; and if I am ignorant of a phenomenon, that is a fact about my state of mind, not a fact about the phenomenon.

Quote #2

The frequentist says, "No.  Saying 'probability 0.5' means that the coin has an inherent propensity to come up heads as often as tails, so that if we flipped the coin infinitely many times, the ratio of heads to tails would approach 1:1.  But we know that the coin is biased, so it can have any probability of coming up heads except 0.5."
The Bayesian says, "Uncertainty exists in the map, not in the territory.  In the real world, the coin has either come up heads, or come up tails.  Any talk of 'probability' must refer to the information that I have about the coin—my state of partial ignorance and partial knowledge—not just the coin itself.