Introduction to Modern Statistics
What's often missing from these introductions is when statistics will not work; and what it even means when it "works". The amount of data needed to tell between two normal is about 30 data points -- between two power-law distributions, >trillion. (And this basically scuppers the central limit theorem, on which a lot of cargo-cult stats is justified).<p>Stats, imv, should be taught simulation-first: code up your hypotheses and see if they're even testable. Many many projects would immediately fail at the research stage.<p>Next, know that predictions are almost never a good goal. Almost everything is practically unpredictable -- with a near infinite number of relevant causes, uncontrollable.<p>At best, in ideal cases, you can use stats to model a distribution of predictions <i>and then</i> determine a risk/value across that range. Ie., the goal isnt to predict anything but to prescribe some action (or inference) according to a risk tolerance (risk of error, or financial risk, etc.).<p>It seems a generation of people have half-learned bits of stats, glued them together, and created widespread 'statistical cargo-cultism'.<p>The lesson of stats isnt hypothesis testing, but how almost no hypotheses are testable -- <i>and then</i> what do you do