B.2 Probability, Statistics, and Causal Inference

Start with probability itself (80 h): Blitzstein and Hwang's free Introduction to Probability , paired with the Harvard Stat 110 lectures, covers random variables, distributions, the law of large numbers, and the Central Limit Theorem. One piece of history: the Guinness brewer William Sealy Gosset developed what is now called the t-test to handle small samples in the brewery's own quality data, publishing it under the pseudonym "Student" in 1908 because his employer barred staff from publishing under their own names. Then move to statistics proper (60 h): OpenIntro Statistics , free, or Freedman, Pisani, and Purves's Statistics for the more intuitive treatment, covering sampling, estimation, confidence intervals, hypothesis testing, and regression, with a short look at the Bayesian alternative to the whole frequentist framework. Causal inference (40 h) comes next: Pearl and Mackenzie's The Book of Why for the concepts, then Hernán and Robins's free Causal Inference: What If or Cunningham's free Causal Inference: The Mixtape for the methods: confounding, directed acyclic graphs, randomization, natural experiments. John Snow's 1855 study of London cholera deaths across two water companies' customers is the historical anchor here, a natural experiment nobody designed.

The last 20 hours take on the replication crisis directly, as a case study in how the machinery above can fail even when everyone involved believes they are doing honest science. Ioannidis's 2005 paper laid out the argument in general terms ; Simmons, Nelson, and Simonsohn's 2011 "False-Positive Psychology" showed the mechanism, researcher degrees of freedom exercised in good faith ; the Open Science Collaboration's 2015 attempt to replicate one hundred psychology findings found that somewhere between a third and just under half held up, depending on which criterion you use . Ritchie's Science Fictions is the book-length version of the whole story. The fixes under way are preregistration, larger samples, and open data.