Comment by shoo

There are some interesting examples in the "The Book of Why" [y] by Pearl and Mackenzie. This book is all about causal inference & has examples from things like drug trials where the analysis and inferences drawn from analysing experimental data depend upon what causal model you assume is generating the data, and if you pick an analysis that implicitly assumes the wrong underlying causal structure then your inferences drawn from the data may be wrong. There's a chapter about the historical scientific debate around if smoking causes lung cancer.

Andrew Gelman has an interesting review of the book [g], from the perspective of someone working within the statistical establishment that Pearl's book often critiques.

[y] https://www.hachettebookgroup.com/titles/judea-pearl/the-boo...

[g] https://statmodeling.stat.columbia.edu/2019/01/08/book-pearl...