1/Curious me took a glimpse at Michael Nielsen's blog, which triggered Gelman's discussion of Simpson's paradox http://michaelnielsen.org/reinventing_explanation/index.html …. Michael is blunt: "[The paradox] shows that some of our ingrained intuitions about statistics are not just wrong, but spectacularly wrong." Yet
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You propose do-operators to avoid the Simpson paradox, right? But you cannot control all variables in the experiment. There might be an uncontroled set of variables that may cause the paradox. That is a feature of probabilities. How to deal with it? By rejecting the experiment?
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No! do(x) does not appear in https://ftp.cs.ucla.edu/pub/stat_ser/r414-reprint.pdf … I just identified where the paradox comes from -- i.e., clash between causal intuition and statistical logic -- and resolved it by replacing stat logic with causal logic. Plain commonsense.
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