 Is there a term I can search for that describes the following: - Study shows that A is correlated with B, r=0.9 The term I'm looking for is the "implied correlation" (my term) of A and C. 1) is it even epistemically valid, 2) how to calculate the implied r My instinct tells me 1) is "sort of" and 2) is simply r1 * r2 but my instinct is often wrong. Also does Bayes' theorem somehow apply here?? 5 comments | Expand all CWs
 @darius ugh, I remember we covered this in stats 101 but I can't remember the answers. I'd leaf through a stats 101 book somewhere in the late-middle parts. @darius faintly reminds me of this: https://en.wikipedia.org/wiki/Instrumental_variables_estimation but that's more about what you can put in a regression in place of something else, not just the correlation
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This is pretty much the answer to 2: https://math.stackexchange.com/questions/284877/correlation-between-three-variables-question Short of it is, given r1=0.9 and r2=0.8, the correlation r3 of A to C must be somewhere in the range of 0.458 and 0.981. So we can infer upper and lower bounds of correlation but not anything precise, and the lower bound is WAY worse than r1*r2 (and maybe this is coincidence but I suspect not, the mean of the range is r1*r2) |
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@darius fwiw this is not something I know off the top of my head - it's probably a thing, but not a super common thing.