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Is Simpson's Paradox always an example of confounding? Or is it possible to have a Simpson's paradox effect without an extra variable lurking in the background?

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    $\begingroup$ This baseball batting average "paradox" en.wikipedia.org/wiki/Simpson%27s_paradox#Batting_averages can be explained based on differing numbers of at bats (divisor for batting average) in the seasons. I don't consider number of at bats to be a "confounding" variable (but maybe other people do?), but it plays a key role in Simpson's paradox being able to occur in this example. $\endgroup$ – Mark L. Stone Jul 1 '16 at 21:51
  • $\begingroup$ Why wouldn't number of bats being a confounding variable? It certainly can be described as such and, if so, implies that that instance of Simpson's paradox could be described as an instance of confounding. Isn't this the case? $\endgroup$ – George Jul 1 '16 at 22:07
  • $\begingroup$ There's no clear relationship between number of at bats and batting average. For instance, in this (first) example, Jeter had a higher batting average in the year he had more at bats, but Justice had a lower batting average in the year he had more at bats. As I said, I suppose it depends on how confounding variable is defined and interpreted. $\endgroup$ – Mark L. Stone Jul 1 '16 at 22:22
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You could imagine forming subclasses based on X, and the relationship between X and Y within each subclass opposes the relationship between X and Y across the sample. You could conceive of the subclasses as a confounder, but if you've artificially imposed them and they come from nothing but the already measured X variable, then no additional substantive confounding variable would have to be introduced.

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No, Simpson's paradox is not always about confounding. In fact, I would say there is no reason to be surprised by sign reversals if you already know the covariate you adjust for is a confounder, you should check this answer here. You can have sign reversal adjusting for colliders or mediators, and without causal knowledge, you cannot know which estimate will give you the correct answer. If you want to play with simulations showing several sign reversals each time you include a covariate for adjustment, you can check the Simpson Machine in Dagitty's website.

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