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In Andrew Gelman's book "Red State, Blue State" he analyzes the fact that rich people within particular states tend to vote more Republican than poor people, but that wealthy states tend to vote more Democratic than poor states.

Is there a name for this paradox?

It seems to me to be related to, but not identical, to the ecological paradox.

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    $\begingroup$ Ecological fallacy also comes to mind and possibly Simpson's paradox too, I think. $\endgroup$ – user603 May 3 '13 at 21:35
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    $\begingroup$ Oops, I meant ecological fallacy, not paradox. These all get a little confusing (even paradoxical!). $\endgroup$ – Peter Flom - Reinstate Monica May 3 '13 at 21:41
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    $\begingroup$ I'm not aware of a special name for it; it's just a case of confounding. $\endgroup$ – gung - Reinstate Monica May 3 '13 at 21:54
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    $\begingroup$ Another related name is the omitted variable bias, if that helps you. $\endgroup$ – gung - Reinstate Monica May 3 '13 at 22:35
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    $\begingroup$ Fallacy of composition seems similar as well $\endgroup$ – John Jan 22 '15 at 18:37
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It's called Red/Blue paradox, see here the reference to Freakanomics web site

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There is no "ecological paradox." Inference is specific to the unit of analysis. To take Robinson's (1950) analysis of 1930 US Census data as an example, it is true that:

  • Individuals who reported being immigrants were slightly more likely to be illiterate (individual illiteracy and individual immigrant status were slightly positively correlated $r=0.12$); and
  • States with a higher prevalence of illiteracy had a considerably lower prevalence of immigrants (state-level illiteracy and state-level immigrant status were moderately negatively correlated $r=-0.53$).

Robinson used these and similar relationships to make the case that extrapolating from relationships between populations (e.g. states) to individuals was a kind of logical fallacy, and he bestowed upon us the term ecological fallacy for describing such.

However, the opposite extrapolation—assuming that the relationships at the individual level must also apply at the population level—as also a logical fallacy... specifically the atomistic fallacy.

So how could both these relationships ($r=0.12$ for individuals and $r=-0.53$ for states) be true? Well... while individuals who were immigrants may have been more likely to be illiterate, states with high rates of immigration (e.g. New York) had the kind of services, and economic & cultural opportunity that drew in new immigrants. Coincidentally, "services and economic and cultural" opportunity tend to arise in commercial and industrial regional economies characterized by higher prevalence of literacy than, for example, in the agricultural heartland which was less an immigrant destination. Red/blue states' association with state affluence versus red/blue individuals' association with individual affluence raises precisely the same issue: the logical fallacy of extrapolating relationships at one level of inference onto another level of inference.

Incidentally, Robinsons' tacit assumption that individual relationships were the ones that really mattered (i.e. his focus on only the population to individual direction of fallacious inference) is itself a kind of psychologistic fallacy, as Diez-Roux (1998) and Subramanian, et al. (2009) make clear.

The tl;dr: statistical relationships are specific to the level of inference of their data and analysis. "'Why do some individuals have hypertension?' is a quite different question from 'Why do some populations have much hypertension, whilst in others it is rare?'"—Rose, 1985


References
Diez-Roux, A. V. (1998). Bringing context back into epidemiology: variables and fallacies in multilevel analysis. American Journal of Public Health, 88(2):216–222.

Robinson, W. (1950). Ecological correlation and the behavior of individuals. American Sociological Review, 15(3):351–357.

Rose, G. (1985). Sick individuals and sick populations. International Journal of Epidemiology, 14(1):32–28.

Subramanian, S. V., Jones, K., Kaddour, A., and Krieger, N. (2009). Revisit- ing Robinson: The perils of individualistic and ecologic fallacy. International Journal of Epidemiology, 38(2):342–360.

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    $\begingroup$ This doesn't seem to answer the original question: "what is the phenomena called?". Your answer appears to address the question "is this a paradox?". And it can be called a paradox without really being one, such as Simpson's Paradox. $\endgroup$ – Cliff AB Feb 3 '16 at 1:14
  • $\begingroup$ @CliffAB It's called "statistical relationships are specific to the level of inference of their data and analysis." There are different ways of violating that, which I named (ecological fallacy, atomistic fallacy). I also addressed the misnomer of "paradox": there isn't one. $\endgroup$ – Alexis Feb 3 '16 at 1:55
  • $\begingroup$ I've heard of the names "Simpson's Paradox", "Sharpshooter's Fallacy", "Two Envelope Paradox" and a few others. I have not heard on an official name called "statistical relationships are specific to the level of inference of their data and analysis". A Google search for the name leads me with only one entry; this page. So I don't think that's the official name for it. $\endgroup$ – Cliff AB Feb 3 '16 at 2:11
  • $\begingroup$ And clearly, the OP is looking for just a name for the phenomena. $\endgroup$ – Cliff AB Feb 3 '16 at 2:11
  • $\begingroup$ @CliffAB "Clearly" we disagree. (Also "Simpson's paradox" is not the "ecological fallacy," but is an example of ommitted variables bias.) $\endgroup$ – Alexis Feb 3 '16 at 2:43

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