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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.

Peter Flom
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    Ecological fallacy also comes to mind and possibly [Simpson's paradox](http://en.wikipedia.org/wiki/Simpson%27s_paradox) too, I think. – user603 May 03 '13 at 21:35
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    Oops, I meant ecological fallacy, not paradox. These all get a little confusing (even paradoxical!). – Peter Flom May 03 '13 at 21:41
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    I'm not aware of a special name for it; it's just a case of confounding. – gung - Reinstate Monica May 03 '13 at 21:54
  • Thanks @gung . I am reviewing a paper that makes this error, and just wanted to use a name, if there was one – Peter Flom May 03 '13 at 22:01
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    Another related name is the omitted variable bias, if that helps you. – gung - Reinstate Monica May 03 '13 at 22:35
  • @user603 - Is this what you were referring to as "ecological fallacy"? http://en.wikipedia.org/wiki/Ecological_fallacy – EngrStudent Dec 16 '14 at 17:54
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    Fallacy of composition seems similar as well – John Jan 22 '15 at 18:37
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    I'm voting for the ecological fallacy. Looking at the wiki page for it, they actually use the Red State/Blue State situation (not specifically Gelman's book) as an example. Similarly, the [fallacy of division](https://en.wikipedia.org/wiki/Fallacy_of_division) is another good label with earlier beginnings. – Cliff AB Feb 03 '16 at 01:22
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    @CliffAB The reason why "the ecological fallacy" is not quite appropriate is because by using that label, and not using "the atomistic fallacy" you are *privileging the direction of the fallacy*, as though individual relationships are somehow what is real. Your "voting 'ecological fallacy'" is an example of the psychologistic fallacy. The Subramanian citation in my answer goes into detail on this, and see Diez-Roux for basic definition of psychologistic fallacy. – Alexis Feb 03 '16 at 21:08

2 Answers2

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It's called Red/Blue paradox, see here the reference to Freakanomics web site

Aksakal
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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.

Alexis
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    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. – Cliff AB Feb 03 '16 at 01:14
  • @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. – Alexis Feb 03 '16 at 01:55
  • 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. – Cliff AB Feb 03 '16 at 02:11
  • And clearly, the OP is looking for just a name for the phenomena. – Cliff AB Feb 03 '16 at 02:11
  • @CliffAB "Clearly" we disagree. (Also "Simpson's paradox" is not the "ecological fallacy," but is an example of ommitted variables bias.) – Alexis Feb 03 '16 at 02:43
  • I did not mean to imply that Simpson's Paradox was the ecological fallacy, or even related to the OP's question, but rather of a phenomena that readers will know by name. Sorry for the confusion. – Cliff AB Feb 03 '16 at 05:22