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Lots of textbooks and websites warn about drawing conclusions from "ecological correlations" which are defined as correlations between rates or averages. All the places I've looked at have used the same 1970 Census example that shows how correlations between averages can be misleading. What is a simple example of correlations between rates being misleading?

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One example, which was true for many decades but might not be true right now, is the correlation between income and political party in the US. If you look at state level data, you would think that higher income is associated with voting for Democrats. But if you look at individual level data, you would see that higher income is associated with voting for Republicans.

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  • $\begingroup$ It's not clear to me this is an example using rates. Are you considering income a rate? Or political party choice? I assumed by rates they meant a quantity changing over time. Like correlation between velocities or something like that. $\endgroup$ May 19, 2017 at 12:41
  • $\begingroup$ @JosephGarvin: At a state level, income is an average (per person) and voting is a rate (fraction). But the key aspect of the ecological fallacy isn't averages or rates. ("Rate" in particular is a very squishy term; it pretty much just means you have divided by something.) The key aspect of the ecological fallacy is using aggregate quantities to form conclusions about individuals. For example, it's perfectly fine to look at this aggregate correlation and conclude that high-income states tend to break for Democrats. It only becomes a fallacy when you extend that conclusion to individuals. $\endgroup$ May 19, 2017 at 17:29

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