Ecological fallacy
Individual and aggregate correlations

Research dating back to Émile Durkheim suggests that predominantly Protestant localities have higher suicide rates than predominantly Catholic localities. According to Freedman, the idea that Durkheim's findings link, at an individual level, a person's religion to their suicide risk is an example of the ecological fallacy. A group-level relationship does not automatically characterize the relationship at the level of the individual.

Similarly, even if at the individual level, wealth is positively correlated to tendency to vote Republican in the United States, we observe that wealthier states tend to vote Democratic. For example, in the 2004 United States presidential election, the Republican candidate, George W. Bush, won the fifteen poorest states, and the Democratic candidate, John Kerry, won 9 of the 11 wealthiest states in the Electoral College. Yet 62% of voters with annual incomes over $200,000 voted for Bush, but only 36% of voters with annual incomes of $15,000 or less voted for Bush. Aggregate-level correlation will differ from individual-level correlation if voting preferences are affected by the total wealth of the state even after controlling for individual wealth. The true driving factor in voting preference could be self-perceived relative wealth; perhaps those who see themselves as better off than their neighbours are more likely to vote Republican. In this case, an individual would be more likely to vote Republican if they became wealthier, but they would be more likely to vote for a Democrat if their neighbor's wealth increased (resulting in a wealthier state).

However, the observed difference in voting habits based on state- and individual-level wealth could also be explained by the common confusion between higher averages and higher likelihoods as discussed above. States may not be wealthier because they contain more wealthy people (i.e., more people with annual incomes over $200,000), but rather because they contain a small number of super-rich individuals; the ecological fallacy then results from incorrectly assuming that individuals in wealthier states are more likely to be wealthy.

Many examples of ecological fallacies can be found in studies of social networks, which often combine analysis and implications from different levels. This has been illustrated in an academic paper on networks of farmers in Sumatra.
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