What is the ecological fallacy?
The ecological fallacy is a common misuse of statistics in which relationships at an aggregated level are thought to imply similar relationships at an individual level. Put another way, the ecological fallacy occurs when we have data on organizations (e.g. states, ethnic groups, countries) and we use that data to make inferences about individuals (e.g. New Yorkers, Whites, French people).
The ecological fallacy can be either positive or negative. A positive ecological fallacy occurs when we say some relationship at the group level (e.g. that states with higher average incomes are more likely to vote for Democrats) to imply that the same relationship among individuals (that wealthier people are more likely to vote for Democrats). A negative ecological fallacy occurs when the lack of a relationship at a group level (e.g. that there is no strong relationship between the proportion of Black people in a state and the proportion of that state's votes that went for Obama) to imply something about individuals (that Black people are not much more likely than White people to vote for Obama).
How does the ecological fallacy occur?
This is best explained by example. As Andrew Gelman showed in his excellent book Red State, Blue State, Rich State, Poor State, states in the New England area tend to be very Democratic and also tend to be wealthy. On the other hand, states in the South tend to be poor and tend to be Republican. (I am simplifying to just two regions here; Gelman covers all 50, and many other relationships besides). So, on a state (or ecological) level, the richer states are more Democratic. However, within each state, richer people tend to be more Republican (the real relationship is more complex, but that is the essence). That is, rich people in (say) Connecticut are more likely than poor people in Connecticut to be Republicans. But rich people in Connecticut are more likely to be Democrats than rich people in (say) Mississippi.
Similarly for the example of race. The states with the highest proportion of Black people are mostly in the South. Yet these states are also very Republican. However, Blacks in any state are more likely than Whites in the same state to have voted for Obama. What happens here, in fact, is that the proportion of Blacks voting for Obama varies very little from state to state, while the proportion of Whites voting for Obama varies a lot. (I am again simplifying; in reality, of course, we need to consider other ethnic and racial groups as well).
Does the ecological fallacy always occur?
After these examples, you might suspect that if you use group level data to make statements about individuals you will always be wrong. This isn't true. Often, you will be correct. For example, richer countries tend to have longer life expectancies than poorer countries; within each country, richer people tend to have longer life expectancies as well. But whenever you have data on groups you have to be careful. The ecological fallacy can be insidious.
For further reading:
http://www.stanford.edu/class/ed260/freedman549.pdf
03 Aug 2012, 12:34 pm
