Ecological fallacy

An ecological fallacy (or ecological inference fallacy, also referred to as the fallacy of division) is a logical fallacy in the interpretation of statistical data in an ecological study, whereby inferences about the nature of individuals are based solely upon aggregate statistics collected for the group to which those individuals belong. In epidemiology, the ecological fallacy is committed when a correlation observed at the population level is assumed to apply at the individual level. This fallacy assumes that individual members of a group have the average characteristics of the group at large. However, statistics that accurately describe group characteristics do not necessarily apply to individuals within that group. For a mathematical explanation of this see how variability of individuals is much greater than the variability of their mean.

Stereotypes, which assume that groups are homogeneous, are one form of ecological fallacy. For example, if a particular group of people are measured to have a lower average IQ than the general population, it is an error to assume that any or all members of that group have a lower IQ than the general population. In fact, any given individual from that group may have a lower than average IQ, average IQ, or above average IQ compared to the general population.

Examples

A study is done that shows people from City A score higher on college entry exams, on average, than people from City B. This does not mean that a randomly selected individual from A will usually score higher than a randomly selected individual from B. This is because the distribution of scores might be very different between the cities. Consider this synthetic example:

• City A: 80% of people got 40 points and 20% of them got 95 points. The average score is 51 points.
• City B: 50% of people got 45 points and 50% got 55 points. The average score is 50 points.
• If we pick two people at random from A and B, there are 4 possible outcomes:
  • A - 40, B - 45 (B wins, 40% probability)
  • A - 40, B - 55 (B wins, 40% probability)
  • A - 95, B - 45 (A wins, 10% probability)
  • A - 95, B - 55 (A wins, 10% probability)
• Although City A has a higher average score, 80% of the time a random inhabitant of A will score lower than a random inhabitant of B.

If a particular sports team is described as performing poorly, it would be fallacious to conclude that each player on that team performs poorly. Because the performance of the team depends on each player, one excellent player and two terrible players may average out to three poor players. This does not diminish the excellence of the one player.

In the United States presidential elections of 2000, 2004, and 2008, wealthier states (states with higher per capita incomes) tended to vote Democratic and poorer states tended to vote Republican. Yet wealthier voters tended to vote Republican and poorer voters tended to vote Democratic. For example, in 2004, the Republican candidate, George W. Bush, won the fifteen poorest states, and the Democratic candidate, John Kerry, won 9 of the 11 wealthiest states. 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.

The ecological fallacy was discussed in a court challenge to the Washington gubernatorial election, 2004 in which a number of illegal voters were identified, after the election; their votes were unknown, because the vote was by secret ballot. The challengers argued that illegal votes cast in the election would have followed the voting patterns of the precincts in which they had been cast, and thus adjustments should be made accordingly. An expert witness said this approach was like trying to figure out Ichiro Suzuki's batting average by looking at the batting average of the entire Seattle Mariners team, since the illegal votes were cast by a unrepresentative sample of each precinct's voters, and might be as different from the average voter in the precinct as Ichiro was from the rest of his team. The judge determined that the challengers' argument was an ecological fallacy, and rejected it.

Origin of concept

The term comes from a 1950 paper by William S. Robinson. For each of the 48 states + District of Columbia in the US as of the 1930 census, he computed the literacy rate and the proportion of the population born outside the US. He showed that these two figures were associated with a positive correlation of 0.53 — in other words, the greater the proportion of immigrants in a state, the higher its average literacy. However, when individuals are considered, the correlation was −0.11 — immigrants were on average less literate than native citizens. Robinson showed that the positive correlation at the level of state populations was because immigrants tended to settle in states where the native population was more literate. He cautioned against deducing conclusions about individuals on the basis of population-level, or "ecological" data. In 2011, it was found that Robinson's calculations of the ecological correlations are based on the wrong state level data. The correlation of 0.53 mentioned above is in fact 0.46.

An early example of the ecological fallacy was Émile Durkheim's 1897 study of suicide in France although this has been debated by some.

Inverse error

The inverse of the ecological fallacy is the fallacy of composition, in which one infers something is true of the whole from the fact that it is true of some part of the whole.

See also

• Ecological correlation
• Modifiable areal unit problem
• Prosecutor's fallacy
• Sampling (statistics)
• Simpson's paradox
• Statistical discrimination