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# Ecological fallacy

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The ecological fallacy, sometimes referred to as the ecological inference fallacy, describes a fallacious inference made about a particular individual/group from aggregate statistical data in reference to whatever population that individual(or group) is part of.[1] It's a fallacy very similar to the fallacy of composition/division or category mistake. It can also be said to apply in contexts where someone assumes that a statistical property for a population applies to subgroups of that population. It would be similar to making a mathematical error in assuming properties of an entire set also apply to subsets within the set, and/or particular elements within said set.

## Form

The ecological fallacy can take several forms:

P1: X has a high average for Y.
P2: A is a X.
C1: A must be be Y.

Alternatively:

P1: X has a higher average than Y at Z.
P2: A is a X and B is a Y.
C1: A must be better at Z than B.

## Examples

P1: Women on average tend to score higher on mathematical calculation when compared to men.
P2: Sarah is a woman, while Jack is a man.
C1: Therefore Sarah is better at mathematical calculation than Jack.

This is a fallacy because the inference about an individual doesn't necessarily follow from the group generalization. In statistics, the average is the sum of all the scores in a given set divided by the number of scores.[2] Sarah's true score does not need to reflect or even be close to the average in order for the population average to hold. So it doesn't necessarily follow that Sarah will be better at math than Jack. Similar reasoning applies to the two examples that follow.

P1: Ashkenazi Jews as a population have a high average for IQ scores.
P2: Dave is a Ashkenazi Jew.
C1: Dave must have achieved a high IQ Score.

Again doesn't necessarily follow.

P1: New York City has a high crime rate.
P2: Jane lives in New York City.
C1: Therefore Jane has likely seen a lot of crime.

In the hypothetical case that New York City had a high crime rate overall it doesn't rule out the possibility that Jane lives in a part of the city that experiences a much lower crime rate than the overall average for the city.

In each of these examples given the inference is logically invalid this makes the ecological fallacy a formal fallacy.