A common problem with the use of available data or existing

A common problem with the use of available data or existing statistics is known as the ecological fallacy. Describe the ecological fallacy and give an example of one such fallacy.

Solution

The ecological fallacy is a type of error in the interpretation of statistical data, in which the nature of individuals is inferred from the aggregate statistics of the group to which those individuals belong. This fallacy assumes that all members of a group show the same characteristics of the group.

An example of ecological fallacy is the assumption that an average of the population has a simple interpretation in considering the likelihood of an individual.

Group A: 10 people. Group B: 10 people.

• Group A: 80% of people have 40 points and 20% have 95 points. The average score is 51 points.

• Group B: 50% of people got 45 points and 50% scored 55 points. The average score is 50 points

One could infer that if we take two people (one in group A and group B), group A would be most likely to win because it has a higher average, Nevertheless if we take two people at random from A and B, there are 4 possible outcomes:

or A - 40, B - 45 (B wins, 40% probability - 0.8 × 0.5)

or A - 40, B - 55 (B wins, 40% probability - 0.8 × 0.5)

or A - 95, B - 45 (A wins 10% probability - 0.2 x 0.5)

or A - 95, B - 55 (A wins 10% probability - 0.2 x 0.5)

Although the group A has a higher average score, 80% of the time an individual random A will mark lower than a random individual B. Therefore assume that the group A is more likely due to the evaluation of your score average is an ecological fallacy.

Another example of ecological fallacy:

\"All Germans are extremely rational\" therefore we must assume that any person who is German must be extremely rational, which is a lie, because the quality of being German does not lead to the quality of rationality, it can be concluded that stereotypes are a kind of ecological fallacy.