Ecological fallacy

An ecological fallacy (or ecological inference fallacy) is a logical fallacy in the interpretation of statistical data where inferences about the nature of individuals are deduced from inference for the group to which those individuals belong. Ecological fallacy sometimes refers to the fallacy of division, which is not a statistical issue. The four common statistical ecological fallacies are: confusion between ecological correlations and individual correlations, confusion between group average and total average, Simpson's paradox, and confusion between higher average and higher likelihood.

Ecological fallacy can refer to the following statistical fallacy: the correlation between individual variables is deduced from the correlation of the variables collected for the group to which those individuals belong.

An example of ecological fallacy is the assumption that a population average has a simple interpretation when considering likelihoods for an individual.

For instance, if the average score of a group is larger than zero, it does not mean that a random individual of that group is more likely to have a positive score than a negative one (as long as there are more negative scores than positive scores an individual is more likely to have a negative score). Similarly, if a particular group of people is measured to have a lower average IQ than the general population, it is an error to conclude that a randomly-selected member of the group is more likely than not to have a lower IQ than the average IQ of the general population; it is also not necessarily the case that a randomly-selected member of the group is more likely than not to have a lower IQ than a randomly-selected member of the general population. Mathematically, this comes from the fact that a distribution can have a positive mean but a negative median. This property is linked to the skewness of the distribution.

Consider the following numerical example:

Assume that at the individual level, being Protestant impacts negatively one's tendency to commit suicide but the probability that one's neighbor commits suicide increases one's tendency to become Protestant. Then, even if at the individual level there is negative correlation between suicidal tendencies and Protestantism, there can be a positive correlation at the aggregate level. The aggregate model correctly measures Protestants' tendency to commit suicide if and only if, inside each religion, one's tendency to commit suicide is not determined by the number of Protestants in one's state.

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