A difficulty that can give rise to faulty interpretations of events. It arises by using associations that seem to hold at an aggregate level (say, the level of a community) as evidence that they hold also at the individual level. It is also known as the ecological fallacy. For example, while the (aggregate) observation that US states with a high proportion of foreign-born residents are also states with high literacy in American English, it does not follow that foreign-born people are more literate in English than the rest. In fact, studies at the individual level have shown that the 'ecological correlation ' of foreign-born and literacy rates arises because foreign-born people tend to settle in states that already have high literacy in English. At the individual level, the correlation between being foreign-born and ability in English is in fact (as one may expect) negative.
A subtler example arises in the analysis of the causes of differences in the average population health and the idea that income inequality may be correlated with (or might even cause) lower average health. If everyone has the same demand for health at a variety of incomes and health (however measured) rises with income but at a declining rate, then more income inequality implies lower average health (ceteris paribus). As income disparities widen, an increase in income for the rich will generate an increase in health that is less than sufficient to compensate for the fall in health generated by an equivalent reduction in income for the poor. Should this be the case, caution is the order of the day in evaluating claims that it is inequality per se that is deleterious to health. Such claims may be right but they are not the only possible explanation: the phenomenon may arise simply because of the underlying income-elasticity of the demand for health and the non-linear relationship between income and health.