In 19th century Europe, suicide rates were higher in countries that were more heavily Protestant, the inference being that suicide was promoted by the social conditions of Protestantism (Durkheim (1897)). According to Carroll (1975), death rates from breast cancer are higher in countries where fat is a larger component of the diet, the idea being that fat intake causes breast cancer. These are ‘ecological inferences,’ that is, inferences about individual behavior drawn from data about aggregates. To continue with Durkheim, the Protestant countries were different from the Catholic countries in many ways besides religion (the problem of ‘confounding’). Moreover, Durkheim’s data do not tie individual suicides to any particular religious faith. The first problem, of confounding, must be dealt with in any observational study. But the second problem—that exposure and response are measured only for aggregates rather than for individuals—is specific to ecological studies. If there is no confounding, the expected difference between effects for groups and effects for individuals is ‘aggregation bias’; in general, the difference is partly attributable to confounding and partly to aggregation bias. The ecological fallacy consists in thinking that relationships observed for groups necessarily hold for individuals: if countries with more Protestants tend to have higher suicide rates, then Protestants must be more likely to commit suicide; if countries with more fat in the diet have higher rates of breast cancer, then women who eat fatty foods must be more likely to get breast cancer. These inferences may be correct, but are only weakly supported by the aggregate data.... read more.