Are foreign-born individuals more likely to be literate (in English) than native born Americans? One would think not, but consider the following information:
Robinson (1950) computed the following two pieces of information: the percent of the population who are foreign-born, and the percent who are literate. Robinson observes that states with a high percentage of foreign-born individuals have higher literarcy rates. There is a 0.56 correlation between a state’s proportion of foreign born individuals and a state’s proportion of individuals who are literate. Does this mean that being foreign-born causes an increase in literacy?
Actually no. This correlation is an ‘ecological’ correlation, because the unit of analysis is not an individual person but a group of people—the residents of a state. In reality, the association is negative: the correlation computed at the individual level is -0.11.
These figures can be explained as follows. Let us assume that high income states have high levels of literacy. Also assume that foreign born individuals have low levels of literacy. Because immigrants are drawn to states with high income and the potential for economic growth, one could see a a positive correlation between literacy and foreign born individuals on a state level. High income states have high literacy among natives, but many foreign born individuals. Low income states have low literacy levels among natives, but also few immigrants. Thus, one could see a positive correlation between proportion of foreign born individuals and literacy on an aggregate level, but a negative correlation on an individual level.
This is the problem of ecological inference. As David Freeman explains, ecological inference occurs when inferences about individual behavior drawn from data about aggregates. Stereotypes are another example of ecological inference. In this case, one assumes that individual members of a group have the average characteristics of the group at large.