Correlation, Regression, and the Ecological Fallacy: A Critique

Abstract

Correlation, Regression, and the Ecological Fallacy: A Critique Frequently, historians interested in quantitatively describing the behavior of individuals have access only to information that pertains to groups. An American polititical historian, for example, studying the Presidential election of 1928, may know the voting records of counties and wards, but not of the individuals who comprise these units. He is thus confronted with the task of disaggregation, which involves inferring individual-level behavior from aggregate-level data. This type of cross-level inference is rarely straightforward; the fact that a particular quantitative relationship is found among aggregatelevel variables does not mean that the same relationship actually prevails among the corresponding individual-level variables. For the remainder of this study, the term will refer to the difference between the expected value of a statistical parameter computed for aggregate-level variables and the true value of that parameter for the corresponding individual-level variables.I In a seminal paper published in I950, Robinson first alerted social scientists to the pitfalls of naive disaggregation. Focusing on the correlation coefficient, Robinson claimed that an ecological fallacy is committed whenever an investigator uncritically assumes an identity between aggregate and individual-level coefficients. Robinson proved that correlation coefficients can be influenced by aggregation bias even to the extent that their sign is reversed. The term ecological fallacy has since been generalized to apply to any incorrect inference from higher to lower levels of aggregation (including the individuallevel).z In a fairly recent research note, Jones advocated a procedure for inferring from aggregate-level data the individual-level voting decisions